Advice is what we ask for when we already know the answer but wish we didn’t.(Erica Jong)

Here is my collection of various pieces of advice on academic career issues in mathematics, roughly arranged by the stage of career at which the advice is most pertinent (though of course some of the advice pertains to multiple stages).

*Disclaimer*: The advice here is very generic in nature; I don’t pretend to have any sort of “silver bullet” that will solve all career issues. You will of course need to evaluate many factors, contexts, and needs specific to your own situation, as well as employing a healthy dose of common sense, before making any important career decisions. I would in particular recommend discussing such decisions with your advisor if you have one, as he or she will be familiar with your situation and will likely be able to provide pertinent advice. Also, it should be clear that most of this advice is targeted towards academic careers in mathematics; of course, there are many other career options available besides this, but I have no particularly informed advice to offer for such alternatives.

- Primary school level
- High school level
- Undergraduate level
- How can one become better at solving mathematical problems? Note that there is more to maths than grades and exams and methods; there is also more to maths than rigour and proofs. It is also important to value partial progress, as a crucial stepping stone to a complete solution of a problem.
- Don’t base career decisions on glamour or fame. But you should study at different places.
- Does one have to be a genius to succeed at maths?

- Graduate level
- It is important to work hard, and work professionally. But it is also important to enjoy your work.
- Think ahead to understand the way forward; ask yourself dumb questions to understand the way before.
- Attend talks and conferences, even those not directly related to your own work.
- Talk to your advisor, but also take the initiative.
- Don’t prematurely obsess on a single “big problem” or “big theory”.
- Write down what you’ve done, and make your work available. In this regard, I have some advice on how to write and submit papers.

- Postdoctoral level
- Learn and relearn your field, but don’t be afraid to learn things outside your field.
- Learn the limitations of your tools, but also learn the power of other mathematician’s tools. In particular, you should continually aim just beyond your current range.
- In your research, be both flexible and patient.
- You should definitely travel and present your research if given the opportunity. But be considerate of your audience; talks are not the same as papers.
- Be sceptical of your own work, and don’t be afraid to use the wastebasket.

I am also (slowly) in the process of gathering my thoughts on time management from the perspective of a research mathematician.

- Here are some general thoughts on this topic.
- Batch low-intensity tasks together to take advantage of economies of scale and to reduce distraction.
- What are some useful, but little-known, features of the tools used by professional mathematicians?

More advice:

- John Baez’s page on career advice.
- Po Bronson’s article on the relative importance of innate intelligence versus effort.
- Fan Chung’s advice for graduate students.
- Lance Fortnow’s “Graduate Student Guide“.
- Oded Goldreich’s “On our duties as scientists“.
- Richard Hamming’s “A stroke of genius: striving for greatness in all you do“.
- Matt Might’s “Illustrated guide to a Ph.D.“
- Gian-Carlo Rota’s “Ten lessons I wish I had been taught”.
- J. Michael Steele’s “Advice for Graduate Students in Statistics.”
- Ian Stewart’s “Letters to a Young Mathematician“.
- Ravi Vakil’s “For potential students“.
- The Princeton Companion to Mathematics‘ section on advice to younger mathematicians, with contributions by Sir Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak.
- AMS advice page for new PhDs
- AMS graduate student blog
- The Mathematics Stack Exchange has a number of questions and answers on career development (and one can ask further questions that have not already been posed on that site). MathOverflow similarly has questions and answers on careers. Finally, the Academia Stack Exchange has a large number of questions and answers on all academic matters, including career issues.

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2 October, 2007 at 7:48 am

SarkeySo amazing when I find your blog. This is the first time I know another foreign citizen of Chinese origin who got the Fields Prize.

I major in Methmatics in China now and I like maths very much. Next year I’ll graduate. Maybe in the future I’ll go to US for my PhD, wish one day I could meet you there!

2 September, 2009 at 9:07 am

ChristianProfessor Tao is an Australian.

20 August, 2010 at 3:35 am

RightWell, a few Australian may have origins in China or in other Countries, and vice versa.

22 August, 2010 at 6:44 am

CorrectionProfessor Tao is now an American, who was born in Australia, with Chinese origins.

15 October, 2010 at 7:25 pm

AnonymousIt is not important but:

>Both my parents are Chinese, and I have lived in the US since 1992; however I consider myself primarily an Australian.

From http://www.math.ucla.edu/~tao/whoami.html

31 October, 2014 at 8:40 am

Jay PatelA very wonderful advice given for satudent.The students from backward regions can easily come to know about careers.It was really amazing.When i gone through it i found many solutions of diffrent career problems.

24 February, 2015 at 5:30 am

pawelProfessor Tao comes from the Earth as all we do

13 April, 2016 at 12:38 pm

esethu thungilizweMe too,however we can meet each other one day

13 April, 2016 at 1:01 pm

esethu thungilizweHy sarkey can tell me the function of mathematician

16 August, 2017 at 2:31 am

Anonymousanother race obssesed loser, we all originate from africa

28 October, 2007 at 8:37 pm

abrahamI am a student doing B-Tech 3rd semester(8 semester course) at National Institute of Technology,calicut,india.i have a ardent interest in mathematics escpecially algebra nd analysis.I like to pursue mathematics research after my btech degree.pls do advice me on how and where to do it?

thanx in advance..

31 October, 2007 at 5:22 am

shibivasishtHi Abraham ,

you have several options considering that you are in the first semester. First thing is to study some linear algebra and little bit of analysis and maybe some abstract algebra the basic stuff that might be covered in a first course. then you can write some exams in your third year for institutes like IMSC in chennai, tifr mumbai, isi in bangalore and kolkata and delhi, harish-chandra research institute in allahabad etc; tifr and imsc also have summer research opportunities which i would strongly recommend. there are several people in places like tifr with an engineering degree. if you want to study in u.s i think you have to take the gre math exam and take several courses in undergraduate math.

best wishes,

Shibi

3 November, 2007 at 9:16 am

sarkI am a doctoral student in the fourth year’s thesis; I have worked for three years on an difficult question in Penalization theory created by the authors “Roynette + Yor + Vallois” :(http://arxiv.org/find/math/1/au:+Vallois_P/0/1/0/all/0/1), it involves several domains of mathematics that I maitraise shortly. Unfortunately, I dont get at any result! .

I do not know what I will do and I do not have any precise broject for my thesis.

so i’m looking for advice for that.

Thanks in advance.

4 November, 2007 at 8:30 pm

abrahamThanks a lot Shibivasisht for ur kind advice.

8 November, 2007 at 10:06 am

Terence TaoDear Sark,

I would recommend that you talk to your thesis advisor on possible alternate projects, either related to your existing project or quite different in nature; I assume in the last three years that you have acquired enough background in your chosen areas of mathematics that you should be aware of other work that is going on and the type of problems to which the tools you have learned may be applied.

28 October, 2009 at 4:38 am

jasdeep singhDear Sir,

Presently I am doing Masters in pure Maths.I am interested in doing Doctorate in Maths from UCLA. Please tell me what are the requirements to get admission there.

Thanks…..

19 October, 2012 at 8:18 am

sneha jainsir i also want to know about this can u please tell me

8 November, 2007 at 6:41 pm

Shibi VasishtDear Professor Tao,

i would like to know what would be the criterion for admission for non math major undergraduates (say with undergraduate degrees in Engineering) if they would like to apply to Graduate School in Math. Do they have to take lots of math courses or do they also need to demonstrate other (research?) abilities in mathematics. Comments and observations are also solicited from other readers of the blog who are in the know of Graduate admissions .

Thanks,

Shibi

9 November, 2007 at 12:29 pm

sarkDear Professor Terrence,

First, thank you for your advice and for all what you do for maths.

I agree completely with you, but my advisor doesn’t have any project for my thesis, he tell me to see what is important for other mathematiciens and doing similar things!; but there are a lot of things that interrest peoples. So, I find myself in the situation: what direction of research one can take ? (which need good vision).

Thank you very much Professor.

11 November, 2007 at 7:04 am

garyHi Terry,

I was wondering how much physics should a maths student aim to know. I plan on going to graduate school next year, and I’m interested in your take on this.

Thanks,

gary

15 November, 2007 at 8:36 pm

GradDear Prof Tao,

Your blog is extremely well writtten informative and I congratulate you for all the good work.

I will appreciate your point of advice on students who are in the initial years of their grad school (having completed the general background courses) and are trying to focus on more specialised research topics from a broader range of their interests (I find myself in such a situation:)).

Thank you

Grad

31 December, 2007 at 12:27 am

JodiDear Dr. Tao,

This blog is full of information that it nearly overflows with knowledge. Thank you very much!

-Jodi

30 January, 2008 at 1:57 am

Thomas RiepeHere a report on the ways of changing information processing in (university) students. IMO very interesting:

http://www.bl.uk/news/pdf/googlegen.pdf

30 January, 2008 at 1:48 pm

MehdiHi Dr. Tao

I’m an engineer student and your advice is very helpful. I can relate to it not only through engineering, but through competitive soccer.

thanks very much!

6 February, 2008 at 12:40 am

Et par gode links - på engelsk at numb3rs[…] svarer til matematikkens Nobelpris, i 2006. Han har lavet en blog, hvor han bl.a. har en del med “Career Advice”, han diskuterer sin forskning, der er et indlæg om kvantemekanik og Tomb Raider, der er diskussion […]

12 March, 2008 at 11:58 pm

Prokrastination oder Blogroll (I): Terence Tao at LEMUREN-Blog[…] nun in einem Buch zusammenfassen und veröffentlichen wird, so findet man dort neben Hinweisen zu “Career-Advice” und “On Writing” einige Beobachtungen zu vergleichsweise elementaren […]

14 March, 2008 at 6:25 pm

AnonymousMore advice on the “Principles of Effective Research” by Michael A. Nielsen:

http://www.qinfo.org/people/nielsen/blog/archive/000120.html

(Thanks to Mark C. Wilson for pointing out the link).

31 March, 2008 at 4:17 pm

zhDo we need to have very good programming skills in order to carry out the mathematical research?

31 March, 2008 at 8:44 pm

Terence TaoDear zh: programming is a useful general skill to have, but I think in most areas of pure mathematics it is not necessary (beyond the rudimentary level of skill needed to use mathematical computation packages such as Maple, Mathematica, etc.). In the more numerical parts of applied mathematics programming skills are of course somewhat more essential.

9 November, 2009 at 7:16 am

Joihn NuttallI am reluctant to express a view different from that of the estimable Prof. Tao, but my recent experience supports my position.

I am a number of years past retirement, and can afford to disregard the advice often given to young people. Thus I have been working on the Riemann Hypothesis (RH) for a year, buiding on work of 20 years and more, but following what may be a new approach.

This problem has been studied for about 150 years, and I do not expect to be able to equal the skills or knowledge of the famous mathematicians of the past who have contributed to the problem. However, I encourage myself with the thought that we now have computational tools that are far in more powerful than the methods formerly in use, which may give us a massive avantage over the pioneers.

It seems to me that perhaps the most difficult part of solving a mathematical problem is knowing (or more likely guessing) what results to prove in order to reach the final solution. In the case of the RH I have used numerical methods to conjecture several possibly relevant results (at least one definitely relevant) that lead to progess in my approach. Without the computer I would never have been able to guess their form. I believe that there is very little chance that these results are incorrect. Of course these results and others yet to be found will have to be proved in other ways before the problem is solved.

The computations that I have been doing do not involve a great deal of programming skill – I use Intel Linux Fortran on an old laptop – but I am almost sure that Maple etc. would be far too slow to produce useful results.

9 November, 2009 at 7:18 am

John NuttallI spelled my name wrongly in the previous post! Sorry.

3 April, 2008 at 7:00 pm

ErdosPuskásThis is a wonderful aid. Thank you.

9 April, 2008 at 12:08 am

cdHi. Some months (maybe alot of months) ago on this blog, there was a talk about some forthcoming notes concering your thoughts on time/work-management etc. How are those notes and thoughts coming along, if at all?

6 May, 2008 at 2:35 am

sandyHi,

I’m a software engineer working for a company in India. I’ve always loved mathematics and now would like to pursue some formal education to understand what’s happening in the area of math. Is there any distant education programmes for pure math? kindly advice.

29 May, 2008 at 6:38 am

kasımDear Professor Terrence,

First, thank you for your advice and for all what you do for maths.

I agree completely with you, but my advisor doesn’t have any project for my thesis, he tell me to see what is important for other mathematiciens and doing similar things!; but there are a lot of things that interrest peoples. So, I find myself in the situation: what direction of research one can take ? (which need good vision).

Thank you very much Professor.

7 June, 2008 at 9:42 am

AnonymousDear Prof. Tao

Thank you very much for the advice. The links to Rota’s advice and to Connes advice seem to be broken.

Best,

Grétar

7 June, 2008 at 10:41 am

Terence TaoThanks for the correction!

23 June, 2008 at 8:06 pm

ブール関数のフーリエ解析 — あほの場所[…] from Career advice […]

13 July, 2008 at 6:34 am

Ochan TokwinyDear Prof Tao,

The career advice you give is universally applicable irrespective of whether one is interested in pursuing mathematics or not. I am for example interested in geology, and would like to pursue graduate studies in this area but have found your advice quite useful.

Iam amazed that given your heavy schedule of teaching, research, lectures, etc, you can still find time to write enormous material about career advice.

Thank you for freely sharing your knowledge and experience, for this is the kind of stuff that can give a lot of inspiration to others.

2 August, 2008 at 10:48 am

NathanMr. Tao:

I will be attending graduate school this fall in mathematics. However, I keep second guessing the school I’ll be attending. Have you ever had a student mention that they were afraid they were not going to a “good enough” graduate institution for mathematics? Don’t get me wrong–I look forward to the one I’ll be attending. I just want to make sure I go somewhere that will prepare me as much as possible for my future in mathematics. I just don’t want to fall behind everyone else at the higher ranked institutions, such as MIT, Harvard, and Princeton. Any advice?

-Nathan

8 August, 2008 at 12:05 am

JonI hope this helps Nathan, who wondered about going to a “good enough” graduate institution.

I went to graduate school at a state school, under an advisor with recent accolades. He had, in fact, recently been nominated for a Fields Medal for his innovative solution to some old open problem. After the tough four years of my Ph.D. I ended up with a nice thesis but no research postdoc and had to work at a small teaching institution. I worked very hard to solve open questions of a big guy in my field, to try to get my feet back in the door of a big research place. I solved one of these questions only to find out that, since it was asked six years before, that the result was known (but still unpublished to my knowledge) and now considered routine to the big guy and his closest followers. My paper was rejected from a decent journal although quite a few experts found it interesting and worthy of publication. Basically, the big guy squashed the paper!

It is my feeling that if you want to work in a flashy area it is most important to work directly under the leader in that area in order to avoid something like this from happening to you. Often flashy fields move quickly and you can easily waste time proving things that are outdated in the ideas of the top expert very soon. It would be beneficial to know when such things are known as soon as you possibly can. This is my biggest regret about my choice of grad school. I had an opportunity to work with one of the best research groups around and chose not to move there for personal reasons, for example since my advisor at the state school was a “hot new fad”. Now I am quite close to quitting mathematics. You should go to the best place you can. Also, if you are at a good place and your relationship with your advisor doesn’t quite work out, then there will be other reputable people to work with. You won’t find yourself “held hostage” by your advisor. In retrospect, unless you like teaching and don’t mind getting mediocre pay, (i.e. if you are dead-set on a research career), I would either go to one of the flashiest places there are (MIT, Harvard, Berkeley, UCLA…) or simply pick another career. This is harsh, but I think it is true. (See John Baez’s career advice link on Terry’s page.) Perhaps Terry can comment if I am inaccurate in my assessment of the situation.

8 August, 2008 at 12:08 am

JonI should qualify that the area I work in is a technical field moving quite quickly at the moment, and this poses many dangers. There are other ways to go. (Atiyah and Singer have an interview online in which Atiyah makes remarks about the dangers of getting “too technical” and working only on a narrow area)

8 August, 2008 at 6:28 am

JonAs an addendum to my depressed earlier posts… (apologies for those). I have recently been contacted by the “big guy” who suggested a journal for my paper and invited me to visit to learn more about his subject. I guess things aren’t so dire after all, and that the big guys don’t squash papers necessarily. Sorry for the (potentially) bad absolutist advice.

9 August, 2008 at 8:46 am

NathanJon, I thank you for the advice! It was very beneficial. I do think I would have quite a difficult time getting in at MIT, Berkeley, Harvard, UCLA, etc. I will be attending NC State this fall. Perhaps if I don’t like the program, I could transfer (although some places do not like accepting a transfer student). At first, I accepted Maryland at College Park. But after searching for a place to stay and seeing/hearing the crime in the town, I chose to go to NC State.

9 August, 2008 at 11:44 am

John ArmstrongNathan, the “crime” in College Park is severely overblown. I did my undergraduate work there, I return frequently when I’m in the area, and I’d accept a position at UMD in a heartbeat without any reservations.

24 August, 2008 at 8:09 am

NathanI am a first-year graduate student, and one of the areas I’m interested in researching is number theory (specifically primes and their distribution). I find several schools that research number theory, but I have yet to find a professor from one of those schools that has anything to do with prime numbers, the Riemann hypothesis, etc. I’m on the eastern side of the USA. Does anyone know professors on this side that research such topics?

25 August, 2008 at 8:55 am

KaonDear Mr.Tao,

I am a masters student in analysis. I have been searching through nearly all web pages of good programs. What I notice is that differential equations are indispensable for analysis. Most of the current faculty in good programs are working analysis mostly in connection with PDE, ODE, geometry or more algebraic aspects like K-theory (operator algebras etc.). Why is this so? In fact, I was quite disappointed because I thought one could work on a purely abstract type of analysis, I mean without calculations, equations or too much contact with applications. Is this supposed to be the way of analysis? Is analysis supposed to have some connection with applications or with other areas like geometry? or is it just the current shape of research in analysis but it might change in the future?

26 August, 2008 at 2:16 am

CristiThere is an informative discussion about the current research in analysis here:

http://www.mathlinks.ro/viewtopic.php?t=193477 .

But I’m sure Mr. Tao can tell us even more about this.

16 October, 2008 at 1:52 pm

AnonymousI took a new academic administrative position but only stayed for four months because my house in another state did not sell. Now that the house has sold and I’m back on the market, but employers seem to be afraid of me.

Help! The situation was out of my control. Sammie

25 October, 2008 at 12:35 pm

Faruk TemurDear Prof. Tao

I am a senior student in Mathematics. It was quite surprising for me to see that a very busy mathematician like you have such a great blog and communicate modestly with students and even laymen. I read some of your career advices and found your advices about importance of hardwork, and relevance of experience in solving top class problems very useful. Upon reading your advices, I understood that it is a great mistake to solely concentrate on one big problem and such a mistake may destroy an entire career.

I will graduate at the end of this year and I have applied UCLA to be a PhD student in Mathematics next year. I hope I will be admitted and have a chance to listen lectures of you.

28 October, 2008 at 3:30 pm

The PHA : links for 2008-10-28[…] Career advice « Terence Tao Advice is what we ask for when we already know the answer but wish we didn’t. (Erica Jong) […]

26 November, 2008 at 1:28 pm

Jennifer SummersYour sage advice can be applied to much more than just an academic career issues in mathematics. Your advice is a sound model of how to approach any career, position or even any problem or goal that you might face or choose.

I particulalrly liek the wastebasket idea which is something that I have been using since Tony Robbins recommended it a few years back. The wastebasket approach helps realx you much more and allows ideas to flow more freely, without tha apprehension and prejudging of any ideas that may arise.

17 December, 2008 at 7:27 pm

gregorychang[…] [via] […]

29 December, 2008 at 10:40 pm

AnonymousHi Terry,

A rather basic question coming from a beginning undergraduate student whose first real analysis class just ended — how does one recall how proofs of basic results are constructed? Do you tend to keep a notebook handy with a small outline of the proofs and the “magic tricks” invoked therein? (I should have done that!) While I was studying for my final exam, I had to go through basic proofs again and understand their construction — even though I had done that for midterms before with success. Heck, some proofs that I actually wrote for previous problem sets weren’t immediately accessible.

Again, this does seem basic. But this also concerns me on the far end of the tunnel since the mathematics that I’ll learn will span different topics (at the undergrad level), and yet it’s very likely I won’t remember much about proofs that I had learned after a relatively short amount of time.

Words of advice would be appreciated.

Thanks,

Jad

30 December, 2008 at 8:30 am

Terence TaoDear Jad,

I think this issue will become easier as you advance to higher levels of mathematics, for two reasons. Firstly, when you study more advanced topics, you will come to realise that many proofs in seemingly different areas of mathematics are in fact special cases of a general argument; once one memorises that argument, there is not as much of a need to memorise all the special cases. (For instance, there are many arguments in analysis that boil down to “check the statement for a dense class of test objects first, and then take limits.”) The other is that in more advanced classes, you will spend more of your time

doingproofs rather than reading them. This is quite difficult to get a hang of at first – it requires different modes of thought than just rote memorisation and pattern recognition – but with enough experience, you’ll see what makes proofs “work”, and understanding other proofs will become easier.Actually, one of the best ways to memorise the proof of X is to cover up the proof and try to prove it yourself. Usually, what happens is that you’ll be able to get halfway through the proof but get stuck on a key point. After you get frustrated, this is the time to uncover the proof, at which point you should quickly see the trick or observation that eluded you before, and then the rest of the proof often becomes quite obvious to you. When done this way, the only thing you need to remember to reconstruct the proof is that key insight, which tends to stay in one’s memory precisely because you didn’t have it before.

(The very best ways to learn the proof of X, of course, are to teach about it in a class, or to adapt that proof for one’s own research, but these options are rarely available at the undergraduate level.)

See also my advice pages here and here.

20 August, 2011 at 3:44 am

Luqing Ye”Check the statement for a dense class of test objects first, and then take limits” .This reminds me of the connection between the L.Hospital’s rule and O’stolz theorem.Wish I do mot misunderstand this sentence.

24 May, 2016 at 12:55 pm

Alexey ZabotkinI’d say doing the proof with your own hands is not simply the best, but the ONLY way to become fluent at math.

5 February, 2017 at 5:04 am

Anonymouswonderful advice!

12 January, 2009 at 8:23 pm

AnonymousI’m sure this blog has a large and diverse readership. However, I would bet a large number of your readers are graduate students and postdocs/junior faculty members. My question is about how to implement your advice, and I think it is probably pretty universal to this group of readers. Most grad students, at some point, reach the conclusion that they are under productive (that they waste too much time doing X, such as: playing video games, watching TV, working out at the gym, talking to office mates, reading politics blogs, playing Frisbee, etc), and that it has come time to buckle down, do all of the things you write about in your career advice pages and, generally, increase their productivity. However, I know of few cases where this has lead to a sustained change in behavior and productivity.

By all accounts you have a near unrivaled level of productivity and time management skill. Did you develop this naturally over time, or did you have a moment (like those described above) where you took decisive measures to improve your productivity? Either way, any thoughts you have on the subject are welcome.

17 January, 2009 at 2:57 am

How to do Research | Nonoscience[…] and excellent advice on a research career in mathematics. His series of essays are collected in a separate page at this […]

1 February, 2009 at 2:02 pm

A People’s History of Mathematics « in theory[…] like very much the philosophy underlying Terry Tao’s essays on how to do mathematics, starting from the opening quotation, and also his essay on what is good […]

11 February, 2009 at 7:02 pm

Announcement « Liu Xiaochuan’s Weblog[…] Please visit this page of Tao’s blog by a click ：Career advice […]

10 March, 2009 at 2:53 pm

Career advice from the Fields medalists and some other mathematicians « Academic Career Links[…] Advice from the blog of Terence Tao […]

10 March, 2009 at 4:24 pm

a shy studentDear Prof. Tao,

I am a Ph. D student in mathematics. I would like to learn answer of these following questions:

1) Should our first paper be originial? namely do we have to prove something new to publish? Genarally, when we start to do research, at the beginning, everything seems very confusing, after a while, we start to figure out what is going on but still we are in the level of proving a new lemma or theorem. In that case should we write survey type papers and try to publish it?

2) do you believe that there is an age limit for being mathematician?Some people say that ”if you did not do anything so far, forget it, you can not do after that” is that right? I believe that passion and hard working are more important but sometimes I tend to believe them.

I really want to thank you with my all heart. I am visiting your blog everyday, you give us hope and motivation. We appreciate your work.

God bless you..

15 March, 2009 at 12:57 pm

AnonymousDear Prof. Tao,

Which method would you say is a good method when studying a new subject (undergrad & grad level)? To make this more precise:

During the class pretty much everyone take notes. However, after that people differ.

1. Some people take their notes and starts reading them just like that, without having a pen or piece of paper at hand.

2. Others have some extra scratch paper and take notes which includes one or several of the following:

2a. Some type down all the definitions.

2b. Some try to solve theorems, propositions etc before reading the solutions.

2c. Some work out their own examples.

And we can go further:

2d. Some retype all the notes so that it looks nice, tidy and is easy readable.

2e. Something else.

Now, doing 2d. takes you through the notes slowly and you learn a lot. But it also takes much time, too much time if you are in a hurry. 1 is a fast method, but I’ve never done that and I am not sure how much one would remember.

Which method that is “the best” probably differ from person to person. But if you’ve been doing math for a long time I am sure one has picked up a few neat study habits. So I would be pleased if I could hear a few tips from yourself and other readers.

Thank you

20 March, 2009 at 3:33 am

Career Advice from the Nobel Prize Winners « Academic Career Links[…] The above materials make for an interesting comparison with the advice from the Fields medal winner Terence Tao. […]

23 March, 2009 at 6:16 am

How to Succeed in Science « Academic Career Links[…] I especially recommend the talk You and Your Research by Richard Hamming, and the advice from Terence Tao, James D. Watson, and Steven […]

27 March, 2009 at 6:52 pm

Career advice for the (would-be) graduate students « Academic Career Links[…] subject is here. For the graduate students in mathematics, Terence Tao provides excellent advice here, and there is a whole new blog on the subject. See also my earlier posts, especially here and […]

29 March, 2009 at 12:31 am

倡议 « Liu Xiaochuan’s Weblog[…] 更多的请登录Terry本人的博客中的一页：Career advice […]

31 March, 2009 at 1:30 pm

Academic Career LinksOne more (perhaps obvious) bit of career advice: build your own network of colleagues and collaborators.

4 April, 2009 at 5:23 pm

Guidelines for paper presentations « Error Correcting Codes: Combinatorics, Algorithms and Applications[…] to give good talks and how to manage career in general. Here are some of them: Terry Tao’s post, Lance Fortnow’s post and Michael Ernst’s page. They also have great career advice […]

12 April, 2009 at 7:14 am

Scientists of KATG[…] […]

26 April, 2009 at 3:40 am

How to do Research « Unruled Notebook[…] and excellent advice on a research career in mathematics. His series of essays are collected in a separate page at this […]

4 May, 2009 at 9:34 am

VijayDear sir,

actually i recently came across ur name in one of the forums.iam currently in INDIA doing by 12th standard ie my last year of schooling and next year i have to join a college.i am very very deeply interested in MATHEMATICS and its my passion.i want to be a mathematician,though i haven’t even passed the REGIONAL MATHEMATICS OLYMPIAD thats conducted in the country.but the problem is i have no idea as to what i should be working so that i can become a mathematician.i have no clue on where i have to join for my under- graduation or what course i have to go for. but the thing is that i very much love the subject and i would practically do anything to achieve my goal.please help me and advice me on which books i should study and which fields should i develop my knowledge more on.

please advice me sir,please.

vijay

5 May, 2009 at 1:19 am

Amit@Vijay,

ISI have good undergraduate program in Mathematics. Besides there is CMI [Chennai] which is also good.

23 May, 2009 at 10:43 pm

Travel Tips for the Conferencing Undergraduate: Part I « Turtle Soup[…] 2) Prof. Terence Tao’s career advice on research: https://terrytao.wordpress.com/career-advice/ 3) Cornell University’s FAQ on undergraduate research: […]

5 June, 2009 at 4:53 am

Essential Career Lessons[…] Tao’s blog discusses many mathematical topics, it also has a Career Advice section. The advice targets aspiring mathematician but it’s applicable to other fields as well. I […]

8 July, 2009 at 1:24 pm

Akhil MathewVijay, the Secret Blogging Seminar recently started a thread (http://sbseminar.wordpress.com/2009/07/03/bleg-book-recommendations-for-an-undergraduate/) on books to read at an undergraduate level, which may be of interest to you as well.

27 July, 2009 at 2:42 am

AbhayDear Sir,

I am right now a 2nd year student of Computer Science at IIT Bombay in India. Recently I have developed a lot of interest in the field of Cognitive Science. I have been reading a few books as well. I would also like to enter the research arena after my graduation. So can u pls. tell me which topics in mathematics will be helpful to me in this field? This will help me in building up good fundamentals in the subject. thanx a lot..

29 July, 2009 at 7:47 am

samiai m a 2nd year student of pre medical

plz help me out what will b best 4 me except this field

right now im preparing 4 my entry test.. m from karachi PAKISTAN

5 September, 2009 at 5:09 am

QwertyDear Prof. Tao (and other professional mathematicians),

What should a student think about before, and during, writing a letter to a potential supervisor he has never met, and can no meet. For example, how about the length of the letter. Is 1 (one) page (A4) enough? What to include in the letter and how much of my background should I give away? I don’t want my letter to be too long and too talky, but not too short, either.

I do not know much details about my subject (alg. K-theory) but some basic stuff. So therefore I can not include things such as “and Theorem B by Quillen made me think of the problem in terms of …” (say) in my letter. Is it normal for student to only have a vague idea of their subject of interest (I guess this varies from subject to subject as some subjects are more accessible for an graduate student (not yet a phd student) than others) or am I better off not ranting about how little I know about the subject I am supposed to be interested in? (although, I want to be as honest as possible in my letter)

Thank you.

4 October, 2009 at 1:46 pm

AMS Graduate Student Blog » Blog Archive » An Interview with Terence Tao[…] There is an extensive list of career advice on your page which I encourage everyone to read. What do you think is the most important piece of […]

5 October, 2009 at 9:40 am

Dr Terence Tao’s Career Advice « memoirs on a rainy day[…] , mathematics Leave a Comment Tags: asides, career advice, mathematics, terence tao Fields Medalist Dr. Terence Tao gives career advice to aspiring mathematicians. It’s sound advice from someone who has excelled in his field for over a decade. Here is Dr. […]

22 November, 2009 at 1:55 pm

AnonymousHello everybody,

I am in the process of writing my first grant proposal. Can anyone offer me some advice? A few successfull samples would be great.

Thanks

30 November, 2009 at 10:59 pm

AnonymousDear Prof Tao,

What is worth doing?Solving any mathematical problem using any advanced method or going for it on the toughest path that is through elementary ideas.

For example we are set up to solve a geometrical problem, we can solve it in quick time using trigonometry but what is your advise if we solve it using elementary ideas of geometry which can take lots of time in comparison to what we have spared with the previous technique.

23 December, 2009 at 7:34 am

PrakashDear Prof Tao,

I am doing undergraduation in Biotechnology. I love mathematics a lot. How can i shape my career such that i’ll be doing good level of mathematics in my profession.

15 January, 2010 at 9:21 am

Agnes Welt » Random Links[…] General: Advices for Master/PhD Writing is a psychological thing … Advices for Career […]

30 January, 2010 at 3:00 pm

RobTerrence,

All my life I have been mystified and astounded of the beauty of mathematics all around us. As an undergraduate, I was a very successful student who worked incredibly hard and did very, very well. I’m currently a first year graduate student who is struggling through every single class, working as hard as I can possibly work only to find failure around every corner. It has always been my dream to pursue a Ph.D. in Mathematics, but due to the recent situations with the courses I’ve taken, I’m almost at the point of losing everything, and I have no idea what to do. Do you have any suggestions!

-Rob

6 March, 2010 at 7:42 am

gregoryDear sir,

I am an 8th semester (8 semester course)B.Tech student of National Institute Of Technology,Calicut, India.We(me and my group) are working on algorithms for efficient recovery of signal from its compressively sampled data given the domain in which the signal is sparse(As a part of our major project-a 1 year project )..Now we are thinking about whether it is possible to convert the l2 norm minimized solutions of a set of undetermined equations to l1 norm solutions by some recursive algorithms.It is evident that accurate l1 solutions cannot be obtained from their l1 counterparts because the conversion is highly non linear and does involve some inherent error.So the question is about converting l2 solutions to l1 solutions with minimum error.Also it is known that the set of under determined equations(with m equations and n variables where n is greater than m) has an l1 norm minimized solution which has only m non zero solutions and rest n-m are zero.With all these in mind is there any method to do this?Please advise me on the same.

Given that finding out l2 solution is computationally less complex in the overall execution time, some methods like these should prove helpful in our project.Please advice on this…

Shortly, I will be posting one crude idea about the same..I would be very pleased if you could verify it to see if there are fundamental errors in the first step assumptions.

Please reply..Thanks in advance…

21 March, 2010 at 10:46 pm

amlan chakrabotydear proffesor tao: I am a student from india , i am very sad at my country’s dismal performance at the imo 2009 (held at bremen,germany ).India got a rank of 28 in 104 countries. I am in class10 ,highly interested in mathematics ,and i want to represent my country at imo.What are the most important topcis for qualifying at regional level as well as in imo? also please tell me what are my foremost priorities for competitng at such a high level? and pllllllllllllleeease do come to india.

1 April, 2010 at 7:28 pm

srivatsaRespected sir,

I have no words to express my happiness.I find very less mathematicians helping out the beginners.Anyway sir i am doing my masters in mathematics specializing in number theory and to a good extent in algebra i have a year left for my completion of my masters degree and plan to take up research the next year.I have deep interest in number theory,analysis,algebra and infact any field of mathematics just interests me a lot….I seek your advice as to what to take up next,is there any universities abroad or even your university that can help me take up my research.

6 April, 2010 at 5:20 pm

malHi Dr. Tao,

I’m a fifth year mathematics graduate student. Throughout my grad years I’ve been wondering what exactly is the role of an adviser. Is the adviser’s only job to give the student books and papers to read and a problem and leave them alone?

I haven’t been getting much help from my adviser on understanding his work. It was difficult to fill in the gaps in his paper without his help. He never gave me enough time to read an elementary book on the subject and got me reading his paper the first thing and since then I’ve just been lost. I’ve done some calculations and yet I don’t see the big picture.

I still have a lot of gaps in my understanding of the subject he works in. I’ve always felt lost and it wasn’t easy communicating to him my problems as he didn’t seem keen on understanding my difficulties in the subject. I still do!

I’m just wondering if I’m too stupid to do math. I don’t know what I should have done. I tried reading other books/papers that were referenced in the paper and it was still hard to understand them.

I’ve always enjoyed understanding and working on math on my own but I guess I’m too slow. I’m completely confused and frustrated about what I should do.

mal.

13 April, 2010 at 5:22 am

Yiwei“Is the adviser’s only job to give the student books and papers to read and a problem and leave them alone?”

I don’t think so for a normal situation. An adviser should discuss with you per week on your progress. Suppose you are new to swimming. Should your swimming adviser just need to point out where he swam, and give you some instruction books or some pictures he took along his route? Shouldn’t he save you when you are sinking in the swimming pool? Nobody will agree with that!

With sympathy,

Yiwei

6 April, 2010 at 9:52 pm

Daily Diary[…] under: Uncategorized — Name @ 12:51 am https://terrytao.wordpress.com/career-advice/ Leave a […]

11 April, 2010 at 1:29 am

YiweiHi Terrence,

Could you share your experience on learning knowledge that was very new to you?

Thanks a lot!

Yiwei

15 April, 2010 at 8:04 am

quochaimy terence tao

i pray for you to win 2 more field medal, abel and wolf prize every day , year after year. i sent you a picture of buddha helped by cri(china radio). TAO tries more. no one in the world look down you.you are considered the second great wall.if you cannot do , i will sad and cry. try much more.my heart always towards you

19 April, 2010 at 3:41 pm

mr PibbThis question may fell squarely into the domain of the Erica Jong quote, but what the hell. More likely it will fail off the tail end of this very long thread of comments.

It’s really two different questions on a related theme.

BACKGROUND

A few years back a did a PhD in “closely related” area to mathematics. Not math, but an area Terry mentions on this blog and certainly knows about and would view as math-ish. I published in good venues, got some nice recognition for my efforts from international socieities and did some postdoctoral work at some good institutions.

But the postdoctoral work was very hard on my marriage, and I ended up cutting the postdoc time a little too short (some peers who stuck it out a few more years got very good appointments).

I tried lecturing at a local university and writing papers. I was able to be productive for a time (ie. published new work and acquired some very positive teaching reviews), but the lack of benefits and very low pay made it untenable in the long term.

I tried my hand at the job market again (only TT, no more postdocs). And the thing was, the only interviews and such nibbles that I got in the USA were from math departments (some quite good). But I got no offers – just some runner up condolences.

So now I am working at a Gigantic Tech company. The salary is no condolence. I hate it every day. I miss doing math (or mathematical whatever I was doing before). I can do some mathy stuff on evenings and weekends, but it is not that much and probably not enough to land a permanent position in a university or at a lab

QUESTION 1: maybe math would have been a more appropriate route

I get to thinking: If all my interest from hiring committees came from mathematics departments yet my PhD was not in math —- would I have done better looking for tenure track research university jobs had I obtained a PhD in mathematics (instead of a “sometimes allied area”)?

and when you get down to it, I always liked the mathematical side of my research more than the applied side or “domain side”.

But that’s all in the past. What about the future?

1. would it all be worthwhile to obtain a PhD in mathematics at this relatively late stage of life (post 30)? presumably I could do this a bit on the quick, seeing as I know how to do research and publish, and I could use the time to broaden a bit

2. would it simply be better to start publishing in more mathematical venues? this would probably be the right answer for somebody who already had a professor job, but it may not be the right one for a person in my position, since “getting back into the system” is a big issue for me

QUESTION 2:

What is the most solid way to re-enter academia after a stint in industry? (surely a relative statement)

My guess is that this is usually done by people that work in “industrial research labs” or in a very applied areas where the boundary between research and industry is blurry.

That’s not really the case here. The kinds of things I am interested in are not really valued by any industrial employers. I am talking about getting back in after being out for 1-3 years.

The only thing I can think of that might work would be to publish as much as possible in free time (nights and weekends, etc), use that to restart my network of collaborators and get some visibility, and somehow use that to get a postdoc or temporary position to be genuinely productive for a year or two and then try to land a TT position after that. Of course, both of those jobs are anything but guaranteed. And most temporary/visiting positions are reserved for fresh PhDs.

Have you ever heard of anybody successfully doing something like that ?

(Re-entering mathematical research after being in “commercial” industry for a couple years by getting a “visting researcher” position and using that to restart a career?)

What are your thoughts on it? Do you think it could work? Do you think that something else would work?

(some pre-answers: while my employer has research divisions, they are very much non-mathematical in methodology and intent, so going there is a bit of a stretch, at least if I want to do something mathematical)

24 April, 2010 at 4:25 am

YiweiHi mr Pibb

You may consider to find a job at a math department in some ordinary University in China, if you really love math. China is a large scale Country, like U.S., yet with much abundant scales, and you will find a scale suitable to your situation without too much efforts.

Good luck!

Yiwei

19 April, 2010 at 4:02 pm

mr Pibbjust some refinements—

The assertion that a mathematics PhD could ever be done “on the quick” is kind of insulting and naive. It would be better if I had said that 3 years seems realistic, if ambitious.

The “Erica Jong” answer is of course to give up on mathematical research and simply find a job in industry that I do not hate. But I find that take on things to be uninteresting.

21 April, 2010 at 10:59 pm

Write in your own voice « What’s new[…] Career advice […]

29 April, 2010 at 1:15 am

abcI have done BCA.Please tell me what should I do next.I don’t want to do MCA.

I am not planning to do job now.I want to study some courses.Please suggest me which course will be better.By doing which course I will be employed in good IT company with good salary and good position?

29 April, 2010 at 1:18 am

AdolfoDear Terrence Tao,

I am a mexican student just about to end the undergraduate degree. Recently I finished my thesis, nothing new, just 2nd order Nonlinear Oscillations (AC. Lazer) and degree theory to demonstrate fixed point theorems. And well, I have an excellent adviser who is dedicated to topological and variational methods applied to nonlinear analysis and PDE’s.

I was accepted for a PhD. or MSc (I specify) at the following places (where I put the subject of possible study and the possible adviser):

– Bonn Universitat (MSc)(geometric analysis, operator theory and PDE) – Lazlo S., Wernard Muller.

– University of Toronto (MSc)(Dynamical Systems, PDE, Global Analysis) – McCann, J. Colliander, Khesin, Khanin… you may know perfectly who may be

– Universidad de Granda (Spain) (PhD.)(Nonlinear analysis) – David Arcoya who works with with L. Boccardo and Ambrosseti.

– Warwick University (PhD)(dynamical systems and ergodic theory) – Mark Pollicot, J. Robinson

– Cornell University (PhD not accpeted yet, but tentaively accpeted, staring in 2 years)(Dynamical Systems, Nonlinear Analysis, etc…) – Yulij Ilyashenko.

This are my options, and well my doubt is not only where, but which subject. Because, somehow I even love combinatorics and abstract algebra, it is a little difficult for me to decide where to go… at least Nonlinear Analysis or Dynamical Systems and I am still expecting someone that tells me: Hey this subject combines them all the time! But… no one have haha.

-I think all of them (maybe some with more fame than other) are excellent advisers, I have talked almost with all of them and I can say they are even better persons. I mean I see the number of areas you work in, but well I consider myself just a “good” prospective not a “genius” prospective haha so maybe choosing the subject is a critical point of my graduate studies. ¿How may I decide the subject?, or if you know of something mixing Nonlinear Analysis and Dynamical Systems it is very welcome.

Recently I have been doing analysis (PDE mostly) and i do like it very much but sometimes I feel there are tooooooo mannnyyyyy technical steps and not the sufficient geometric intuition that I expected (maybe something that sound like too much of rough analysis).

-¿Maybe you recommend reading something of Harmonic Analyisis?

-One last thing, do your recommend choosing a masters option first and going to Cornell (mexico has a very high level at undergraduate studies) or directly to PhD (although sometimes not very sure of my subject)?

Thanks,

Adolfo

30 April, 2010 at 6:05 am

AnonymousHi, unfortunately I need to keep this posting anonymous. I hope this can be still an open issue that can be discussed here.

What should a graduate student do when, within his group -starting from his own personal experience, and have that spread through every other student and postdocs in the group- there is an objective and well established issue of mobbing? The situation is critical, ranging from free insulting by the head of the department, to continuous discouragement towards each one hard work. From dictatorship and threatening (“I will not admit you to defend your thesis if … ” is a constant), to continuous control over your own work and over the contacts that a student may be searching outside of the research group.

A postdoc can leave at any time, and search for another position, but it is more difficult than that when a student is at his (supposed) last year of graduate studies.

Thank you in advance for this blog, and for the entire webpage. An invaluable source for graduate students.

3 May, 2010 at 6:44 am

ChristianDear Professor Tao,

what requirements should have sb to give an excellent mathematical lecture either to a research audience either in a class of University where the audience are the students and the instructor of the course?

16 May, 2010 at 2:24 am

TusharDear Professor Tao,

I have just finished my first year in college, and am studying in IIT Kanpur. I am pretty interested in number theory, but unfortunately my college does not offer a course in number theory, instead offers loads of analysis courses but not number theory courses. :( ..So, I would like to know what should i do? as in, any book that you may refer for me(keeping in mind, i hve jut finished my first of undergraduate college).

thanks,

Tushar

23 May, 2010 at 1:09 am

AnonymousLiterature is what we ask for when we already learn the knowledge from the textbook but wish we didn’t.

22 June, 2010 at 9:07 pm

History and Motivation « DaFeda's Blog[…] reason I am creating this blog is something I read on Terrence Tao’s blog, What’s new. He has a career advice section where he amongst other things writes how important expository writing is in learning […]

24 June, 2010 at 6:46 am

NicWhen it comes to graduate careers, don’t jump in blind. Have a plan so that you have some kind of structure but at the same time, don’t worry if you have to stray from that plan. Don’t worry if what used to be right for you is no longer right, it happens. The only thing worse than jumping in without a plan is ploughing on with a plan that’s going to make you unhappy.

24 June, 2010 at 7:04 am

AnonymousWell, the only thing works in this game is the potential you have established, plus a good luck.

28 December, 2010 at 6:50 am

SteveI do not believe in luck.

4 August, 2010 at 10:45 am

Ishahii

I recently completed my b.tech in electronics & communication(2010) from kurukshetra university..i just want some suggestion how would i get a good job..I have given resumes in a lot of companies..suggest me any consultancy or should i go for ceritification program??I am seekin for a job in electronics as well as in IT sector..

waiting for your reply..

Thnks

Isha

13 August, 2010 at 8:26 am

AnonymousDear professor Tao,

Is been a first class mathematician a high pressure, in the sense of having to try hard all the time to not to make a ‘silly mistake’? Or you simply don’t care if you make a mistake that would be considered elemental to every mathematician? I’m not talking about a computational/numerical/algebraic error like 2+2=5 but more on comprehension error like stating wrongly the hypothesis of a well known theorem that undergrads are supposed to know well.

Thanks! =)

13 August, 2010 at 8:26 pm

J VermaDear Terry,

I just joined a graduate programme in Mathematics at some state university in United States. I am a sort of not enjoying here. I mean I didn’t like the town, I m still looking for place to live and the peer group here, I mean the senior & the fellow students, is not very interactive and I haven’t met anybody who is working on my area of interest. And the students are not very much interested in mathematics. Moreover the weather is not very pleasant here, its very hot. I studied in Cambridge, UK for masters before. I feel that I don’t belong here, I am really uncomfortable here.

I am planning to apply to some other Universities for spring or next fall sem. What do you suggest. Please reply.

18 August, 2010 at 3:09 am

AvinashDear Prof Tao,

I am pursuing my Phd in economics. Research work requires techniques from different fields of mathematics. Questions range from proving the existence in a model, to figuring out the weakest assumption required for conclusion, solving models etc.

Now we obviously can’t afford to spend all our time studying mathematics either. Only feasible solution is to use mathematics in an ‘opportunistic’ and ‘need to know’ basis. My question is what are the ‘core tools’ one needs to master in mathematics so that one can study any field as and when needed?

28 August, 2010 at 3:40 pm

Wickless CandlesMost of your advice is right on target for people studying in any field. I especially liked the suggestions to the Graduate Level Students. Going to talks, writing papers, and taking the initiative are all very important in promoting your future success.

Great article. I also loved the links! Thanks!

26 September, 2010 at 10:10 am

bobAnother puzzle some of us have is the school you chose to join as a prof!,

You could have gone anywhere (Princeton, Harvard, Berkeley,etc) but chose UCLA (nothing wrong with it, but..).

Was it location or other researchers in the same area of Math (but you are so versatile in so many sub disciplines).

Would be nice to know why and how you decided.

26 September, 2010 at 11:10 am

Terence TaoI discuss my opinions on these issues in the subpages

https://terrytao.wordpress.com/career-advice/which-universities-should-one-apply-to/

and

https://terrytao.wordpress.com/career-advice/don%E2%80%99t-base-career-decisions-on-glamour-or-fame/

3 October, 2010 at 6:32 pm

Mukesh KumarDear Prof Tao

I(Mukesh Kumar) have recently(2 months back) completed my bachelor of engg in electronics & communication from a indian university.

As from my childhood i am astouned of the beauty of mathematics ,and now i’m willing to make my carrer in mathematics field….so i need your valuvale suggestion that what should i do….from where i can start

Plz give me the valuable suggestion as soon as possible

4 October, 2010 at 1:51 am

mishabuckoDear Terence,

I’m inviting You to my blog, and- especially- this post:

https://mishabucko.wordpress.com/2010/10/02/my-problems/

Hope You could help me in some way as I’m dedicating my life to Kierkegaards, Goedel, Perelman and Ramanujan’s type of work.

Cheers,

Misha

11 October, 2010 at 5:16 am

Diane LaddI especially like your opening quote from Erica Jong! This is a very useful collection of advice. I would agree in many ways with the openning quote that many people simply need to be reasured that they are headed in the right direction. As far as time management is concerned, have you ever looked at “getting things done”?

14 November, 2010 at 12:34 pm

Maria DroujkovaAdvice on family math clubs (preschool/middle school)

http://naturalmath.wikispaces.com/Math+Clubs+article

5 December, 2010 at 2:37 am

Yousef RezaeiHi,

I am an undergraduate student in applied mathematics in Iran.

I found a polynomial time algorithm for Hamiltonian Cycle Problem, But I don’t know how to publish my article to mathematical Community. I have a proof of correctness of my algorithm. It takes at most O(n^4) time and is a kind of genetic algorithms. [ in dense graghs it takes O((n^2)(Log n)) ]

I need your advise and help. thank you a lot.

9 August, 2011 at 8:55 am

AnonymousHi Yousef,

As a tip, never try to claim that you have solved a big problem.Professonals normally do not welcome such claims. Instead, try to develop a more general problem, solve it, and let the solution of the big problem be included in your solution of the general problem. Besides, never try to benifit from your solution of any big problems: there are much more things you could benifit from.

5 December, 2010 at 3:39 am

Maria DroujkovaYousef, try this site: http://mathoverflow.net/

14 January, 2011 at 11:18 am

science and math@maria

Thanks for the link.

17 January, 2011 at 10:19 pm

.I have two questions:

1) How old a student of Mathematics can be to seriously think of it as a career? (Any rule of thumbs depending on a persons background?)

2) How do you consider yourselves compared to other historical Math prodigies who have also made their mark? And how lucky or how talented you would consider yourself to be compared to them – there should be some uniqueness about you since you are a Fields Medal winner at a young age?

10 February, 2011 at 7:02 pm

surekha29Yousef Rezaei, maybe you can post it on the arXiv and get feedback from people?

14 February, 2011 at 11:54 am

Idle EthnographerDear Prof. Tao,

– How often, if at all, do people change subject from humanities to mathematics?

– Do you know anyone who has done, or wants to? What would you advise such adventurous/moonstruck people on how to proceed, where to start, what to consider?

(The background: I’m 29, in my fourth year of sociology PhD (the qualitative kind, more like history than economics, hence my nick). I loved mathematics in high-school, but I chose a different path and have not studied any since I was 19. I do enjoy qualitative sociology (most of the time) and am good at it, and I am considering a research+teaching career. Yet, I find myself thinking all the time that I would enjoy, and be more productive, motivated and generally better at, research in pure mathematics or philosophy of mathematics. I’m not motivated by earnings and I love teaching.

I realise that instead of doing ‘forum research’, I could have spent my time building my math foundations. I did some self-study last year (now I am up to date with most high-school stuff), but now I’m writing up and have little time before I need to take proper career advancement steps.

I’m not underestimating the difficulty of even just a foundation degree in mathematics, let alone proper research: in fact, I am both intimidated and uninformed, and this is partly the reason for my reticence. I also suspect that the wise thing at 30 to do is stick to doing what I’m good at. I agree with the Erica Jong quote: I probably know the answer, but there is always a hopeful ‘what if?’. Even if I never succeed, it would be interesting to find out about others who have.).

16 February, 2011 at 9:05 am

yucaoDear Prof. Tao,

You put different advises into different levels. Do you think there is some clear cut for these advises? I think, even the advise like “learn and relearn your field”, on which most teachers don’t emphasize at all, in the postdoctoral level is absolutely very useful for the graduate students.

16 February, 2011 at 10:34 am

AnonymousHm, I think your second paragraph has already answered my questions:-)

[C.]

14 March, 2011 at 5:14 am

math dictionaryNice.

I am a 18 year old student and I dream to become a mathematician one day.

17 March, 2011 at 10:09 pm

Essential Steps of Problem Solving in Mathematical Sciences | Gaurav Happy Tiwari[…] Career Advice By Terrence Tao […]

30 March, 2011 at 11:03 am

DavePPerhaps some of your readers are interested in pursuing a career in industry. I have an undergraduate Applied Math degree from a major university and have found it to be invaluable in my career. I pursued a technical career and actually used some math early on. But the most useful aspects of this degree were first, all of my peers and supervisors assumed I was very smart and second, they all assumed I could do pretty much anything I said I could do. As a result, I was not pigeon holed early in my career, I was always given difficult assignments (reward is definitely proportionate to the level of perceived difficulty of accomplishment) and I was able to gain a great degree of freedom and flexibility.

I was able to leverage this to eventually become the Chief Technology Officer of a Fortune 100 company. Training in mathematics provides the basis for a life long ability to learn and grow. I definitely felt I had an advantage over the normal engineering background.

12 April, 2011 at 12:37 pm

Vivek KaulDear Dr Tao,

I was doing research on the corona problem and I found a student from UCLA whose PhD is in harmonic analysis. He says that he completed thesis Harmonic Measure on Subsets of a Lipschitz Graph and the Corona

Theorem two quarters ahead of schedule. The thesis resolved a twenty-five year old

conjecture concerning the maximum ideal space of bounded analytic functions. http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.pm/1298670085&page=record I was thinking the Corona problem is still an open problem. Has this problem been solved?

25 January, 2013 at 5:41 pm

Umarhttp://en.wikipedia.org/wiki/Corona_theorem

“It remains an open question whether there are versions of the corona theorem for every planar domain or for higher-dimensional domains.”

you could ask on math.stackexchange.com or mathoverflow.net if you want more updated specific reliable answers.

19 April, 2011 at 12:29 am

anonimousDear prof Tao.

Maybe this is a silly question. Is near to the problem of time management. I speak directly with an example so maybe i’m clearer. I’m and undergrad student,and i find on myself this really frustrating phenomenon when i’m left to myself,e.g when i’ve no professor in a little neighboroud of time, to give solution to problems,exams or other things: the effort and the results start to become less and less regular; it happens that i can stay 1 week with no other thing that doing exercise,try to improve my problem solving skills, and learning some theory(for the final exams,and for my interests);then tiredness cumulate and arrive all togheter, and for some days i can do just very soft thinking process(like think about something more qualitative and vague at the best;or just take walks for the whole day);but then it’s always quite difficult to start again the first step.i didn’t find here a sistematic way to start again;but just it happens that i’m quite lucky to find a not too hard but nice thing to think about and it starts again. I’m quite scared of this:i would like to do math in life, but if i’ll become a resaercher i’ll often be in this “free” situation that seems hard to manage in to a regular thinking life. And i don’t find this healty, both for the math and for the one’s life. Do you have any advice to find more a straight way when one is just left to himself? In any case thanks very much for this amazing blog:is a great source of inspiration.

25 January, 2013 at 5:42 pm

UmarYou can ask on meta.math.stackexchange.com or academia.stackexchange.com or some math forum if you want

16 June, 2011 at 4:16 pm

Cogito Interview: Terence Tao, Mathematician and Fields Medalist | Cogito[…] Read more from Terence Tao in his blog, https://terrytao.wordpress.com, which includes answers to more questions about being a mathematician. […]

24 August, 2011 at 8:40 pm

JohnDear Prof. Tao,

I learn from your Analysis(vol. I and II) that I have to first of all do analysis “by hand”. One needs to go through a very rigorous level in mathematics in order to get “accurate” intuition. I am nearly mad that every time I do/read analysis, I should go back to the very beginning — Peano axioms in your analysis I. Or sometimes I go to another extreme — for example, I can only do the multivariable calculus without any rigorous proof. Actually, I asked a lots of my friends that who can give a rigorous proof of the divergence theorem. The answer is an absolutely NO.

How do I know when I can “get rid of” the rigorous level and have the precise intuition? However, it seems that, on the other hand, if I go beyond the “rigorous level“ too fast, I cannot even convince myself that I really understand the topic I learn. For example, I use the divergence theorem again and again in my PDE course. But I don’t think I can give a satisfying proof for the result.

That seems to be a “stupid question”. I read your career advice again and again to find something. If my question is not “well-defined”, I will try to improve it.

25 August, 2011 at 9:14 am

Anonymous“Advice is what we ask for when we already know the answer but wish we didn’t.” Try to answer the question yourself. :-)

10 October, 2011 at 7:49 pm

AnonymousLooks like Terry will be superseded soon!

http://seattletimes.nwsource.com/html/localnews/2016447952_gabriel09m.html

13 October, 2011 at 7:06 am

KarishmaDear Prof Tao,

i am a B.E graduate in electrical engineering.i want to do my higher studies in mathematics.kindly guide me the institutes in mumbai,india that offer courses in mathematics after engineering.

i would also like to know the careers in mathematics,jobs related to the mathematics field and what is the eligibility to get it,do we need to write any entrance exams for it .Thanks in advance

27 October, 2011 at 3:44 am

Why build a website to archive your research? | jbdeaton.com[…] about how to do great research. I’m thinking of people like Daniel Lemire, John D. Cook, Terence Tao, Matt Might, Matt Welsh, Michael Nielsen, John Regehr, Rob J. Hyndman, and many others (these are […]

3 November, 2011 at 8:56 am

ronnie74Just wanted to say that I especially enjoyed your article on “Advice on Gifted Education”. Thank you.

24 November, 2011 at 7:12 am

Maintenance KomputerPerhaps some of your readers are interested in pursuing a career in industry. I have an undergraduate Applied Math degree from a major university and have found it to be invaluable in my career.

14 December, 2011 at 2:51 pm

“La matemática es más que rigor y demostraciones” | blocdemat[…] sección que es una joya de leer es la de “career advice“. Hay una entrada en particular que me encanta, que es esta: There’s more to […]

23 December, 2011 at 1:04 am

Hiatus and some holiday reading | Degree of Freedom[…] with a gift for explanations. The blog posts tend to be fairly high-level stuff, but the section on careers advice and the list of selected articles (in the sidebar; scroll down quite a long way to find it) are […]

26 December, 2011 at 7:40 pm

Interesting and Must Read Papers and Articles in Mathematics | MY DIGITAL NOTEBOOK[…] Advice (A Collection of Some very good advices) https://terrytao.wordpress.com/career-advice/ Terence […]

10 January, 2012 at 2:59 pm

» 论教育 Not "Not Even Wrong"[…] 在过去一两年里，我写过一些关于菲尔兹奖获得者，数学家Terence Tao（陶哲轩）的文章。他本人目前科学创作非常活跃，在好几个分支都是领袖人物，他几乎每一两个月都有很好的成果，已经包揽了有关系的所有一切的科学奖章。他可以说是一个Child Prodigy最后获得成功的一个特别好的例子。Tao是我们这个行业中的一个明星数学家，他也很喜欢写关于数学的杂文，他给青年数学家写的career advise（职业建议）写的非常详细，而一篇观点类的文章，What is good mathematics（什么是好的数学）被相当广泛的流传。然而我不打算在本文中过多的谈论他，——我以往已经谈过很多了。我只想提到一点，在我跟他父亲Billy Tao先生通信的时候，Billy经常向我提到“幸福”是人生的目的。我一开始不理解如果“仅仅”是追求幸福，Tao怎么可能在事业上取得这样的成就，后来我慢慢明白了一件事，正是“幸福”，那种发自内心的满足感以及某种意义上的成就感，给人带来非常正面的力量，而正面的力量是可以非常强大的。是的，我认为，“幸福”本身就是令人拥有成就感的一项伟业。 […]

13 January, 2012 at 5:37 pm

论教育（转） | proudwolflc[…] 在过去一两年里，我写过一些关于菲尔兹奖获得者，数学家Terence Tao（陶哲轩）的文章。他本人目前科学创作非常活跃，在好几个分支都是领袖人物，他几乎每一两个月都有很好的成果，已经包揽了有关系的所有一切的科学奖章。他可以说是一个Child Prodigy最后获得成功的一个特别好的例子。Tao是我们这个行业中的一个明星数学家，他也很喜欢写关于数学的杂文，他给青年数学家写的career advise（职业建议）写的非常详细，而一篇观点类的文章，What is good mathematics（什么是好的数学）被相当广泛的流传。然而我不打算在本文中过多的谈论他，——我以往已经谈过很多了。我只想提到一点，在我跟他父亲Billy Tao先生通信的时候，Billy经常向我提到“幸福”是人生的目的。我一开始不理解如果“仅仅”是追求幸福，Tao怎么可能在事业上取得这样的成就，后来我慢慢明白了一件事，正是“幸福”，那种发自内心的满足感以及某种意义上的成就感，给人带来非常正面的力量，而正面的力量是可以非常强大的。是的，我认为，“幸福”本身就是令人拥有成就感的一项伟业。 […]

6 February, 2012 at 4:01 pm

QuoraIs paying $100,000 for masters degree in Statistics a reasonable investment?…A good grad school (and good environment) can change a lot about your life, way more than you can think !!! Whether it is worth it depends on what you want from there. I have heard this about MIT, that it is like drinking from a fire house. Quite liter…

18 March, 2012 at 2:54 pm

Terrence Tao’s Career Advice page | Enlighten and Evolve[…] getting ready to move to the next part of your educational or working career, check this page out! What a great resource, and not just for math […]

20 March, 2012 at 12:39 pm

Mark T.I work in insurance, and from my experience our industry drools overs math majors, especially those who have statistics backgrounds, which enables you to move forward with actuarial exams. If there are math majors out there who just arent sure about things, research actuarial science because there is a HUGE market for it.

4 April, 2012 at 4:20 am

Graduate JobsThis is a good website if you want help writing your CV. They always have great demand for maths students or similar courses. Check them out they really helped me.

11 April, 2012 at 12:39 pm

MartyDr. Tao: Steven Krantz has given some good advice to young mathematicians in various places. He’s written a book or two about it, e.g.:

http://www.amazon.com/Mathematicians-Survival-Guide-Graduate-Development/dp/082183455X/ref=sr_1_3?s=books&ie=UTF8&qid=1334176654&sr=1-3

Here’s some free advice he published a few years ago:

http://www.math.wustl.edu/~sk/books/newsurv.pdf

27 May, 2012 at 9:31 am

LuqingI translated it into Chinese:http://blog.sciencenet.cn/home.php?mod=space&uid=604208&do=blog&quickforward=1&id=575653

18 June, 2012 at 12:18 pm

Advice (collected) by a young mathematician « regularize[…] we are at it, there is this must-read page by Terry Tao: This page on his blog (and its outdated old version here) which also features great […]

27 June, 2012 at 9:22 am

D. SarmahDear Prof. Tao,

I am presently doing my B.Sc. (undergraduate) in Mathematics in India. And studying Physics as a subsidiary subject. According to the University rule, every student have to do a research project in the summer vacation. So sir, I would like to have your advice on possible project topic on Applied/Theoretical Mathematics as my knowledge is limited. I am interested in Gravitation, Black-hole, Differential equation, 3-dimentional curve….etc.

Your valuable advice will help me to a greater extent.

28 July, 2012 at 8:48 pm

To Qual or to fall « Derek Zhang's OR Thinking[…] discussion about what it means by the qualifying exam. Some general career advice by Terrace […]

14 September, 2012 at 4:16 am

RajeswariHi

currently am working in a mnc as a research analyst.

i have 4 years of experience in e publishing industry. but am not interested in that field. am looking for a career change.

am interested in live projects

direct interaction with customers

what kind of profile i can choose

my graduation is Msc IT

22 September, 2012 at 6:36 am

anjanasir i have completed my B.C.A and right now persuing for M.C.A .i have a keen intrest in I.T sectors .so plz advice me some part time courses which i can pursue to enhance my computer skills.

27 September, 2012 at 7:59 am

kulturystyka sklepI am a student doing B-Tech 3rd semester(8 semester course) at National Institute of Technology,calicut,india.i have a ardent interest in mathematics escpecially algebra nd analysis.I like to pursue mathematics research after my btech degree.pls do advice me on how and where to do it?

1 October, 2012 at 2:01 am

jak szybko schudnacIt’s interesting advice, but it dones’t work in all countries.

6 October, 2012 at 1:49 am

Things to stop doing « Noncommutative Analysis[…] lots of advice pages out there, for example (my favorites) this extremely broad, kind and generous page by Terry Tao or this very focused one by Doron Zeilberger. But like any advice giver who respects […]

23 October, 2012 at 10:40 am

ballI am a student doing B-Tech 3rd semester

31 October, 2012 at 2:13 am

Anonymousi m a student of 10th class

3 November, 2012 at 11:48 am

Some advices to young mathematicians « Research and Lecture notes[…] The blog of Terence Tao is also an excellent source for advices on writing mathematics and academic careers. […]

29 November, 2012 at 3:09 pm

AnonymousHi, I was wondering if I could ask you a question. I’m not sure who to ask, but your blog seems very active so I thought I’d try here – if you don’t mind of course.

I’m about to start a PhD in a few months. However, recently I’ve been having some (well, a lot, to be honest) self-doubts.

I like maths a lot, and in my undergraduate I worked very hard to understand things. That I worked hard is a good thing, obviously, but I’m also thinking that it may also be a sign that I’m not clever enough to actually do things once things get too hard. For example, in one part of your blog you talk about the “three stages” (essentially, pre-undergraduate, undergraduate, and graduate and beyond – if I’m not mistaken). I feel I made the transition from the first to the second, through hard work, but I can’t help but doubt my ability to move to the third. I’ve been looking through graduate books in preparation for my PhD and I find them really difficult. I can struggle through them and get by from line to line, but I know that I struggle to see the big picture. Let alone the idea that I can actually contribute anything. I feel that I’m simply not clever enough (never mind how much I work) to gain a sufficiently deep understanding of something to be able to come up with any sort of original work.

The thought of not attempting to do a PhD seems very sad to me though, because I really do want to do one and I want a career researching maths. But I’m just so scared of failing. I just fear there is a threshold of natural intelligence required and I don’t have that.

6 December, 2012 at 9:41 am

GuestDr. Tao, I’m a graduate student in Physics, and am probably guessing you’ve got this question innumerable times before. Do you think the character Charlie on the TV series “Numbers” is based in whole or part on you, especially with you being based on the west coast like the shows setting? I tried searching your blogs for previous posts related to this question.

respectfully,

6 December, 2012 at 10:05 am

Terence TaoNo; according to http://www.maa.org/devlin/devlin_02_05.html , the character is loosely based on Richard Feynman. (Although my former colleague, Tony Chan, was one of the consultants for the pilot.)

7 December, 2012 at 11:11 pm

andrescaicedoGary Lorden from Caltech, another consultant for the show, used to say that “based on Richard Feynman” meant that they copied his hairstyle.

6 December, 2012 at 3:35 pm

MaxHello,

I don’t come from a wealthy family and was “obligated” by my parents to study computer science. I am currently doing my master’s degree and only go to finals because I don’t really enjoy CS andI don’t find it “challenging” so I have a lot of free time, I am teaching myself theoretical physics which inspired me to also study the mathematics behind it in depth. Would you happen to know references to learn from ? I can’t find many online courses for mathematics…

Also do you think it’s possible for someone who didn’t study a particular area to be accepted by scientific community ?

Thanks,

Max

30 December, 2012 at 6:08 pm

Starting and finishing tasks |[…] I also enjoy talking with others about how they work. A nice draft of similar ideas is available on Terry Tao’s blog. I will probably re-state some of the exact same […]

10 January, 2013 at 11:12 am

Terry Tao on Mathematical Career | enjoymathematics[…] Terry Tao on Mathematical Career […]

24 March, 2013 at 12:15 pm

RamiDear Professor Tao, I have to choose between two graduate schools that accepted me for their PHD program in pure math. Each one of them contains a researcher who is very strong in the field that I want. What should I do next? Is a considerable difference in the rankings between the two enough as a criterion? (20 US news and 35 NRC, one appears in the top 100 QS subject ranking in math, the other doesn’t.). Or should I take other criteria into consideration? I should note that one of them has a large department, while the other has a small department, and both contain outstanding faculty members.

31 March, 2013 at 2:55 am

LiliDear Professor Tao,

I am studying Mathematics(a master’s program). I intend to continue my studies in math in U.S . The university in which I am studying now is different from my undergraduate university.Things are really harder here.

I need some recommendation letters for my applying process and this is what has ruined my life!

I talked to one of my professors to be my adviser and to write one of the recommendation letters for me at the end of the work.He asked me to work on some material in a determined period of time.I started working but it was harder than what I imagined.At the same time I ran into some problems in my individual life.Now, that determined time has finished , I haven`t finished that material and I had bad grades last semester.My professor says I should work harder. I have a lot of work I haven`t done.

I loved mathematics very much but now I don`t enjoy it.I can not concentrate on what I study. Studying just for letters of recommendation or trying to write a paper just to get admission of a good university is very boring.I can`t enjoy mathematics anymore .And I can`t even progress in my work.

How can I change this situation? How can I make progress? And could I find strong letters of recommendation in 9 months?

I think some of my undergraduate professors could write good (not strong) letters for me.

6 May, 2013 at 12:35 pm

Role of a Statistician | James Li[…] advice is probably very biased towards a statistician geared towards industry. See Terrence Tao and J. Steele and Greg Mankiw for more advice for aspiring […]

20 May, 2013 at 6:31 pm

the perfect pointe bookFirst off I would like to say wonderful blog!

I had a quick question in which I’d like to ask if you don’t mind.

I was curious to know how you center yourself and clear

your thoughts prior to writing. I’ve had trouble clearing my thoughts in getting my thoughts out. I do take pleasure in writing however it just seems like the first 10 to 15 minutes are lost just trying to figure out how to begin. Any ideas or tips? Cheers!

19 June, 2013 at 6:01 am

anelim10-15 minutes? How do you do that? I know people who have writing block for MONTHS.

2 June, 2013 at 12:32 pm

Mathew GeorgeSir,

I am an undergraduate mathematics student at a university in India. I would like to know whether the only option for a person who has completed his undergraduate course is to go for PhD and a become a mathematics professor or a scientist. Not that I am not interested in being a mathematician and doing research, but I want to know various other opportunities available. Please help me out.

25 June, 2013 at 3:16 am

emmanuelSir,

Am emmanuel prabakaran i have finished my B.Tech this year 2013 in india.

I did’t get any campus interview ,still i has being seek job but not yet.

My question is to whether i keep seek on job are better to do any course for my career ..

i basically computer science department core ,so tell me what i do for next step.

6 July, 2013 at 10:59 pm

IzzatullahHi,

I’m Izzatullah from Malaysia. Currently in the final semester of BEng. of Petroleum Engineering.

I am planning to pursue my master in applied maths and involve with mathematical physics field because I lost my interest towards oil and gas industry, and I wanna focussing on my main interest since high school which maths.

Is it a wise idea? What would be the preparation I need to make?

19 October, 2013 at 6:29 pm

cainiaozrAre you sure that you are interested in mathematics?

11 July, 2013 at 4:32 am

TuHello I am a Chinese high school graduates. Now learn calculus in the holiday. I have often been the problem of “how to understand the” infinite infinitesimal “how much” and if you think that university mathematics, more space for development?

11 July, 2013 at 11:41 am

LinDo not listen to other people’s advice and find your own path.

19 October, 2013 at 6:28 pm

cainiaozrPlease read mathematical analysis, and understand the concepts of epsilon-delta definition.

19 July, 2013 at 6:47 pm

KevinTranNice post

5 October, 2013 at 1:05 pm

Goal Setting for a Successful Job Search | Goal Setting With Rosie Sorrel[…] Career advice | What's new – WordPress.com […]

24 October, 2013 at 2:00 am

PDF.js viewer | Goal Setting With Rosie Sorrel[…] Career advice | What's new – WordPress.com […]

24 October, 2013 at 9:05 pm

career pathHi arica Jong!

I really got something big from these collection of various pieces of advice on academic career of yours. I’m an education graduate, and looking forward to find my path to the best career!

7 November, 2013 at 2:31 pm

coolmathYou are my lead generation coach and you have just inspired me to give it my all! Thanks!

10 November, 2013 at 9:31 am

ZephProf. Tao,

I don’t have a mathematics background (engineering background), but I try and learn when I am not working. I want to study cognitive science, and I believe that would also allow me to learn mathematics along the way. Can you please advise me if this is accurate? If not, how should I proceed given my background and interests? Is it advisable to do a math-heavy cognitive science program, and pursue mathematics at a post doctorate level or as another doctorate? What areas of mathematics would be relevant?

18 November, 2013 at 6:04 pm

Math Blog Snippet | the Cyclic Grizzly[…] Terence also has a blog category for non-technical posts, aimed at a more general audience, and offers helpful advice on mathematical careers. […]

8 December, 2013 at 2:46 am

ZhenghongDr. Tao, I really want to make some process in math, but I always can’t well grasp the degree of difficulty of the problems. For instance, I’m thinking about a problem recently which is also a question to ask for that there exists n-primes at least between n and n^2. The history or any reference of it or other research subjects usually can’t be found. What’s wrong with me？

8 December, 2013 at 4:32 am

Victor PortonSometimes complexity of a problem is seen in its structure or structural complexity. Consider for example Fermat Last Theorem. It involves powers, powers are defined through multiplication, and multiplication is defined through addition. So powers are “third level of complexity”. I believe this (indirection when referring to properties of addition) is the reason why FLT is so hard to prove. (Well, this works not always: a. Some structurally complex problems are nevertheless very simple; b. Some hard problems are of much less structural complexity than FLT.)

8 December, 2013 at 10:51 am

FanHint: Prime Number Theorem (or even Chebyshev’s bound)

12 December, 2013 at 7:28 pm

Essential Steps of Problem Solving in Mathematical Sciences | MY DIGITAL NOTEBOOK[…] Career Advice By Terrence Tao […]

14 January, 2014 at 6:42 am

Self Tests by Psychology Today | Goal Setting With Rosie Sorrel[…] Career advice | What's new – WordPress.com […]

15 January, 2014 at 10:17 pm

Billy MillerThe best career advice I have heard is: Do the best you can. Hang in there.

4 February, 2014 at 1:51 am

shabeeri am shabeer, i have completed master of computer application degree.but right now i am in saudi arabia , i dont get any job related with my studies ,still i am woking as technician for printer and totally changed my career goal .How i can reverted to software jobs please gave me an valuable advice

9 February, 2014 at 11:49 am

When you hear these advice, think at least twice. | the blue surreal[…] https://terrytao.wordpress.com/career-advice/ […]

10 February, 2014 at 10:49 am

RAMi am ram, i have completed my 12th a year ago, i just want your advice that what can i choose for my career firstly, i cant go for engineering because maths is not my cup of tea and cant go for medical because i hate bio so what can i choose for my career except theese two. pls rply

11 February, 2014 at 1:55 am

AnonymousHello Professor,I’m a postgraduate student researching bit coin Do you think its algorithm can be cracked? And did you buy any :)

15 February, 2014 at 4:13 pm

Lean In | 一期一会[…] Terry Tao writes on learning math and a lot of other things. […]

28 February, 2014 at 6:03 pm

Getting to Know A....MATHEMATICIAN!![…] a living, so its best to get started now! A good source of advice can be found in Terry Tao’s blog. __reach_config = { pid: '526eeaba97b0c9f447000003', title: 'Getting to Know A….MATHEMATICIAN!! […]

2 March, 2014 at 3:29 am

Surbhi sharmahi……..I m surbhi. I m doing chemistry honors. from delhi university. i m a 1st yr student. I m totally confused about my carrier. what sort of carrier can i have in the field of chemistry.?? pls advice me..I also want to settle in abroad.. so pls tell me wht type of carrier i can have their in the field of chemistry…?? pls give me advice n show me a path

8 March, 2014 at 9:28 pm

fubarioHello Dr. Tao, are you familiar with the Moore-method of teaching? Just thought you might be interested in it as it seems to me to be the way of learning mathematics and teaching it.

12 March, 2014 at 9:36 pm

Anonymouswow, professor Tao. This page is so informative. I really wish I read you blog earlier. This website needs more publicity than it has atm.

16 April, 2014 at 1:52 am

S A IrfanGood Day Sir,

I am a big follower of you.

I am a Graduate student started my Ph.D few days back, I am interested in Mathematical modeling, My supervisor offered me a project on chemical engineering to model it using diffusion equations and all. But I am worried about the importance of the project as a mathematicians because it has less mathematics involved in it. Will you please give me a advice on how to make these chemical project more mathematical for a good Ph.D as a mathematicians.

Thanks in advance

20 April, 2014 at 5:31 pm

AnjalHello,

I have completed my Bachelors in Aeronautical Engineering from China.Now,i have planned to go Australia for Masters program but I am confused to choose a subject area.I want to live in Australia after graduation and work there..I want to find a high paid salary job after graduating from Australia.Please advice me about choosing suitable major for my Masters degree

22 April, 2014 at 11:32 pm

JOEDear Dr Tao,

I think this is probably the wrong place to put this but I read your previous article ”Does one have to be a genius to do maths?” and I think I must be ailing from one of the condition you spoke of. Now where does the Navier-Stokes problem come in; well I threw much of myself into tackling this one for 2yrs now. I am no proffesional mathematician but I believe I may have cracked something; like I have found the main basis of boundedness in the NSE; smoothness isnt that hard to achieve afterwards.

I wish to publish these findings but I am discouraged by the fact that as an amateur I will be taking down an icon in an already protective scientific community & I dont mean Prof. Otelbaev. Having gone through Otelbayiev’s own work I have found an error consistent with other peoples attempts at attacking the NSE.

Dear Dr Tao, I love your new way of looking at this problem and something interesting hit me! Forgive me for suggesting this but would you mind looking into whether you could fit this idea into galactic clusters, I thought Gamma ray bursts but it would be interesting to see what you might come up with. By the way, can you give me in your proffessional capasity advice on what to do?

Thanks.

25 April, 2014 at 2:29 am

sachikahii,,, i have recently given my 12th papers,,i am from commerce without maths.

i hate maths n dnn want to study maths. please suggest me what should i do after having my result,,what courses should i opt for ,from where to opt n ol d necessary details regarding the same.PLEASE HELP ME SOON AS THE FORMS FOR COLLAGES ARE ALREADY OUT.

5 June, 2014 at 2:08 am

ANIMESH HAZARIKAwish i could just copy and paste what you just said here…its all over same with me.let me know if someone advice you the best..

2 May, 2014 at 4:55 pm

HUNHallo Prof Tao im a final civil engineering student somewhere in Southern Africa , I have very poor mathematics skills which cause me a lot in almost all my career task which im given and I really make a lot of errors which are very irritating however through hardwork I have made it to my final year… how can I improve and still succeed in my field of study and become a top Civil engineer

2 June, 2014 at 4:46 pm

Why build a website to archive your research? | Only A Model[…] about how to do great research. I’m thinking of people like Daniel Lemire, John D. Cook, Terence Tao, Matt Might, Matt Welsh, Michael Nielsen, John Regehr, Rob J. Hyndman, and many others (these are […]

5 June, 2014 at 10:54 pm

Annuhello!

i need guidance ,

i have passed my 12 board with 91% marks and don’t know what todo rigt now.

to do b.sc or b-tech?

but as i have got only 52 marks in my jee main exam ,i can’t get govt. college for b-tech so i have to drop in order to prepare for iit jee advance exam, so, please,please tell me that i should join du delhi or go kota for preparing iitjee.

10 June, 2014 at 6:36 pm

Marc BessonProfessor Tao,

I am so happy to have found your page. It is informative in a great number of areas that are important to me.

One thing I would like to ask you is this; could you speak a bit about the relevance of your Fulbright year doing research? I am currently a Senior doing Mathematics, and my intention was to go straight to grad school. However, some programs seem interesting. What are your thoughts on programs like these?

Even if you do not reply, thank you very much for maintaining this site. It is enormously helpful.

Marc Besson

16 June, 2014 at 10:25 pm

Arunima MaheshwariHi my name is arunima. I m very much confused in selecting my btech college. my uptu rank is 10033 and in girls it is 750. my ggsipu rankis 6645.I also appeared in upes (dehradun)and i got 2327 rank in it.I am general category ,delhi outsider. kindly advise me soon as my upes counselling is on 24 june and i have to pay an amount of 90,000 in it.

waiting for the reply…..

27 July, 2014 at 5:47 pm

ThubeyHie… Would like to receive more email and advice on study habbits and carrier guidance when doing maths,accounts annd mob in my Alevel ….looking forward to chart with you

27 July, 2014 at 5:50 pm

ThubeyWant ur help guys,,so please be my study advisor and l strong believe you can give me a good direction in carrer guidance..

28 July, 2014 at 9:54 am

IfeoluwaDear Professor Tao,

I am a Nigerian student currently in the first year at the University,I major in Physics and Electronics..I have a huge interest and likewise passion for mathematics which was even made stronger when I discovered the living man with the highest IQ is a versatile mathematician which so happens to be your very humble self..I hope perhaps you can help me with some good study techniques and I.Q exercises…as I’m more than willing to be your Cyber-protege.

14 August, 2014 at 5:12 am

Gaikwad Shraddha DilipI want to do something different .but I haven’t good guidance from anyone.

17 August, 2014 at 10:59 pm

fx910525Dear Prof. Tao,

Thanks for your so much advice on career, I have benefited a lot since I followed many years ago.

Could you give some advice on how to take notes during reading a math textbook? or do you take notes when you learn a book at first time? I find that if I don’t take some notes I forget easily, but taking notes can take lots of time and reading becomes slow. Also, after taking notes, I normally don’t want to go back to the notes, making the notes kind of useless.

I keep wondering whether I was wrong in taking notes. I have tried many kinds of notes: writing summaries, drawing logical charts, collecting important points, or list all the def, thm, props… And because it takes time, normally I will start to doubt my way of taking notes and give up at last.

Sometimes I decide I should not take notes, just read by heart and try to understand them at that moment. But problem is as time flies, memory fades, or because of much study in other things, previous study goes unfamiliar.

Recently, I got an idea from your blog to make some lecture notes. I have heard that teaching others can make oneself more familiar with the topic. I guess this is a good way to try. But I am wondering if this is a good method in the first-time study.

I guess many students have the same problem with me when trying to study efficiently.

Really hope you can share some experience and good methods in this aspect. I feel it will also be helpful not only in study of maths.

I am a student in physics as well as maths.

Thank you!

17 August, 2014 at 11:21 pm

fx910525Dear Prof. Tao

There is another small question. You say you like to do many small projects in the same time, so you can switch among them by, say, your mood. Is that also true for learning? For example, if now I want to learn Lie group, real analysis, Riemann geometry and quantum field theory, is it better to learn one thing at a time and finish them one by one, or learn all of them a little a day? Do you have such experience before?

looking forward to your reply

Thanks again.

27 August, 2014 at 2:56 am

jakdownThere is another small question. You say you like to do many small projects in the same time, so you can switch among them by, say, your mood. Is that also true for learning? For example, if now I want to learn Lie group, real analysis, Riemann geometry and quantum field theory, is it better to learn one thing at a time and finish them one by one, or learn all of them a little a day? Do you have such experience before?

27 August, 2014 at 12:47 pm

Terence TaoI’m assuming the question here concerns self-directed learning, outside of a classroom, a reading course, or other form of directed study. In that case, I think the more important factor is to have a good motivation for learning whatever it is you are trying to learn, and in particular to have a reasonably focused and feasible goal; for example, you may get more out of figuring out everything about how to prove Theorem 6.7 from a textbook because you need this theorem or a very close variant of it for an application, than trying to digest the first six chapters of that textbook in linear order. Examples of such goals include answering “dumb” questions that you asked yourself, relearning your field, finding out more about a specific breakthrough in another field and how it relates to your own work, figuring out just enough to know how to improve one of your tools, or understanding a key counterexample or obstruction that limits the reach of that tool.

See also this response by Matt Emerton elsewhere on this blog to a related question (more focused on arithmetic geometry, but many of the points he makes are more broadly applicable).

31 August, 2014 at 8:45 am

MA Adili am very interested at maths and physics which career should i choose !

Will IIT fits for me ?

I am studying in 10 th .which way should i choose in future ?

31 August, 2014 at 8:49 am

portonIf you want an occupation related with math, you have the following choice: teacher and/or researcher in: math. physics, engineering (including electronics), computer science (including programming, or as they call advanced programming “software engineering”) and also quantitative economics or biology. In every of these fields there are many subfields, and we cannot enumerate all of them. Has I forgotten any major fields?

1 September, 2014 at 5:20 pm

Glen MashalaMr Tao currently I studying a Bsc Electrical engineering, 21 years old and I’ll be finishing the degree in 2017…I want to quit engineering and do a Bsc in applied mathematics but I am not quite sure whether I’ll be making the right decision because I can say I am not very good at math but I love it and I just think I can learn…How can you advice me on that one or rather what’s your advice for people like me?

6 September, 2014 at 12:18 am

SHDear Prof Tao,

I’m a PhD student and I have what I see as a critical problem in my career. I think there is a number of people that have similar issues, so maybe you could address this on your blog. The problem is simple: I made a mistake with choosing a PhD advisor. Of course, it is my own mistake, but in my defense I can only say that this takes place not in US and you have to choose someone directly after your undergrad. Additionally, you have a very limited time to complete your PhD, so the time pressure is enormous.

The way in which my advisor is bad is also simple: he is really bad at Math. This seems like a very arrogant thing to say about a superior, but I could not believe this myself and needed a very long time to actually realize this. Which makes the time problem even more critical. My advisor has found some ways to trick people into believing he is real, getting on other peoples’ papers, doing public lectures etc, and there is no way I as a PhD student can confront this in any useful way. I would quit and start over, but I think the funding agencies don’t give you a second chance, especially when you say that your advisor is to blame for starting over. And the said advisor is not going to help me get out of this situation either.

For a very long time I thought that the problem was in myself, that I somehow didn’t get how to be a PhD student (even though I had a very good track record, finishing a Famous School with very good results). But no, other students, it turns out, do actually talk with their advisor from time to time, and they actually talk about Math.

Is there any way you can see out of this situation?

6 September, 2014 at 8:10 am

Terence TaoI personally happened to have a very good experience with my own advisor, so do not have any particularly informed advice to offer here, but a quick search on academia.stackexchange.com seems to turn up a fair bit of discussion on similar topics.

7 September, 2014 at 12:07 am

bapi karmakarsir i have complete my graduation at orissa in arts strem and now i have no idea for any course or job….!’

so plz kindly help me…..

tell me for any course to lead a good job….

11 September, 2014 at 4:14 pm

Career Advice For New Graduates | New Job Today[…] Career advice | What’s new – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

13 September, 2014 at 9:37 am

היחידה לצפייה ישירהA great advice ! recomaneded to read

22 September, 2014 at 1:02 pm

What My Career Objective | New Job Today[…] Career advice – What’s new | Updates on my research and … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

23 September, 2014 at 6:33 am

What Is Career Values | New Job Today[…] Terry Tao’s career advice – What’s new | Updates on my … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

26 September, 2014 at 12:45 pm

microsoft silicon valley TCS research lab shuts down— easy come, easy go | Turing Machine[…] 8. Career advice | What’s new / Terence Tao […]

30 September, 2014 at 2:02 am

QuoraWhat good advice could be given to a young mathematician?You might want to take a look at the pieces of advice by Fields Medalist Terence Tao: https://terrytao.wordpress.com/career-advice/

9 October, 2014 at 2:55 am

SwatiI am IN 12th now from maths field what i have to do after 12 i want to do banking or p. O what i have to do for this??

12 October, 2014 at 3:20 am

Nikhil BeraDear Prof. Terri Tao,

I’m a post graduate student from India. I have been suffering from a problem from my 1st year graduate courses. I want to do mathematics. But there is some other problem. I sub-consciously turn to find a meaning for life. What does it mean to live a life? We live we die and everything apparently gets finished. Then what does it mean to live a life?Sometimes I tried to find a answer, a logical answer, which will be the most believable to me, but never got a permanent satisfactory answer. Now a days I’m trying ran away from this problem so that I can concentrate in mathematics properly.Please reply to me. Give me a answer please or a motivation to forget this question.

14 October, 2014 at 12:07 am

mayank kumarsir plz tell ,, if i do m.sc. by any iits then what r the job opportunities after that????, do iits give placement after doing m.sc from iits….i m student from INDIA n doing graduation in maths from lucknow university ……. n also sir plz tell what is scope of doing m.sc. in maths from any institude

14 October, 2014 at 11:38 pm

Nikhil BeraDear Prof. Terri Tao,

I’m a post graduate student from India. I have been suffering from a problem from my 1st year graduate courses. I want to do mathematics. But there is some other problem. I sub-consciously turn to find a meaning for life. What does it mean to live a life? We live we die and everything apparently gets finished. Then what does it mean to live a life?Sometimes I tried to find a answer, a logical answer, which will be the most believable to me, but never got a permanent satisfactory answer. Now a days I’m trying ran away from this problem so that I can concentrate in mathematics properly.Please reply to me. Give me a answer please or a motivation to forget this question.

15 October, 2014 at 12:32 am

muziI was in the commerce class n I passed my matric with a b symbol but I fail maths and it not showing on m certificate and got level 3 on my accounting so I’m struggling to see any option for me in order to develop a career and finding a job that won’t wants mathematics please help me find options thank u

17 October, 2014 at 3:52 am

Amit kumarSir please advice me i don’t want to do engg… because my interest in math should i left engg or not please tell me soon

20 October, 2014 at 5:20 am

Hk SmartBoySir please advice me i don’t want to do engg… because my interest in math should i left engg or not please tell me soon conversation chemistry book

5 November, 2014 at 9:42 pm

Best Career Advice Books | New Job Today[…] Terry Tao’s career advice – What’s new | Updates on my … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

7 November, 2014 at 3:40 pm

What Graduate Career | Develop My Career[…] Terry Tao’s career advice – What’s new | Updates on my … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

9 November, 2014 at 4:15 pm

What Job Would I Be Good At Quiz | Develop My Career12 November, 2014 at 12:32 am

What Is My Ideal Career | New Job Today[…] Career advice – What’s new | Updates on my research and … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

14 November, 2014 at 1:05 pm

Career Advice For Graduates | New Job Today14 November, 2014 at 10:19 pm

What’s The Right Career For Me | Develop My Career[…] Career advice | What’s new – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

15 November, 2014 at 1:13 am

What Is My Career Vision | Develop My Career[…] Career advice – What’s new | Updates on my research … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

24 November, 2014 at 11:22 am

Teenage Girl Advice Blog Career | Cuties Live[…] Career advice – What’s new | Updates on my research and … – Advice is what we ask for when we already know the answer but wish we didn’t. Here is my collection of various pieces of advice on academic career issues in …… […]

29 November, 2014 at 3:48 pm

Math studentDear Prof. Tao,

I have a question regarding research: How many projects should one do at once? Should one focus all one’s energy on one project, or do maybe five projects at the same time?

(by ‘project’ i mean a collection of related things one wants to prove or algorithms one wants to invent, basically the work behind one paper)

29 November, 2014 at 3:54 pm

Math studentAlso, as a young mathematician, how broad an area of mathematics should you learn? Should one try to become an expert in one area or in many different?

Further, what is a good balance between

-doing exercises

-leaning new theory

-doing research?

Is it a possibility to just learn on what you stumble through your quests through a research problem? Or is that ineffective?

27 January, 2015 at 1:10 am

Math StudentTerence Tao has answered the first question of the second post here: https://www.youtube.com/watch?v=eNgUQlpc1m0

You should learn a broad area of mathematics. One reason might be, that in research problems, in order to make progress one often has to apply a certain step of reasoning or a certain theorem to get another conclusion, and it is better to be able to choose from many theorems to apply.

1 December, 2014 at 6:18 pm

ukashbozdurmaukashbozdurmaSir please advice me i don’t want to do engg… because my interest in math should i left engg or not please tell me soon http://www.guvenlibozdurma.com/

24 December, 2014 at 5:21 pm

H. SchoenichProf. Tao:

It’s not uncommon for a young man to be very capable as a mathematician. This does not make him capable as a sage. Wisdom is not a product of just intelligence. I think your experiences, as well, are so unique, as to be unrepresentative.

I am older and wiser. I know what I am talking about. It is presumptuous for you to keep this part of your blog. I understand the value of other parts; this part should be eliminated. You don’t have the vista, and suggesting you do is at a minimum unattractive hubris.

H. Schoenich

December 24, 2014

25 December, 2014 at 10:23 am

Math studentDear Prof. Tao,

please do not listen to H. Schoenich. I have profited a lot from your hints, and hope that others will do too.

Your experiences are far from unrepresentative. The only difference are some advantages you have in terms of speed and creativity, but the things written here are valuable for most professional mathematicians.

Wisdom is the product of logical thought, and intelligence helps with that.

Please do not deprive the world of this wonderful source of knowledge.

With the greatest possible respect.

1 January, 2015 at 10:53 am

preethii need ur help …. i’m pursuing Ph.D in finance. i completed my 2 years. i know its not a my cup of tea. its too tough. i can’t complete it . here is 2 years course work its more than other universities. i want to do MA in economics correspondence because my Ph.D is regular during Ph.d i can’t do any job its prohibition. plz give me some suggestions regarding it . plz help me . what i do . should i continue my Ph.D and also take admission in MA economics as correspondence. or i quit my Ph.D plz….

3 January, 2015 at 8:20 am

AnonymousDear professor,

If by any chance you are reading this, I would like to hear your opinion concerning the following matter. I live in a country where mathematics research is not well funded and established due to the political turmoil. However, I managed for the past few years to study some advanced mathematics by myself. I have not yet graduated from college, and I fear that I will face a dead end upon graduation.

Also, the only type of research conducted at the local university is not what you would call “up to date”, and nearly no one works in the ‘big’ areas of math.

I would very much appreciate any suggestions.

Thanks,

A.A

24 January, 2015 at 5:52 pm

Career Advice | Insurance1 February, 2015 at 7:47 am

emadHI Dr. tao and everyone

There is a problem in my relationship with math and i need a little guidance. I like mathematics and i wanted to study it in university, and my problem is that i’m afraid. i’m afraid that i can’t pursue it, i afraid of this that what if i chose math and in the middle of the path i couldn’t do it.

and this fear made me like math lesser because it seems my brain resists toward things that make it feel bad.

actually now, i’m more of a math stupid than a math genius.(i don’t think just math geniuses can do math!).

anyone may think this fear is stupid and it indeed is. this fear roots from a big mental loss. due to some incidents i lost about 40% of my intelligence, and when i realized it was to late to do anything.(it dropped about 76-80 points!, i checked it.). before that loss i didn’t have any problem comprehending concepts in higher mathematics way beyond my age.(i’m not gonna start whining so i stop it)

so, what do you think i should do? should i stick to math or should i find another field like philosophy or literature or history or … ?

7 February, 2015 at 5:28 am

Math studentDear emad,

If 40% of your intelligence were 76-80 points, then that’s a good sign :-) Keep in mind that neither your intelligence nor your ability to solve math problems are fixed. Both are presumably proportional to how many exercises you solve and how many ‘NEW steps of reasoning’ you understand when reading a textbook or anything. This proportionality actually becomes more apparent in chess, where I find myself making progress if and only if I solve lots of tactics puzzles.

I personally would strongly recommend you to study mathematics, but you should follow the advice in the articles which Prof. Tao offers above. Read all the articles; they are very well written. Ask yourself silly questions, and if you don’t comprehend something fully, ask yourself silly questions until you do.

And also consider the following: Our brain has something called ‘mirror neurons’. They make you feel an emotion if you see that somebody else feels that emotion. That might be one source of that fear. I can not be certain that it is, but it might be.

19 February, 2015 at 3:40 am

Ankit parmari am b.com final year student expecting 55% in the finals. I want to know job opportunities in relavent field after 3 years

2 March, 2015 at 7:41 am

AnonymousDear Professor Tao,

What advise you could give, in general, to a math-related major(e.g. economics, physics) undergrad student who want to pursue math PhD in grad school?

8 March, 2015 at 2:47 pm

calogero galvanohttp://www.siculiana.info/2014/12/sullinternational-mathematical-forum-un.html

10 April, 2015 at 5:41 am

ankita pandeyi read all above ideas bt I’m in psychology student and I’m want to become psychologist .i want to qualify idhas entrance test but doesn’t know that how i do qualify entrance test please help me ,and give me right suggestion

10 April, 2015 at 5:48 am

ankita pandeythere are more opportunities but in psychology field there are no more opportunities

8 May, 2015 at 6:10 am

jolyn angGood advice, shall past this post to my students at H2 math tuition

12 May, 2015 at 7:37 pm

Advice for picking a supervisor | my mathpad - Josh Chen[…] https://terrytao.wordpress.com/career-advice/ […]

22 May, 2015 at 7:52 am

QuoraHow does one become a great mathematician?You cannot ensure that you will become a great mathematician. Hard work is essential, of course, but native ability is also an important factor. And luck plays more of a role than you might think. Some research fields turn out to be more fruitful than…

23 May, 2015 at 12:11 pm

Some advice on Research | Existence[…] Terry Tao: Write down what you have done; work hard […]

27 May, 2015 at 6:26 am

sumeetI have studied applied mathematics in my engineering course of electronics but i would like to further study mathematics what to do?

24 June, 2015 at 10:39 pm

debanjan111I want to know one thing,the complex mathematics will not be intelligible to common people.What is the direct relationships of higher mathematics with the problems of society and technological development.

15 July, 2015 at 3:39 am

SphiweI need help im doing grade 12 and want to do software engineering next year but i got an aps of 28 and a 40% on maths and 52% on physical sciences and i dont know where to apply for my course and wondering that if i decide to go to college will i still be able to get a bursary?im confused

27 July, 2015 at 6:41 am

seemaDear Sir,

I am a masters in biotechnology from karachi,Pakistan.I have done some basic research in human genetics field. I would like to go for PhD but currently not getting a good job in here. Will further study be a good idea in my case.

27 July, 2015 at 6:45 am

seemaResearch oriented fields are competitive and there are less jobs here in Pakistan.

28 July, 2015 at 6:50 pm

bitcointorrentHello Professor Tao,

I like your advice. What I was wondering is do you recommend caffeine abuse for a mathematician? Do you think this is personal preference? Also I was wondering what advice you might have for consistent high-level mental performance. For a little while I could wow my professors, but then i fogged over and became like the other students.

29 July, 2015 at 1:32 pm

Looking for job? | ilovecagayan[…] Read More […]

5 August, 2015 at 10:58 pm

Articles/Links I liked. | mEssy bYtes[…] Career Advice – Terence Tao […]

14 August, 2015 at 10:07 pm

Career advice - THE MATHS PACK[…] dose of common sense, before making any important career decisions. I would in particular recommend discussing such decisions with your advisor if you have one, as he or she will be familiar with your situation and will likely be able to […]

17 August, 2015 at 7:31 am

Chantell Neo KekanaI am currently in grade 11,I school at waterberg high and mathermatics is my favourite subject.My father recently lost his job and he is now struggling to pay for my fees.I wanted to ask if there is a bursary I could apply for,my number is 0733683418.please respond me if there is a way you can help me

21 September, 2015 at 6:44 am

Jean PaulI need advice on the advantages of have a Phd in mathematics

19 October, 2015 at 1:01 am

Il problema della discrepanza: provata una congettura di Erdős? | OggiScienza[…] Sul suo blog Tao ha appena pubblicato “consigli per la carriera” raccomandati agli epsilon e […]

19 October, 2015 at 7:39 am

Jinhui YangHi,Prof Tao,

I learn a lot from the advice.What do you think about the development of pure math in the future and could you give me some advice on learning statistics?

21 November, 2015 at 4:35 am

BernadetteDear Pr. Tao,

I really enjoyed going through different subjects of your blog, more precisely about “career advice” and so one. I am currently doing a Ph.D in number theory…

In fact, I have two questions: what kind of mathematics one can classify to be “recreational mathematics”?

How to gain “self-confidence” when one is doing mathematics(or research in general)?

I think it will be a good thing(if not yet done) if you can add a section on your bloc about those two subjects.

Thanks!

4 December, 2015 at 10:22 am

shah gvery nice advice

24 December, 2015 at 1:02 pm

Review: A PhD Is Not Enough | The Intellectual Journal of Daniel Ang[…] Tao’s career advice, especially the importance of learning and relearning your field. (This is meant for […]

9 January, 2016 at 10:47 am

ashutosh joshisir I m doing my btech from ece (3rd year) currently

my percentage is not so good to be placed directly in campus interview & moreover I have no plans for my future still so plzzzz lead me

22 January, 2016 at 10:04 am

portonA 12 year old boy with 71 average in his 7th grade in Israel wants to become an electronic engineer. I desire to “convert” him into pure mathematics. What’s your advice? He doesn’t live in the same city of Israel as myself. (I am an amateur but serious math researcher.)

13 February, 2016 at 6:14 am

ayush singhHi terry tao sir first of all i want to say that i am your very big fan. i love your potential. i writing this mail to you because i want your guidance. i am a very poor student in mathematics, i try many times to improve it but at the end i loose, give me some method or give me some guideline so that i can improve my mathematics.How can i focus on the maths problems , how to make my mathematical skill better, how to overcome with the hard math problems. Please give me the direction. i am very much impressed by your mathematical skill and determination on solving the problems.I live in a small state in country india were there is not so much resource , guidance and help for improving my maths. i really need somebody who can help me out and give me the direction so that i can improve my mathematics. I really love maths. And i really want to do some great things in mathematics. i am in high school in 12th class.. i realllllllllllllllly nead your help sir.

28 February, 2016 at 9:05 am

Deep Beniwalsir i am a student of science(maths) .I am just passed my 12th class and i wants to know about my best carrier options and also i am from a poor family please help me someone so i can make my future bright and also i am wants to hard work… Please give me some suggestions…!!!

4 March, 2016 at 2:54 am

Sathishkumar JaganathanHi I’ve finished my b.com and i have a experience in procurement field.. further i want to do my higher studies can you please advice me..

3 April, 2016 at 3:14 am

Raj MsOne of my friend is pursuing BA (Bachelor Of Arts). Se want to do MA in English Literature. Is this will B hepl full for her in future to get a Job.

13 April, 2016 at 12:30 pm

esethu thungilizweI want to be a mathematician and I love maths.this year I am doing grade 9.what can do?

18 April, 2016 at 1:07 pm

AnonymousWhat was mathematical rigor in the time when people didn’t have ZFC yet?

25 April, 2016 at 2:41 am

Here’s How to Teach Yourself Physics and Math – The Fifth Column[…] Mathematician Terence Tao, who is also a Fields medalist and a Breakthrough prize winner,gave some beautiful advice on pursuing a career in math here. […]

10 May, 2016 at 12:02 pm

Verity NezkrotnyProfessor Tao,

Your career advice has been invaluable. Thank you for finding the time to share this. In my concern for earning the top grade on exams, I began to entertain the idea of subjugating real understanding to memorization and other such methods that usually earn higher grades on exams. You have talked me into being alright with an A- or B here and there in exchange for feeling good about spending hours getting to the bottom of one quandary that will probably not be on the exam. After all, this is why I want to be a mathematician– true understanding, not grades and scores and notoriety.

I have had an intuition about the role of intuition (ha!) for some time now, and I constantly defend it to my peers and professors in casual conversation. I was also beginning to wonder if my ideas about intuition were not rational since I met so much disagreement– but your article “There’s More to Mathematics than Rigour and Proofs” has not only convinced me I am correct about the role of intuition in mathematics, but further it has given me a structure for understanding the importance of formalism and how it will bolster my intuitive capabilities in the long run! Thanks for being such an inspiration.

27 May, 2016 at 8:22 am

EateshHi I am doing b. Com 2year and, what course after b. Com please advice.

7 June, 2016 at 1:07 am

Links – Notes on Disordered Matter[…] Terence Tao’s Career advice. While focussed on an academic career in mathematics, it is relevant also for natural sciences. […]

15 June, 2016 at 5:07 am

MarkusGreetings from a Swedish student!

Given your experience, professor Tao, what are your thoughts on the forgetting? How have you handled the challenge during your own development and during your time as a teacher?

Background:

Personally, I’m often chocked by how much of what I’ve learned that is lost after I move on to new material. My retrieval ability simply silently slips away — and most others that I’ve asked share the experience, especially when it comes to compact university courses. Thus it comes as no surprise that research on learning singles out dealing with the forgetting curve as a part in becoming a sophisticated learner. On the other hand, repetition is time consuming, and the time is taken away from acquiring new knowledge. As you put it in your post about expository texts, some forgetting is quite okay though. Lost insights can be relearned quickly when needed, and new material often build on the prior learning, cementing the knowledge. Still, given that ones courses or projects often don’t prevent the problem on their own, the effective learner ought to assure that what’s important is keep. Or so I believe at least, which leads to the above question.

Regards Markus.

5 July, 2016 at 10:18 am

solomonso good

20 September, 2016 at 3:49 am

rajesh Kumar nayakI do bsc .in cs by correspondence .and I want to join defense in future .so,that time I got some problem because of distance education in future.

22 October, 2016 at 9:57 am

AnonymousIafter 12 th I did bsc in mbbc for 1 yr in which I passed only in 1 st semester, in 2nd semester there are 3 subject back. then I took 1 yr gap for the preparation of mhcet medical entrance exam. I have not choosed in mbbs and bds courses but still there is one hope that I have been appeared in remaining round. but if I have not been appered then what can I do because there will be no chance for admission in bsc in any college. I don’t know what will I do. I don’t want to waste my year. I m in bigg touble plse guide me. please, please

9 November, 2016 at 3:55 am

Marble IndiaYou have a very inspiring way of exploring and sharing your thoughts. It is very uncommon nowadays, lots of sites and blogs having copy pasted or rewritten info. But here, no doubt, info is original and very well structured. Keep it up.

13 November, 2016 at 5:55 am

Avinashhi sir, am Avinash i live in Bangalore I have studied BBM ( finance ) present am working in housing finance company as a sales officer but my question is that am very much worried that I choosen a right job or not because our job is completely based on real estate . Am having a confusions that should I continue or change the job. Please any one help me out

1 December, 2016 at 1:34 pm

Sanjay jatariaSir/Mam , i was the btech student till June 2016 and i got back in five subject , in which first two backs are breaks my motivation in First semister, and then i got three backs in third semister. Now Sir/Mam my problem is my btech is already been completed and now these back paper are pressuring me very much and i am helpless because my parents force me to go for engineering but my mind was setup for non-techincal degree and now i am heavily pressurised which make me frustrated and i am not able to sleep in night and mostly i always got headache due to which my behaviour for my parents are changing day by day. So please kindly give me a suggestion what to do and how to do. Or i go for non-techinal degree after wasting my time in engineering degree and it is possible to fo so.

10 December, 2016 at 7:09 pm

AkshadaWhat study should I start doing now to meet my career

7 January, 2017 at 5:26 am

KrishI am doing electrical engineering in ug level after completing this i want to do masters in IT Professional in Canada can I change course this way??

7 January, 2017 at 5:28 am

Krish RawalI am doing electrical engineering in ug level in India after completing this i want to do masters in IT Professional in Canada can I change course this way???????

18 January, 2017 at 5:33 am

monajainMath

24 January, 2017 at 10:10 am

Amanuel denderIt is a grate thing to lerarn from others experience so n I’m the one now to join u guys so i hope it’s a grate opportunity for me to share something new …… Keep it up … !

3 February, 2017 at 7:16 pm

Anonymous3x+1 when x=>4,(4,2,1,4),when x=<-2,(-2,-1,-2).

19 February, 2017 at 10:26 pm

Rajani duttaI am an M.sc in mathamatics.My family is very leady.They cannot help me financial in any case.I have to do some financial help for my family now.But i want to stay in educational field.Now,i puzzled with my next decision for this.My father and mother is now very ill,even my only brother is an abnormal baby.so please please help me to take any decision for my career.please give me a suitable idea.

29 March, 2017 at 10:07 pm

Làm sao để tự dạy bản thân môn Toán và Vật lý? – Trang Chang[…] vàng giải toán học Fields và chiến thắng giải Breakthrough đã đưa ra một số lời khuyên hữu ích cho những ai muốn theo đuổi nghề nghiệp liên quan đến toán […]

12 April, 2017 at 9:35 pm

Arnoldo TischnerMy friend and I have been talking about individual blogs and online journalism. She feels that personal feelings and such should not be expressed in such accessible blogs. I have no issues with it. Share your thoughts:. 1. Do you blog or post?. 2. Do you prefer visual expression of thoughts over written communication?.

22 April, 2017 at 4:47 am

Maths studentI have some advice which applies at all ages: Ride your bike!

http://www2.le.ac.uk/offices/estates/environment/travel/bicycle/10%20reasons%20to%20ride%20your%20bike

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3768113/

Once you figured out where to bike, you can do math in your head while cycling.

27 April, 2017 at 5:49 pm

Tere Tao’s career advice – Welcome[…] Career advice […]

7 May, 2017 at 11:56 am

AmitHello, i am first year MCA student i am not interested in coding. And also I have failed in all subjects in first sem what can I do now try solve and continue or quit?

27 May, 2017 at 2:31 am

Aleksandar PavlovićTerence Tao, please send me e books in english and maths and programming which will help me to learn about Artificial Intelligence from the begining. i’m 40 years old now. so we must hurry. i intent to study at uopeople.edu what do you think about it ? Alexander

3 June, 2017 at 9:46 am

Bill Thurston’s “On Proof and Progress” or as I like to think – Why do I, as an individual, matter? | My Neat Blog[…] 3rd Update: I forgot to mention that Terry Tao also writes roughly the same argument here on his blog under career […]

9 June, 2017 at 7:02 am

Long Bien Bridge – What to do( by Xì Trẹt Blogger)[…] hết mọi thứ, là những bài blog đầy sự hiểu biết và cởi mở của giáo sư Terence Tao về việc theo học ngành Toán, là những video gợi trí tò mò, đầy kết nối […]

9 June, 2017 at 9:52 pm

AnkurI am in my 5 semester b.tech, after it , I like to do something in maths , calculus and trigonometric, and algebra are my favourite topics . Plz suggest me something I am an

INDIAN

9 June, 2017 at 10:10 pm

Career advice – 多项式[…] 来源： Career advice […]

12 June, 2017 at 6:12 am

WrongAdviceThree of the most consequential mathematical breakthroughs in the last 20 yeas were produced by people who worked alone in secrecy:

– Andrew Wiles: Fermat’s Last Theorem

– Grigori Perelman: Poincare’s Conjecture

– Yitang Zhang: establishing the existence of infinitely many pairs of prime numbers separated by 70 million or less

Also, while still under scrutiny, Shinichi Mochizuki’s Inter-universal Teichmüller theory increasingly seems to be one of these.

Given these examples, shouldn’t it be clear by now that the best advice anybody interested in working on a very difficult and challenging problem should have is this: “work in secrecy, don’t tell any one about what you are doing and only when you are 300% sure your work is correct, put your work in arxiv.org and let others fight for the credit of understanding your work”.

The evidence seems pretty overwhelming that the advice contained in these pages is about careerism in mathematics, or any other field for that matter, not about producing great results. To put an analogy with the business world, this advice is about how one can climb the corporate ladder, not about how one can become a successful entrepreneur. I am not claiming that the intersection between careerism and being a great entrepreneur is an empty set -there are examples of successful entrepreneurs who started their careers as careerists- but careerism and entrepreneurship seem to be very different beasts.

[The cases of Wiles, Perelman, and Zhang are discussed at https://terrytao.wordpress.com/career-advice/dont-prematurely-obsess-on-a-single-big-problem-or-big-theory/ . In particular, it is instructive to look at the earlier work of these three mathematicians, prior to their most well known breakthroughs, as they all followed the more traditional path of working openly within the mathematical community, while also laying the groundwork for their later work. -T]22 June, 2017 at 5:07 pm

Terence TaoThe cases of Wiles, Perelman, and Zhang are discussed at https://terrytao.wordpress.com/career-advice/dont-prematurely-obsess-on-a-single-big-problem-or-big-theory/ (including the comments). In particular, it is instructive to look not just at the most well known works of these three mathematicians, but also on their earlier works, which follow the more traditional path of working openly within the mathematical community. It is safe to say that the expertise gained by these mathematicians in that earlier work was essential when they then focused their attention on their respective “big problems”.

It’s also a good idea to take survivorship bias into account when trying to extrapolate from only the most successful examples of any given endeavour.

25 June, 2017 at 1:58 pm

WrongAdviceThanks for replying. I get your point but I would like to add a couple of things:

– I read the aforementioned link and it definitely applies to both Andrew Wiles and Grigori Perelman. Both had produced important results prior to going rark to work in their respective problems. However, that is not the case for Yitang Zhang. Zhang didn’t have any meaningful career in mathematics (other than getting a PhD and teaching undergraduate math after having held a series of menial jobs) prior to publishing his result on primes.

– My most important objection though is that mathematics is very different from other scientific endeavors in that all you need to produce good mathematical results is access to the relevant research -which has never been easier thanks to the internet-, a pen and a piece of paper. In terms of resources, it has a relatively low barrier of entry although ironically, in terms of intellectual rigor, it has a pretty high barrier of entry. Given the high stakes and that, as you mention, mathematicians have had their reputations damaged for publishing erroneous results, why would anyone want to work publicly on an important problem? I remember watching NOVA’s documentary “The Proof” on the work of Andrew Wiles and I remember him saying -I am paraphrasing- that the work he did in secret was very fulfilling and enjoyable. No matter how tough things seemed, he enjoyed every minute of it. On the other hand, when he had to work in the public eye for around 1 year fixing his original proof he experienced a lot of pain. Peter Higgs also mentioned that under the current “publish or perish” environment in academia he would probably have not discovered the particle that bears his name and for which he got a Nobel prize. To be clear, I am not saying that publish or perish should be abolished or that a person’s publication record shouldn’t be the main criteria when making hiring and promotion decisions in academia, what I am saying is that given that in academia the “publish or perish” mindset creates a particular environment that is not for everyone, perhaps that environment is not even the optimal when it comes to enabling work like that of Wiles, Perelman or Zhang. Of the three only Wiles had tenure or a tenured like job when they did the work for which they are celebrated. And none of them did said work as part of a traditional “tenure track” process. Further, given mathematics low barrier of entry -in terms of resources- perhaps an alternative path is more conductive for those who love math but who lack the stamina -or simply don’t want- to put up with the rigors of the tenure track process.

21 June, 2017 at 12:10 am

RavishI live in India. It is the most tallented country but here talent is not given importance. The day when Indians will be encouraged. All professor Tao’s will come from India.

24 September, 2017 at 8:46 pm

FirasrafMy first impression on this blog, even I didn’t know who is Terence Tao, I’m still shaping advances on Calculus, cause my primary job as designer prevent me to finish my undergraduate level.

And this blog is the best guidance for me to learn the wholehearted of mathematics. Not only technical or motivations, now my priority moves to the struggling of math. Thanks for your aspirational posts.

8 October, 2017 at 11:22 am

SamehHi Terry! Hope you’re well! I was wondering if you had any thoughts on individuals switching to graduate studies in mathematics after non-math (though still technical) undergraduate degrees. I’m a final year engineering undergraduate in the UK and am hoping to study math in my masters. I realised early on in my first year that my passion was for math, but was unable to switch due to the UK’s somewhat restrictive undergraduate structure. I’ve tried catching up on some foundational topics like real analysis, linear algebra and point-set topology but am worried about the lack of formal study. How do professors feel about graduate applicants who’ve been forced to self study to a large extent? Do you know of people who’ve made the switch?

11 October, 2017 at 1:07 pm

jvannameThe best career advice for a career is that a private sector job is typically better than a public sector job and useful mathematics is better than useless mathematics. After all, it is easy to study large cardinals if one has no practical applications in mind, but it is very hard to find practical applications of large cardinals.

8 November, 2017 at 2:52 am

Trying to be a mathematician | Trying to be a mathematician[…] much gives the exact advice of the previous paragraph. He has a great page of career advice at https://terrytao.wordpress.com/career-advice/, which should be read. All I can offer here is offer my own take on […]

9 November, 2017 at 7:49 pm

MatthewHello Prof. Tao, I had a question for you. I am a first year student in college. I love math very much and wish to learn and pursue it to become a mathematician either in applied or research. I know while I work my way through college I will learn harder mathematics. Is there any steps I can take to learn the advanced mathematics, rather than waiting through years of college? Like things i can do to get more in the math community and learn. I am beginning the basic,linear algebra, matrix theory, analytic geometry and etc.

16 November, 2017 at 8:32 am

IB_Mathematical_Pinion (not pinyin)This seems like a good relevant question: In terms of career advice what has he got to say about versatility of maths degrees and combining them with expertise in another field. What would one do with a maths degree and a music degree combined?

As for the name change,it is true, reading your advice could easily make a person more humble, hard working yet somehow quite popular as well, putting these sorts of qualities that make a good mathematician ‘into a bottle’ and distributing it globally is actually only the history of the internet years old, which is about a fraction of one per cent of the history of mathematics…?????

Here’s hoping to be a positive form of serendipity…

16 November, 2017 at 10:20 am

IB_Mathematical_Pinion (not pinyin)Yep, it’s obviously minion….

Here’s a first class quote by Terry, it’s ace, his blog and the many contributors make lots of ace quotes:

“Actually, one of the best ways to memorise the proof of X is to cover up the proof and try to prove it yourself. Usually, what happens is that you’ll be able to get halfway through the proof but get stuck on a key point. After you get frustrated, this is the time to uncover the proof, at which point you should quickly see the trick or observation that eluded you before, and then the rest of the proof often becomes quite obvious to you. When done this way, the only thing you need to remember to reconstruct the proof is that key insight, which tends to stay in one’s memory precisely because you didn’t have it before.”