*行**名失己, 非士也 [One who pursues fame at the risk of losing one’s self, is not a scholar]. *(莊子 [Zhuangzi], “大宗師 [The Grandmaster]”)

Going into a field or department simply because it is glamorous is not a good idea, nor is focusing on the most famous problems (or mathematicians) within a field, solely because they are famous – honestly, there isn’t that much fame or glamour in mathematics overall, and it is not worth chasing these things as your primary goal. Anything glamorous is likely to be highly competitive, and only those with the most solid of backgrounds (in particular, lots of experience with less glamorous aspects of the field) are likely to get anywhere.

A famous unsolved problem is almost never solved *ab nihilo*. One has to first spend much time and effort working on simpler (and much less famous) model problems, acquiring techniques, intuition, partial results, context, and literature, thus enabling fruitful approaches to the problem and ruling out fruitless ones, before having any real chance of solving any really big problem in the area. (Occasionally, one of these problems falls relatively easily, simply because the right group of people with the right set of tools hadn’t had a chance to look at the problem before, but this is usually not the case for the very intensively studied problems – particularly those which already have a substantial body of “no go” theorems and counterexamples which rule out entire strategies of attack.)

For similar reasons, one should never make prizes or recognition a primary reason for pursuing mathematics; it is a better strategy in the long-term to just produce good mathematics and contribute to your field, and the prizes and recognition will take care of themselves (and be well-earned when they eventually do appear).

On the other hand, it can be worth researching *why* a problem or mathematician is famous, or *how* an institution or department earnt its prestige; such specific information can help you decide whether this problem, mathematician, or department would be of interest to you. See also “Which universities should I apply to?“

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25 February, 2008 at 5:44 am

AnonymousDear Dr Tao,

I appreciate very much your advices you post here in your blog.

I apologize in advance for my not-very-good english.

I work as a computer programmer (c.p.), but I like maths a lot.

I would probably leave the c.p field and became a matemathician, if it weren’t for one fact.

As a c.p I have a lot of work in my country, and so to say so it is a well paid profession.

As a matemathician, who will pay me a cent and why? I’ts not my intention to offend nobody but my opinion is this one:

The workers that give more value to humanity are matemathicians, without them today there wouldn’t be any tv, radio, computers, phones, we wouldn’t have gone to the moon, no cars, no trains, in fact no technology would be possible without maths, at last no sophisticated technology.

All the things I mentioned (tv, radio, train, etc, etc) are powerful business now, winning millions of dollars and paying lots of good salaries, but not even 1 cent was given to the matemathician that made it possible.

Why?

Because businessmen are interested in profit made in a lifetime (a short amount of time), as otherwise they wouldnt have a return of their investment before they die. And on the other hand the practical applications of maths offten takes several years/decades/centuries to make some new tech possible.

Thats why businessmen prefer to pay a salary to a “man that put a brick over another in a world where someone invented houses for free” instead of a man that “makes mathematics to make houses possible or even better”.

The closer I can see of making any profit as a matemathician is as a college professor, and it’s salary is not even close to that as a c.p. (as far as I know).

So I’m not sure whether to base my career on what I really like (mathematics) or what really gives me a better economical life (c.p).

Because of course, I can not coun’t on saying, for example, “if I solve one of the millenium problems I get 1m bucks”, because that’s of course to bet my life on something it surely isn’t going to happen.

25 February, 2008 at 10:55 am

Terence TaoDear anonymous,

The patent system, despite its imperfections, does offer a means by which innovators can be compensated for ideas that eventually create enough value to be profitable. (I have my name on one patent myself, with Emmanuel Candes, though so far there has been no commercial interest in it.) Of course, if one works at a research institution (which is presumably providing various types of administrative and logistical support to one’s research), such patents are typically shared with the institution. There are also a few mathematicians who have founded some technology companies based on their research ideas (Akamai is one well-known example).

That said, if one’s primary career objective is to become very wealthy, I would have to say that academic research (mathematical or otherwise) would not exactly be the optimal way to achieve that objective, although an academic job can offer various non-monetary benefits (e.g. tenure, flexible schedules, academic freedom, etc.) which are not always present in more lucrative occupations. As you point out, it is also unrealistic (and more than a little risky) to rely on monetary prizes, rather than salary, as a major source of income (this is true in virtually any profession, actually, with the possible exception of the topmost tier of a sporting profession, of which mathematics is not an example); in most cases, the true value of an award or prize lies in the prestige and recognition it bestows, rather than the direct monetary amount awarded. But there are certainly many well-paying professions which put a premium on mathematical ability, for instance in the finance and IT industries; see the discussion at

https://terrytao.wordpress.com/2007/03/13/article-in-the-new-york-times-and-maths-education/

23 March, 2009 at 7:10 am

Don’t Choose a School Based on Prestige[…] as a person. As Terence Tao, a world-famous mathematician, says “It is common to focus on the general prestige of the institution, but actually it is the specific strengths of an institution which should play a more important […]

5 June, 2009 at 4:53 am

Essential Career Lessons[…] 1. Build solid foundation first Anything glamorous is likely to be highly competitive, and only those with the most solid of backgrounds (in particular, lots of experience with less glamorous aspects of the field) are likely to get anywhere. (source) […]

10 March, 2010 at 8:46 am

AnonymousI would call this very wealthy:

http://ucpay.globl.org/index.php?campus=LOS+ANGELES&name=TAO+_+TERENCE+CHI-SHEN

(Plus retirement.)

18 April, 2015 at 6:25 am

Yu-Chi HuangI think Prof. Tao deserves more to be honest…

The fact is that he earns much less than many professors in medical school.

For example, Prof. Ronald W. Busuttil earns over $2,000,000 a year.

But don’t get me wrong, I don’t mean those professors in medical school are not worth their money, what I mean is that a best of the best scholar like Prof. Tao doesn’t get paid fairly compared to them.

12 March, 2010 at 4:32 am

terrorhow can one chose a career that will benefit him or make him enjoy doing it

16 March, 2010 at 10:18 pm

AnonymousWinning the fields medal is probably one of the hardest ways to make 400k a year. He’s not doing it for the money.

16 March, 2010 at 11:41 pm

DanielDear Professor Tao,

I have a keen interest in graph theory and especially algebraic graph theory. I find it a hard choice. I do not think that I am the best aspiring mathematician around (or in the top quantile) although I do enjoy mathematics a lot.

Some people recently warned me that algebraic graph theory is not a good field to go into… This is the source of my doubt. I do want to find a job after my phd. If this is really an unattractive field (where I am it certainly is not with 2 professors in this field) and I indeed turn out to be below the top, then it might be private sector for me. As I understand it, the private alternative is mainly for those with fields related to statistics, stochastic calculus, numerical mathematics and the like.

Could you shed some light on how you feel about (algebraic) graph theory? And some related fields?

23 March, 2010 at 9:04 am

Which universities should one apply to? by Terence Tao « Press4ward: faith, hope and love[…] is common to focus on the general prestige of the institution, but actually it is the specific strengths of an institution which should play a more important […]

5 June, 2011 at 5:09 am

CorOne who pursues fundings at the risk of losing one’s self, is not a scholar.

5 June, 2011 at 6:21 am

Cor IIThe same philosophy might be applied to Journal selection.

6 June, 2011 at 4:01 am

Cor IIIOne who pursues tenure at the risk of losing one’s self, is not a scholar.

19 May, 2013 at 5:46 pm

AnonymousDear Professor Tao,

Thank you very much for this wonderful article. I had a question regrading the choice of graduate institution. Do you think it is possible to have a successful math research career, if that person has not done his doctoral work in a reputable school ? I’m asking this because all mathematicians I know are actually from reputable schools (say top 50).

4 July, 2013 at 9:17 pm

FanSecond line in the last paragraph, earnt -> earned, or is it Australian variant?

14 September, 2013 at 11:49 am

Jack Zixiao XuDear Terence Tao,

I really appreciate your advices posted on your word press. It makes me feel moved when I learn to understand what a super-great mathematician thinks about.

I am a student in the final year of high school in Ontario, and I read your name seven years ago when I was a little kid in a primary school in Xuzhou, Jiangsu, China. I remembered the first question of a provincial-level Mathematics contest at that time was that who received the Fields medal in 2006, and yes, it was the only question based on “memorizing” not “measuring” or “calculating”.

I developed an interest in Mathematics back to those years; also my Chinese Literature and History were as good as my Mathematics and Science. Time flied, and now I will soon become a high school graduate, and face the question “which program I need to apply for”. One of my ideal options is to study Finance in the University of Waterloo, Ontario, since I think I can handle some challenges both in the society and in the mathematical field, while I am not sure if I should study Finance or pure Mathematics. I am very interested in basic Calculus and Linear Equations courses taught in universities for the 1st and 2nd years, but I feel not sure these are enough. I mean I am afraid I am not solid in the understanding of Mathematics, I know this subject is a tremendous huge pool of information and knowledge.

To me, “set theory” is more fascinating than “stock markets”, because Mathematics seems have immeasurable “power” to create new engines and modify old engines for the progress of human society, it is like a giant magnetic field, and more “applied” fields, such as Accounting, Auditing and Financing seem have limited “power” to benefit us. I do not know whether my analogy is correct: studying Mathematics is like researching a “mine”, while studying business-related fields is like training to be a “mine worker”. In the future I might not work in a pure Mathematics research environment, but work in a field where Mathematics applies in (Finance, Pharmacy, …), but still I consider I should very well polish my theoretical thinking.

In which direction I need to go?

7 July, 2014 at 7:04 pm

$3M Breakthrough Prizes now awarded in mathematics! | Turing Machine[…] only scratching the surface. if there are winners, then there are also losers. speaking of “Tao” & double-edged swords & paradoxes, that reminds me of some “famous” poetry from […]

19 August, 2014 at 9:37 pm

lomojorYou speak Chinese? I’m from Suzhou, China.

6 February, 2015 at 5:26 pm

Career Advice by Prof Terence Tao, Mozart of Mathematics | MScMathematics[…] one should not focus overly much on a specific artificial benchmark, such as obtaining degree X fromprestigious institution Y in only Z years, or on scoring A on test B at age C. In the long term, these feats will not be […]

27 April, 2015 at 8:24 am

Vedanth BhatnagarSir,

To begin with, I regard you as the greatest mathematical genius of this century, and to be honest, I sometimes feel jealous of your being a prodigy in the field. But, on the other hand, it was you who inspired me to get interested in this beautiful field of mathematics.

Many times, I get attracted to maths as it is lucrative, in the sense that we may become famous. But, when I actually start thinking and follow a line of mathematical thought, I don’t feel that way. Sometimes, I also feel that I’m not being honest to myself in having chosen this field as a future career path. But, I really want to go there. I really want to contribute to the field, in my own little way. I want to do something great in this field. I mostly enjoy thinking in Mathematics, for it is intriguing.

In the above article, you have mentioned not to follow a career for fame or glamour. I would like to ask you that if such a feeling keeps arising in one’s self constantly, how does one stop it? How can one motivate one’s self for doing it just for the enjoyment one shall find in it?

To make myself known to you better, I am an INFP personality type. So, mathematics isn’t a ‘natural’ career for us. But, I really want to contribute. How must I do it? Please do advise.

Thanking you,

Yours obediently,

Vedanth.

2 June, 2016 at 9:04 pm

Terrence Tao’s Advice – ashadianand[…] should not focus overly much on a specific artificial benchmark, such as obtaining degree X from prestigious institution Y in only Z years, or on scoring A on test B at age C..Of course, one should still work hard, and […]

19 August, 2017 at 5:10 am

Anonymousi want prof like tao but i have only low quality of iq

19 August, 2017 at 5:12 am

Anonymousone day my curiosity and labuor get me to meet terence tao

19 August, 2017 at 11:29 am

cstheory‘A famous unsolved problem is almost never solved ab nihilo. One has to first spend much time and effort working on simpler (and much less famous) model problems, acquiring techniques, intuition, partial results, context, and literature, thus enabling fruitful approaches to the problem and ruling out fruitless ones, before having any real chance of solving any really big problem in the area. (Occasionally, one of these problems falls relatively easily, simply because the right group of people with the right set of tools hadn’t had a chance to look at the problem before, but this is usually not the case for the very intensively studied problems – particularly those which already have a substantial body of “no go” theorems and counterexamples which rule out entire strategies of attack.)’

Everything you say is true in complexity theory and algorithms except last sentence but there are really not that many ‘no go’ theorems in coming up with known algorithms and these are common knowledge.

Typically this is what I heard. Olympiad preparations take about several 100 hours and they solve a problem in 3 hours and so the time effor ratio is less than 1:100. In outstanding doctorate they prepare for several 1000 hours and come up with a good problem and manage to get the insight (after background, intuition in the preparation period) to solve within a week. Again can we say something similar about solving outstanding problems? Your opinion will mean something since you have made a mark on at least two tough problems – primes in progression and erdos conjecture. But if you can translate it into level of effort what a regular mathematician might need that will be more useful.

10 March, 2019 at 2:22 pm

On Graduate School – MathWorks[…] is common to focus on the general prestige of the institution, but actually it is the specificstrengths of an institution which should play a more important […]

22 May, 2022 at 7:39 am

做數學一定要是天才嗎？ – 嘎嘎酷[…] 當然了， 如果我們不使用「天才」這樣極端的詞彙，我們會發現在很多時候，一些數學家比其他人會反應更快一些，會更有經驗，會更有效率，會更仔細，甚至更有創造性。但是，並不是這些所謂的「最好」的數學家才應該做數學。這其實是一種關於絕對優勢和比較優勢的很普遍的錯誤觀念。有意義的數學科研的領域極其廣大，決不是一些所謂的「最好」的數學家能夠完成的任務，而且有的時候你所擁有的一些的想法和工具會彌補一些優秀的數學家的錯誤，而且這些個優秀的數學家們也會在某些數學研究過程中暴露出弱點。只要你受過教育，擁有熱情，再加上些許才智，一定會有某個數學的方面會等着你做出重要的，奠基性的工作。這些也許不是數學里最光彩照人的地方，但是卻是最健康的部分。往往一些現在看來枯燥無用的領域，在將來會比一些看上去很漂亮的方向更加有意義。而且，應該先在一個領域中做一些不那麼光彩照人的工作，直到有機會和能力之時，再去解決那些重大的難題。看看那些偉大的數學家們早期的論文，你就會明白我的意思了。 […]