This site is currently hosting

- updates on my mathematical research;
- expository articles (such as my articles for the Princeton Companion to Mathematics, or for the tricks wiki);
- discussion of open problems;
- talks that I have given or attended (such as the Distinguished Lectures Series at UCLA);
- my advice on mathematical careers and mathematical writing;
- information about my books and applets;
- my lecture notes on ergodic theory, on the Poincaré conjecture, on random matrices, on graduate real analysis (245A, 245B and 245C) and introductory graduate probability (275A), on Hilbert’s fifth problem, on expansion in finite simple groups of Lie type, on higher order Fourier analysis, and on analytic number theory;
- and various other topics, usually related to mathematics.

While most of the posts are aimed at those with a graduate maths background, I will also occasionally have a number of non-technical posts aimed at a lay mathematical audience. My selection of topics is guided by my own personal taste; I do not take requests for specific topics to post about on this blog.

I welcome comments from people with all kinds of mathematical backgrounds and levels of expertise; my only requests are that the discussions are kept constructive, polite, and at least tangentially relevant to the topic at hand. Comments which are spam, self-promoting, off-topic, or otherwise not fulfilling the above requests will be summarily deleted; repeated offenders in this regard may be subject to blocking. In particular, comments devoted primarily to promoting one’s own research are subject to deletion. Also, comments which essentially duplicate previous comments may also be deleted, or used to replace the previous comment, as appropriate. Finally, comments whose sole purpose is to solicit an answer to a homework problem are discouraged, and will be deleted if they are unlikely to lead to any discussion of wider interest. (However, questions *inspired* by a homework problem, for instance inquiring as to further connections between two mathematical topics connected by such a problem, or questions centred on a very specific technical point in the solution of that problem, are welcome.) Of course, I will not be able to personally respond to all the comments made on this blog.

I have enabled the ability to rate comments on this blog. However, this rating system is unregulated and should not be taken as any sort of official evaluation of one’s comments. In the interest of constructive criticism, negative ratings should be used sparingly. To discuss the ratings system, please visit this thread.

Any discussion, feedback, questions or suggestions not related to one of these topics can be placed as a comment to this “About” page, or at my open thread. Comments about formatting and presentation can be made at this page.

See also the Google+/Google Buzz feed that complements this blog; details of this feed are available here.

Terence Tao

[*Update*, Mar 31 2007: Opened this page to comments.]

— Some technical remarks —

WordPress has the ability to insert LaTeX math code (e.g. ) into both posts and comments. The format for this is “$`latex `*[Your LaTeX code]*$” (without typing the square brackets). See this announcement for details. Note that LaTeX macros and environments are *not* supported, similarly, double dollar signs $$ do *not* create LaTeX displays (one can use \displaystyle to get an approximation of these displays, though.) Also, line breaks are not allowed within a LaTeX code.

There used to be a number of quirks with the WordPress LaTeX plugin, but they have now largely been fixed. If you find any problems, please report them at this page.

WordPress also supports a certain amount of HTML. As a consequence, be careful with using the < and > signs in a comment, they may be misinterpreted as HTML tags! You can use < and > instead. (Inside of a LaTeX environment, you can use \lt and \gt.)

In case a comment really gets mangled up by formatting errors, you can contact me and I can try to manually correct it.

I have heard that it is possible to configure wordpress so that comments can be previewed; if anyone has any specific knowledge on how to implement that feature, I would appreciate knowing about it. [*Removed*, Apr 8 2007, in response to comments.]

If a comment does not immediately appear after you submit it, it may have been accidentally flagged as spam (this in particular can happen for a post with an excessive number of links). In that case, please contact me and I will de-flag it.

I do not have PDF copies of my posts. However, the “print preview” feature in your browser should convert the post to a format which is suitable for conversion to PDF, with the sidebar and header removed. Also, at the end of every year, I convert many of my blog posts into a book format; see this page.

I have occasionally been asked for the formatting I use for my own posts. I use the Tarski theme with a modified CSS, in order to do things such as boxed theorems. (To use the CSS, one needs to purchase a CSS upgrade.) I also use Luca Trevisan’s LaTeX to WordPress converter to write the more mathematically intensive posts.

— Copyright etc. —

Readers are welcome to copy, link to, quote from, or translate reasonable portions of the content of this blog (e.g. a single article) into other media, though for items longer than one or two paragraphs, I would appreciate it if a reference or citation to the URL that the content originates from is provided. If you wish to copy a significantly larger fraction of the content (e.g. an entire series of articles), please contact me about it first.

## 165 comments

Comments feed for this article

19 July, 2013 at 12:15 pm

AnonymousIs there a way to add a “more…” link to additional recent comments?

19 August, 2013 at 7:19 pm

Mohammed AhmedMr Tao? I have a question.

You are one of the smartest people in the world. So why don’t you get involved in the Mathematics that is involved in Physics? The subject needs another Einstein, there are so many things that we do not know about the Universe, and as a Mathematician I am sure that you could go a long way toward solving such problems.

12 October, 2013 at 1:35 pm

AnonymousHi Prof. Tao,

I have a question: Assume that we have a box with n red and m blue balls, but we do not know the numbers n ,m . You can draw balls with replacement from the box as many time as you can. And you are only allowed to do so. The question is that can you determine exactly the numbers n,m? if you need to put the extra conditions on n,m to solve the problem, what would be the minimum condition?

Thanks

16 October, 2013 at 12:35 pm

5 Things Everyone Should Know About Copyright and Open Access - TECHStyle[…] that a number of Fields Medalists already maintain high-profile blogs (A quick search found What’s New, maintained by 2006 Fields Medalist and UCLA mathematician, Terence Tao), and the panelists seemed […]

8 November, 2013 at 9:04 am

Patrick PoirierHello Prof. Tao,

I am currently running a crowd funding campaign for my upcoming educational game Sweet Math. I was wondering what is the process to get a story out on your blog.

Here’s more information about the game itself: http://www.kickstarter.com/projects/89952638/sweet-math

—

For those of you who think education is a key to make the world a better place check out our educational game Sweet Math. We are currently at 69% of our funding goal and the campaign will end on November 14th. We accept donation for as low as $1. http://www.kickstarter.com/projects/89952638/sweet-math

The game let player practice arithmetics with their entire family.

18 November, 2013 at 6:04 pm

Math Blog Snippet | the Cyclic Grizzly[…] theme with a modified CSS (to do things such as boxed theorems). As stated on his About page, he uses Luca Trevisan’s LaTeX to WordPress converter to write his more mathematically […]

28 November, 2013 at 7:40 pm

ShangDear Professor Tao,

I’m a college freshman from China. I’m interested in math, but I’m never good at math, math is really hard for me. Do you think it requires talent to learn math well? because I see some people do math really good without working hard to learn it. I think I don’t have much talent, but do you recommend any method to study math, or any book? (I read your math book about how to solve math problem and it is still hard for me). I really like math and I want to learn it well.

Thank you!

27 December, 2013 at 10:42 am

SanaDear Tao,

Thank you for creating such a wonderful website. I have just come across this site, and I want to take this time out to appreciate your efforts and share my own with you..

I have created a Mathematics website that is aimed to help kids from grade 1 to grade 12 practice and learn Mathematics. It is called http://www.ipracticemath.com .. This website maintains a progress report for each and every kid who registers themselves on the website. Both kids and their parents can see this progress report whenever they want.

I would like you to view my website and provide me with your worthy feedback and suggestions, thank you.

Best,

Tayyab

14 January, 2014 at 4:53 am

About | Statistics Hacks[…] remarks are borrowed from Terence Tao’s blog) WordPress users can insert LaTeX math code (e.g. ) into both posts and comments. The format for […]

26 January, 2014 at 6:14 am

HindHello Prof Tao,

I’m an undergraduate physics student, and I’ve recently gotten interested in random matrix theory, but haven’t had much hope in learning the actual mathematics of it as the books I tried reading (including yours) seemed inaccessible to all but graduate level math students. I was wondering if you knew of any resources I might benefit from?

Thanks

29 January, 2014 at 6:29 am

preethi shreeyaHello Professor,

I have been working on a project relating to compressed sensing. My Guide and I have a few doubts that needs to be addressed to. It will be really helpful for me if you can give me an idea about how to proceed with the problem statement.

Given: I have a beam fixed at one end and lose at the other. It obviously results in vibrations due to the disturbances in the environment or when induced.And this system can be represented using a differential equation. The vibrations are sensed using sensors, analysed and reduced. Now, the sensing is done through compressed sensing technique.

My question is how is it possible to find the optimal sensor placement (minimal number of sensors along with the details of it’s spatial position) just with the help of the Measurement matrix (that we design in compressed sensing for reconstruction purpose)?

5 February, 2014 at 5:37 pm

Anonymoushello mr. Tao,

I am in 10th grade and am currectly working on a project about your for my functions, stats, and trig class. you seem like a very amazing and cool person. i was wondering if you had any hobbies?

5 February, 2014 at 5:42 pm

AnonymousHello Professor Tao,

I am in 10th grade. my partner and I are currently working on a project about your for our functions, stats, and trig class. you seem like a very amazing and intelligent person. The project requires us to teach about your personal life as well as your academic contributions.Your academic contributions are easy to research, but not so much your other interests. so I was wondering if you had any hobbies currently? Also, what did you like to do for fun as a kid?

Thanks for any help,

Zachary Mahalak and Cooper Homic

9 February, 2014 at 6:52 am

largeurhi Tao ,

I like this blog . we know , you’re the best mathematician n the wrld . wht do u think about beal cnjecture ?

9 February, 2014 at 11:47 am

SimaDear Terrance,

I wonder if you ever think about other problems in the world. The problem of people who can not get along with each other over their difference in opinion. I also wonder if there are mathematical solutions to our political/social/economical problems and if there are such solutions whether or not you communicate them with the leaders of the world?

I know it takes long but currently, those who advise our leaders have not been very effective in ridding the world of many harmful human behaviors so far. for example, Islam and its radical anti-human ideology which I believe is going to destroy humanity and all it’s achievements if not stopped.

If I had a son as genius as you, I would encourage him to spend some of his time on these issues because I, know that there IS a solution and some smart person just needs care enough to take the time and find it.

I am not a very smart person but I am tired of seeing the people of this world suffering over our ignorance. I wish to see the world in harmony and peace in my life time.

Love,

Sima

10 February, 2014 at 5:06 pm

MagnusOther mathematicians have worked at a solution to the Middle East conflict, see:

http://www.ams.org/journals/notices/201310/fea-saaty-with-link.pdf

However, political decision makers may not always follow logical solutions. Other factors may dominate their decisions. These other factors are the main issues, which no mathematician can help with.

10 February, 2014 at 8:17 pm

SimaDear Magnum,

Thanks for sending your reply and the article. It is a fascinating proposal. Not that I understand any of those formulas. :)

It must be extremely frustrating for the two professors to see that their mathematically perfect solution to the middle east problem is not being implemented due to human arrogance and ignorance.

However, since Terrance Tao has a unique gift of seeing things much more clearer and has the ability to find solutions to much more complected equations with infinite unknown elements and factors then perhaps, he is the only one that can solve this conflict. (With the cooperation of the political decision makers of the world, of course.)

I truly believe that he can use his genius to bring peace to the world.

Sincerely,

Sima

25 June, 2014 at 11:03 am

Petar MaymounkovMath is a system of knowledge that is unambiguously stored within an

“accounting” grammar, underlying all ever written on the subject that is held

in common agreement.

That language is—by choice of taste and agreement—acyclic: It begins with

axioms (of Set Theory) and grows with operations of logic.

Acyclic graphs are not the only one we know. Systems of truth can be

circular—as if suspended in air without axioms— and their sophistication can

be accomplished by refinement as opposed to growth.

That very argument would seem to give hope in resolving two painful paradoxes

in math: the correlation-cause-effect confusion and the question of existence

of one-way functions. And the resolution would simply be to rethink the

language of mathematical expression so that those two characters are one and

the same, thereby going from two conundrums to none.

I find it odd that experimental sciences (when they are correct) report: “The observations

report a correlation of … and we are going to use some side theory to disambiguate

between cause-and-effect.” What side theory?

The very side theory they are appealing to is Math and Math resolves their

meaningless and inane (due to cognitive bias and short historic memory)

question (of “Is correlation cause or effect?”) into another

meaningless one, which is the collection of paradoxes intrinsic in Math—the

provider of the answer.

But if Math wasn’t serving to the asking experimentalist and rather aiming

to build a lanuage that explains everything as seen and observed and testified to

by its users (people), in a consistent and non-arguable manner, it would have

to offer a new tool to record and reason about correlation without breaking it

into cause and effect. No?

Thank you

Petar

28 June, 2014 at 3:55 pm

KHOA TRANDear Prof. Tao,

Would it be a good idea to record your university lectures in Youtube so your talks can spread wider?

Best regards!

Khoa

26 July, 2014 at 3:08 pm

Test post |[…] with a discussion of peculiar issues. Some other also interesting remarks can be found in the About page of Terence Tao’s blog What’s […]

29 August, 2014 at 4:54 am

arconjelloHello. I’m a middle school student in Republic of Korea. I love Number Theory very much, and I love to do research in Number Theory. I written a (small) article in Number Theory, and I was going to upload this article, But I must get an endorsement from another user to submit an article to category math.NT. But I’m not university student, graduate student, professor. Can U give an endorsement to me? I’m sorry to that write this comment in Ur blog. My e-mail address is pr_116@naver, and My usernames arcon. My real name is Hyeongjin Bae.

1 October, 2014 at 7:57 am

Share information: Luca Trevisan’s LaTeX to WordPress converter | Statistics Hacks[…] as Terence Tao’s blog remarks, WordPress users can insert LaTeX math code (e.g. ) into both posts and comments, […]

10 November, 2014 at 10:40 pm

Anonymoushi Dr. Terence !

i admire your exposition and your prodigy. I would like to have your suggestion about my present research on number theory specifically about prime numbers. i revisited Wilson’s theorem and generalized it. Among the results that I deduced is the fact that every prime numbers of the form 2n+1 where n is even is a divisor of some number x^2-1. Further proved that x=n! mod 2n+1. What do you think of the result?? thanks

13 November, 2014 at 2:25 am

uldissprogisDear Tao, you are a talented busy man but in your free time consider going to uldissprogis.com to expand your analytical powers to other areas of life. SCIENTIFIC THESAURUS is my book which I recommend for you because it has the logical definition of about 7000 words with subsets, frequency, probability and other mathematical and scientific concepts included to make them logical definitions. Someone with your youth and genius may be able to benefit by my lifelong efforts. Best wishes. Uldis

P.S. If you email me at uldissprogis@gmail.com I can send you a copy of SCIENTIFIC THESAURUS for free. It is my attempt at trying to make language more logical and therefore smarter and less emotionally biased as is the case today with all languages.

19 December, 2014 at 10:05 pm

bobsdfaHi Terence, I believe the reason you are intelligent is because you have a large brain. People with large brains tend to have higher IQs, etc and have better working memory and more processing power.

From visual inspection of your head size and unique shape it is clear you have a huge cranial capacity. You mostly likely wear an extremely large helmet size.

If you would take a head MRI brain scan you will see that your brain has huge volume i.e massive cranial capacity. Just something you should know one day before you pass away.

21 December, 2014 at 11:23 pm

H. SchoenichOn the Twin Prime Conjecture.Prof. Tao and this participating in the polymath project:

Please permit me to make a few conjectures related to this conjecture, which is the holy grail of the bounded prime polymath project.

After recent work, it is my view that a group of the polymath project should be able to solve the Twin Prime Conjecture within a year if properly organized. The problem is not that difficult, despite the lore. (More on that to come.)

1. Prof. Tao has provided one important element for the polymath project to succeed. That is, a forum for the collection and ready dissemination of information and ideas.

2. The success of the project on bounded gaps depends, as with all polymath projects, on the correct incentive structure. While Prof. Tao has taken the first step, there is no general structure of incentives — simple good will — to give individual contributors with very good ideas an incentive to share them rather than to make them their own. (I will add more about this in a subsequent post if Prof. Tao reposts my post as a main entry for the day, say, tomorrow, December 22.)

3. The best incentive structure for organizing group activity involve incentives where the group and the individual can benefit at the same time. In economics, these result in what are known as Pareto optimal exchanges. That is lacking in the polymath project — it is like saying, “go forth and do good.” It is a nice idea but all kinds of conflicting incentives undermine the collective goal.

4. It is my view, given what I know about the Twin Prime Conjecture, that the collected group of participants in the polymath project on bounded prime gaps could solve the problem within a year.

5. Hint: Bombieri-Vinogradov and Zhang approach are unlikely to yield a solution, if they yield approximations for relatively large bounded gap. That is bounds much greater than 2, 4, or 2^n, for n < 6.

6. If the project does not organize itself with better incentives, I am willing to help. The most powerful incentives are going to encourage (a) monetary self-interest, and (b) sharing of ideas amongst the group — seemingly conflicting goals, but there are well-known ways for creating such incentives in market arenas.

7. I believe I can likely solve the Twin Prime Conjecture within six months but it will require me to put aside other work, and health permitting. I will not provide a better hint than the one in item 5. I am at a stage in life, of an age, and with sufficient professional accomplishments, that my main interest is in seeing the problem resolved. I also have the personal incentive that I would like to see others solve it, and I am quite happy to see others obtain the credit. I would strongly prefer that a polymath group solve it (think Manhattan project — though there the government organized and basically sequestered the group — so they couldn't freelance or avoid sharing insights).

8. If the group of polymath mathematicians forms itself, but does not solve the problem within a year, I am willing to then step in and attempt to solve it. I will not share credit, because it will involve too much personal sacrifice, even if my healthy holds out. I believe I can solve it in six months but certainly no more, at this point, than two years of diligent work — modulo the time needed to convey the ideas in LaTeX format, which always considerably slows down my output. As Montgomery says, "I believe LaTeX is a conspiracy to reduce my productivity." He is definitely correct.

(cont'd)

21 December, 2014 at 11:23 pm

H. SchoenichThere is the challenge. The gauntlet thrown down. Not to be embarrassed, as a group, by a single mathematician, who in fact cares not a wit if he gets credit.

You say you want more than a hint, you want a full path laid out? Well, that is like a child asking for you to do his homework when you are the parent.

I will, however, try to help with the incentive structure if a specific, credible request is made by a group (of some defined nature, but not a group closed to new admitted). Some form of joint prize is likely to be necessary; how to ensure that the prize cannot be appropriate by a few is the trick.

As background motivational material, I do not want to see this happen, as recited by Prof. Godfeld at some length — and about which I have seen numerous similar, frankly silly, childish and egotistical attempts to gain individual credit for a process that yields results over time:

http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

That two of the finest mathematicians between 1940 and 1980 should have had such a dispute is evidence of the extreme power of individual incentives, against the collective, unless a structure is put in place to harness those incentives.

One year; I conjecture I can do it in two if folk don’t start posting ideas to form a collective effort to do so, without free-rider incentives, and incentives for people to “cherry-pick” for self-aggrandizement, in blunt terms.

If the challenge is not accepted, I will, reluctantly given my other time commitments, step in and attempt to solve the Twin Prime Conjecture, which, without hints to you, I believe I can do given what I now know within no more than two years.

I look forward to notification that Prof Tao takes this seriously enough to post it as other than a mere comment.

H. Schoenich.

December 22, 2014

25 December, 2014 at 5:46 pm

H. SchoenichHow does one attach a Latex document?

I think the moderator should be able to review and cut and paste as much into a post as he/she likes. I have a hint for others, on a problem, but I don’t want to include the entirety of my hint, without a moderator making their own judgment — knowing of course that I have taken the time to write up the hint, in weighing how much of it will be passed along.

26 December, 2014 at 6:34 am

Bullsh!t WikiDear professor Tao

I just wanted to say that this is an awesome blog about math. Learned a lot through it. Thank you.

I also wanted to ask you if you could add a link to my website on your link list. It is a free wiki about mathematical proof: http://proofs.wiki/.

Best regards, Brunner Nathan

27 December, 2014 at 8:14 am

brianphilpOn twin primes: Many years ago, looking for heuristic evidence that there were infinitely many twin primes, I noticed that around 1 million there were 5 twin pairs with no primes in between. This surprised me as Sierpinski believed that anything that happened, happened early on in the natural numbers. A while ago I continued the search and come across an interval with 8 twin primes with no primes in between. The endpoints are: 1107819733063 to 1107819732823. Gaps with 5, 6 occur many times while 7 is rarer. I wonder if there are arbitrarily large such gaps.

30 December, 2014 at 5:20 am

Samuel ChuDear Prof Tao,

I observed one interesting prime factorization of the three consecutive numbers 2013, 2014 and 2015, 2013=3x11x61, 2014=2x19x53 and 2015=5x13x31, they are all factorized into three distinct primes. I guess there should be no other three consecutive numbers with this property but I can’t find a proof. What do you think?

5 January, 2015 at 7:46 pm

CapablancaDear Prof. Tao

I’ve read that professor Durán (a mathematician from Venezuela) claims to have the proof of the following conjectures; “There is an infinite number of Mersenne primes” and “there is an infinite number of Fermat primes”, this is the link that i found: http://www.el-nacional.com/sociedad/Venezolano-demostro-teorema-planteado-anos_0_550145051.html, and, As a consequence of it he said that is completly proved the infinity of perfect numbers, these are the papers:

1. Mersenne Primes Cardinality (2013): http://www.open-science-repository.com/mathematics-70081967.html

2. Fermat Primes Cardinality (2014); http://www.open-science-repository.com/mathematics-45011817.html.

I hope you can read this comment and take this seriously enough to post about it.

Capablanca. H

9 March, 2015 at 11:56 am

Robert ClarkHello. Professor Tao. I am very impressed about your ability to make important contributions to very different fields of mathematics.

A question I’m interested in is the validity of climate models that show a large human contribution to global warming. These global climate models are quite complex mathematically. Perhaps you could offer some new insight into the validity of such models.

Bob Clark

23 March, 2015 at 3:39 am

LukeHi Professor Tao.

I am a high school mathematics teacher in Australia, but have been recently working with an 8 year-old boy who is having mathematical discussions with me that go well beyond the Australian National Senior Curriculum.

I am in the process of trying to provide him with opportunities to be challenged in his mathematics (Senior Level) while still provide social and emotional connection with his peers. Do you have any advice or programs or resources that would be useful in ascertaining what the capabilities of this young boy are? His interests are so far beyond his age that I am sure there gaps in his understanding of mathematics if it were to be taught in a linear, scaffolded manner. I want to provide a focus and purpose to his mathematical studies, including filling in the gaps, without tempering his natural curiosity and interest to push the boundaries of what he is capable of understanding.

Any advice would be much appreciated.

Regards, Luke

23 March, 2015 at 2:17 pm

Ronnie BrownThe book “Men of Mathematics” by Bell records that the parents of the young Cauchy took advice on what mathematics he should be taught. That advice was that there was lots of time for maths, but he should be taught to write his own language! Look this up to see if I have got it right, and to what extent you agree!

You can also look at articles on popularisation on my web site. At Bangor we have run Masterclasses for selected 13 year olds and covered a variety of topics: spherical geometry, higher dimensions, knots. See also my presentation “Out of Line”.

Hope that helps.

23 March, 2015 at 6:16 pm

Terence TaoThe Australian Mathematics Trust http://www.amt.edu.au/ may have some suitable programs or suggestions for this.

2 April, 2015 at 6:17 pm

Ashley C. FernandesDear Prof. Tao,

I have written a book on problem solving using puzzles and games. Would you know or recommend anyone to proof the book?

Someone with basic math skills and an eye for detail would be desirable.

Please view the samples, and you are welcome to comment of forward the link.

http://ashley.mypressonline.com/puzzles-games.html

Have a nice day.

25 May, 2015 at 12:26 am

Category Theory Anyone? | Category Theory[…] he doesn’t offer any classes in the Spring or Summer and we haven’t managed to talk Terence Tao into offering something interesting à la Leonard Susskind, we’re all at a loss for what to […]

28 May, 2015 at 4:11 pm

AnonymousDo you have any thoughts on the Erdős–Straus conjecture?

12 December, 2015 at 10:52 pm

BillIt’s been solved. Just type William Bouris into YouTube, and you’ll find it among the list of my videos. Thanks! Bill

26 July, 2015 at 9:03 am

Ed Gerck, Ph.D.Dear Prof. Tao,

Mathematics education in US middle and high-school, albeit generally acceptable, is literally in the 1900’s level in several key areas (even for AP courses). For example, Gibbs vector analysis (not even useful for Physics in three-dimensions), complex numbers, and linear algebra.

I wonder what your thoughts or plans might be on this topic. I can volunteer to help, and would love to also have your participation in some of our “experiments” in La Jolla / San Diego.

As a physicist, I see that not only the exponential increase in scientific knowledge but also the increasing jargon (err, language specialization) in physics and mathematics has driven this situation — i.e, keeping modern knowledge insulated — to an extreme lag of more than two centuries. Only the humanities might be further behind in US middle and high-schools (e.g., look at the essay level we see there).

Thank you for your blog and space for mathematical science as well as gifted-child education.

16 September, 2015 at 5:53 am

Bill TaoDear professional Tao

I’m a Chinese sophister majoring in finance.There being extensive applications of analysis in equlibrium theory and others, I started to learn it and choose the translation of your masterpiece. But there exists an problem:Lack of correspondent answers,I’m not sure whether my proof was acceptable or not after I finished some of the exercises in the book.So would you please tell me how to get complete answers of this book?Thanks a lot for your help.

Bill

2 October, 2015 at 10:38 am

Right To Learn, Part 2 | Minds on Fire[…] development across domains. They are out-of-sync not just with their peers but within themselves. Terry Tao, currently one of the world’s leading mathematicians, scored a 760 (out of 800) on the math […]

2 November, 2015 at 6:41 pm

Andrew PalfreymanDear Professor Tao –

I’ve run across what seems like a peculiar property of a particular subset of primes; namely, those generated by Euler’s polynomial n^2 – n + 41. For each 41-cycle (barring the 1st which is 100% primes), a simple quadratic sieve identifies all composite numbers with 100% accuracy, thereby leaving only primes. Sieve quadratics in adjacent 41-cycles are related by expressions which are easily derived. I am surprised that it only takes a set of simple quadratics to produce a perfect prime number generator which works forever. Do you have any insight here? Should I publish?

12 December, 2015 at 10:49 pm

BillDo you realize that NO ONE should be coming to you for advice, and that YOU should not be giving any of it? LOL

22 January, 2016 at 12:03 am

Lost_In_SpaceThis page tells me nothing “About” Terrence Tao, and is so overloaded with comments that it takes forever to load, thus amounting to its own Denial Of Service attack. I think I’ll join a Christian monastery. Waiting for the second coming is certainly a much more appealing thought than queuing behind the plethora of worshippers here just to find out “About” Terry.

29 January, 2016 at 1:45 pm

AnonymousThis page is about “Tao’s blog”, not about Tao himself.