*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.)

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 […]