*No profit grows where is no pleasure ta’en;*

In brief, sir, study what you most affect.

(William Shakespeare, “The Taming of the Shrew“)

To really get anywhere in mathematics requires hard work. If you don’t enjoy what you are doing, and do not derive satisfaction from your contributions, it will be difficult to put in the sustained amounts of energy required to succeed in the long term.

In general, it is much better to work in an area of mathematics which you enjoy, than one which you are working in simply because it is fashionable. For similar reasons, one should base one’s work satisfaction on realistic achievements, such as advancing the state of knowledge in one’s specialty, improving one’s understanding of a field, or communicating this understanding successfully to others, rather than basing it on exceptionally rare events, such as spectacularly solving a major open problem, or achieving major recognition from one’s peers. (Daydreams of glory may be pleasant to indulge in for a few moments, but they are poor sustenance for the patient, long-term effort required to actually make mathematical progress, and overly unrealistic expectations in this regard can lead to frustration.)

Enthusiasm can be infectious; one reason why you should attend talks and conferences is to find out what other exciting things are happening in your field (or in nearby fields), and to be reminded of the higher goals in your area (or in mathematics in general). A good talk can recharge your own interest in mathematics, and inspire your creativity.

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7 June, 2008 at 10:36 pm

Advice to the Bright and Young « Essays by Danielle Fong[...] Terry Tao also describes ‘one of the hazards’ of mathematics (though this is shared by many fields), focusing prematurely on a single big problem or theory. His advice? Don’t. Try instead to be patient, and flexible. Work hard. And above all, enjoy it. [...]

14 June, 2008 at 11:32 am

这等牛人也在wordpress上写blog！ « Just For Fun[...] still have weaknesses in some aspects of mathematical research. As long as you have education, interest, and a reasonable amount of talent, there will be some part of mathematics where you can make a [...]

1 July, 2009 at 4:07 pm

nikOf course, it’s nice to be able to work on what one is really enjoying… But it’s not so easy if one seriously takes into account the job-market we have. It happens to me the problems I would mostly enjoy to work on are very hard and their study is to far extent speculative (theo-phys) what makes progress in small steps quite difficult. They don’t promise reasonable results in any declared time, however it’s still pure fun to think or work on them. Yet, I decided to shift them to the “hobby” area to be able to work professionally on problems which I don’t enjoy so much but which give me results in finite intervals of time. I don’t feel really happy about it but I am aware that in order to apply for next positions I will have to show results, not only dreams. Concentrating on my “hobby” might be too risky for the continuity of the career. Is there a way out?

1 July, 2009 at 9:40 pm

Terence TaoDear Nik,

Hopefully, you can locate some intersection between the set of mathematical topics you find interesting, and the set of mathematical topics that you can make progress on (though perhaps one may first need to enlarge one or the other of these sets). But if not, then perhaps you may wish to switch into another field (you mentioned theoretical physics, for instance).

See also my articles ‘be flexible’, ‘be patient’, and ‘don’t prematurely obsess on a single “big problem” or “big theory”‘.

2 July, 2009 at 2:07 am

nikDear Terry,

thanks for your reply! I’m slowly getting to the point that I should switch the field. However, I find it psychologically somewhat difficult to leave a field where I feel quite comfortable, have gained knowledge, published my most results and established contacts with people all around a world (you know that most projects one is involved in are open-ended, so there is no natural point to quit). I write this because I suspect many people may have this dilemma…

Best wishes

4 January, 2010 at 12:56 pm

A frustrated math majorI am about to graduate with a math degree from a governmental university in a developing country. I am really frustrated at the low quality education (which is understandable in a third world country) I have been receiving and am considering seriously to change fields after my graduatioin. I really do hate math now and don’t enjoy doing it anymore, and I am really sad about the years I have spent in this country. I am devastated.

What do you think I should do?

4 January, 2010 at 5:57 pm

Pacha NambiPlease don’t hate math just because you had bad teachers. Mathematics is a beautiful subject. Consider switching to applied mathematics where you may be able to make useful contribution. Please don’t love or hate a subject based on grades you received. Grades are just a passing thing and do not reflect the abilities of a person in the long run. My 2cents worth suggestions!.

29 September, 2012 at 5:54 pm

Posts from Terry Tao | 10 years of endeavor[...] http://terrytao.wordpress.com/career-advice/enjoy-your-work/ [...]

9 December, 2012 at 2:25 am

[Skills] Làm việc chăm chỉ – GS Terrence Tao | Nguyen Hoai Tuong[...] làm việc chăm chỉ cần: yêu thích công việc, hướng đến kết quả (nghĩa là làm phải có kết quả cụ thể), luôn nghĩ về [...]

21 May, 2013 at 3:44 am

Bisogna essere un genio per fare matematica? - Maddmaths[…] loro delle debolezze in alcuni aspetti della ricerca matematica. Fino a che riesci ad imparare, hai delle motivazioni, e abbastanza talento, ci saranno sempre alcune parti della matematica in cui potrai dare un solido […]

24 October, 2013 at 9:47 am

Terry Tao: On Hard Work | Fahad's Academy[…] course, to work hard, it really helps if you enjoy your work. It is also important to direct your effort in a fruitful direction rather than a fruitless one; in […]

13 November, 2013 at 1:51 pm

LiamAs a mathematician myself, I could not agree with this more. One word of warning to mathematicians is, speaking from painful and harrowing experience is that overbearing family members and every obnoxious idiot west of the Thames will interfere with this, unwilling to understand that mathematics works differently to other professions and that their self-involved notions of career, whether academic or professional are limited t their own careers.

These days it is tougher and tougher to excel in mathematics and the game is about being good at hard maths – this is where enjoying maths is important

14 November, 2013 at 1:24 pm

LiamSorry, prematurely ended my post. Point I was speaking from personal experience, maths is one of a few subjects where enjoyment is most directly proportional to success. This is whether becoming an industry strength problem solver or researcher. Unfortunately the problem facing mathematicians these days is the unpredictability of research or industries.

There is a perception from outside the math community that you can lug along and take a standardized approach and simply become an actuary if all else fails (sort of an adjunct of the way lawyers or doctors might have a stopgap career) but in today’s results driven environment employers won’t employ mathematicians on that basis and academia isn’t as easy as people think it is as a profession (worse politics than industry in some cases) and as a result nowadays career changes are tough anyway, but for mathematicians they are virtually impossible. What that means is that for mathematicians that do something they don’t like, to sort it out and change career can involve additional masters degrees or PhDs ON TOP of whatever postgraduate degrees they May have already done.