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, it will be difficult to put in the sustained amounts of energy required to succeed in the long term. 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.
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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1 July, 2009 at 4:07 pm
nik
Of 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 Tao
Dear 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
nik
Dear 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