- The best teacher is the one who suggests rather than dogmatizes, and inspires his listener with the wish to teach himself. (Edward Bulwer-Lytton)
While you should talk to your advisor, you should not be completely reliant on him or her; after all, you are going to have to do mathematics primarily on your own once you graduate!
If you feel like you want to learn something, do something, or write something, you don’t have to clear it with your advisor – just go ahead and do it (though in some cases other priorities, such as writing your thesis, may be temporarily more important, and you should of course keep your advisor updated as to what you’re doing mathematically).Research your library or the internet, talk with other graduate students or faculty, read papers and books on your own (both in your field and in nearby fields), attend conferences, and so forth. (See also “ask yourself dumb questions”.)
One specific suggestion I have is to subscribe (either by RSS, or by email) to be notified of new papers which appear on the arXiv in the subject areas that you are interested in.
In a somewhat related spirit, while it is certainly acceptable to have mathematical role models, one should not try to mimic them too slavishly; you need to develop your own personal style, exploiting your own strengths and mitigating your own weaknesses, which will not be identical to those of your role models. Ultimately, it is better to follow the mathematics than to follow a mathematician.
6 comments
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4 December, 2008 at 3:11 am
Anonymous
Hi Professor Tao,
Do you think it is good for an undergraduate to write a senior thesis? or are there other things better for an undergraduate to do instead?
Also, do you think a graduate student should try to get into doing some research early? like in the first year in graduate school.
Thanks much,
-student
16 May, 2021 at 5:48 pm
Edward
You should start doing research as early on as possible. Even freshmen year is a good starting point. For the question: “do you think a graduate student should try to get into doing some research early”, chances are you will need some research experience in the first place to convince graduate school admission committees that you are a qualified candidate to be considered.
19 January, 2010 at 6:30 pm
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17 September, 2012 at 4:36 am
Anonymous
Dear Dr.Tao,
I noticed how you have placed emphasis on listening to one’s advisor while maintaining one’s individual style. But how does one go about undergraduate research when one does not have an advisor at all?
(The country I hail from has no tradition of undergraduate research and there are very few avenues for even graduate level research as there is no provision for a formal thesis;instead there are compulsory courses, unlike most universities in the US where one has access to all that I do not have access to)
I request you to comment on how one can carve out a mathematical career with a definite amount of individual effort and initiative.
Your comments are highly valued.Thank you.
6 February, 2015 at 5:26 pm
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