1 There’s more to mathematics than grades and exams and methods. As an undergraduate, there is a heavy emphasis on grade averages, and on exams which often emphasize memorisation of techniques and theory than on actual conceptual understanding, or on either intellectual or intuitive thought. However, as you transition to graduate school you will see that there is a higher level of learning (and more importantly, doing) mathematics, which requires more of your intellectual faculties than merely the ability to memorise and study, or to copy an existing argument or worked example. This often necessitates that one discards (or at least revises) many undergraduate study habits; there is a much greater need for self-motivated study and experimentation to advance your own understanding, than to simply focus on artificial benchmarks such as examinations. Also, whereas at the undergraduate level and below one is mostly taught highly developed and polished theories of mathematics, which were mostly worked out decades or even centuries ago, at the graduate level you will begin to see the cutting-edge, "live" stuff - and it may be significantly different (and more fun) to what you are used to as an undergraduate!
[Plenty more on the original article. -Ed.]
Original Article: Terence Tao: Career Advice 1 (ZT)_闻笛赋_新浪博客
