The more problems I do on a specific topic the slower it takes to reach graduate level mathematics. Tao: I hava translated this essay into chinese, I’m sorry I couldn’t translated it well enough, as my ability in english is as poor as mathematics.
On the other hand, if I just do the homework problems I feel I won’t be fast enough for answering questions during exams. Your blog is Gospel to those who are interested in Professional mathematics.
the fact that you graduated high school and university and earned your doctorate so young), I’m wondering if you think you possess something that only a few others have in terms of intellectual ability or not.
I have always believed that if someone applies himself and puts in enough time, effort, concentration, and perseverance they can accomplish whatever they set their mind to.
I also have a post on problem solving strategies in real analysis. Thanks for your advice on Solving mathematical problems. [Corrected, thanks – T.] Dear Professor Tao, here are two articles on the benefits of clever note-taking for math problem solving: PS_R_A_with a strong emphasis on math competitions and Hi dear Professor Tao, I am very interested in elementary geometry and higher dimension Euclidean geometry, could you please upload chapter 4 in your problem book (I see it is about geometry), thank you very much.
I hope you are interested in elementary geometry, too, nice to meet you here! Hi Prof Tao, As an undergraduate student I often face the problem of deciding how many textbooks problems I should do before moving on, for example, Is ten questions per chapter of Rudin’s Principles of Math Analysis adequate?to expand out the definitions, solve some special cases, and isolate key difficulties) is also a very important measure of progress (see this previous post of mine on this topic), as is the practice of constantly asking yourself “dumb” questions in the subject (as discussed in this post).One should also not focus on the most difficult questions, but rather on those just outside your current range.I do have a book on how to solve mathematical problems at this level; in particular, the first chapter discusses general problem-solving strategies.There are of course several other problem-solving books, such as Polya’s classic “How to solve it“, which I myself learnt from while competing at the Mathematics Olympiads.And I don’t think that’s arrogant or unrealistic.I wanted to get your honest opinion. Hey Leif, This book might be useful in pursuing the answer for your question: Disclaimer: I just read the summary and reviews of that book. I’m, at the moment, too busy with studying Maths stuff. Tao, I am a high school student, I loved math got good grades in my middle school years.But I find math hard and i often make many mistakes now.However, I don’t see why it’s not possible for me to develop mathematical abilities as strong as my linguistic abilities or even pursue a career in astronomy (which I love) or physics or even pure mathematics.And I know you say similar things on your career advice blog, and I know it’s important to be realistic and plan for graduate school and beyond I just really don’t like how people put this label of genius or prodigy on certain people to (in my opinion) make them seem able to achieve things that most other people cannot–even the levels of Einstein or Mozart.In fact ,i think i can work out many problems while doing my homework . Dear Professor Tao, I am a fifteen year old student currently in high school. Should I study some analysis or is it group theory that you recommend? Well, after calculus, one usually studies multivariable calculus. While trying to solve problems from my text books (like Stein’s Complex Analysis ), I notice that very often I cannot solve the hardest problems from them.But i am very nervous during my math exams and i almost forget everything i have learnt. I am currently self-studying some non-rigorous calculus. Try to see if you’ve learned everything in regular calculus, and then go onto . Since research is about hard problems, does that mean I don’t have what it takes to be a mathematician?