*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.*

As you are still several years away from having to attack research-level mathematics problems, your current skill in solving such problems is not particularly relevant (much as the calculus-solving skill of, say, a seventh-grader, has much bearing on how good that seventh-grader will be at calculus when he or she encounters it at the college level).

The more important consideration is the extent to which your problem-solving skills are improving over time.

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.

Solving homework problems is an essential component of learning a mathematical subject – it shows that you can “walk the walk” and not just “talk the talk”, and in particular identifies any specific weaknesses you have with the material.

It’s worth persisting in trying to understand how to do these problems, and not just for the immediate goal of getting a good grade; if you have a difficulty with the homework which is not resolved, it is likely to cause you further difficulties later in the course, or in subsequent courses.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.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?If you want to be a millionaire, there are easy ways and there are hard ways to achieve your goal.Solving any one of the Millenium Problems is a guaranteed way to earn

It’s worth persisting in trying to understand how to do these problems, and not just for the immediate goal of getting a good grade; if you have a difficulty with the homework which is not resolved, it is likely to cause you further difficulties later in the course, or in subsequent courses.

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.

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?

||It’s worth persisting in trying to understand how to do these problems, and not just for the immediate goal of getting a good grade; if you have a difficulty with the homework which is not resolved, it is likely to cause you further difficulties later in the course, or in subsequent courses.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.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?If you want to be a millionaire, there are easy ways and there are hard ways to achieve your goal.Solving any one of the Millenium Problems is a guaranteed way to earn $1 million, but it's also probably the hardest possible option for earning the money.I am not saying I don’t believe some people are naturally more gifted at certain things or develop stronger skills or have stronger talents than others.I just think it’s possible to achieve levels of excellence and brilliance even in your weak areas through consistent practice. After all, they made their share of mistakes and setbacks but did not give up and they were not superhuman or genetically enhanced as far as I know..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.

million, but it's also probably the hardest possible option for earning the money.I am not saying I don’t believe some people are naturally more gifted at certain things or develop stronger skills or have stronger talents than others.I just think it’s possible to achieve levels of excellence and brilliance even in your weak areas through consistent practice. After all, they made their share of mistakes and setbacks but did not give up and they were not superhuman or genetically enhanced as far as I know..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.

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