*For related reasons, one should value partial progress on a problem as being a stepping stone to a complete solution (and also as an important way to deepen one’s understanding of the subject). Note: My English is quite poor, you may experience this in the solution.*

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.

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.

For instance, if after failing to solve a problem, you receive the solution and study it carefully, you may discover an insight or problem-solving technique that eluded you before, and will now be able to solve similar problems that were previously out of reach.

## Math Problem Solve

One should also bear in mind that being able to partially solve a problem (e.g.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.The long-term goal is to increase your understanding of a subject.A good rule of thumb is that if you cannot adequately explain the solution of a problem to a classmate, then you haven’t really understood the solution yourself, and you may need to think about the problem more (for instance, by covering up the solution and trying it again).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?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.That’s why I disagree with this post by astronomer Julianne Dalcanton which i found linked from your page where she doesn’t believe most people can reach the level of Feynman-Einstein-Hawking smart. And isn’t part of their fame due to circumstance and perhaps even chance-not their intellectual ability but I mean their status and the fact that their discoveries happened to be earth-shattering or were given more attention by the public at-large beyond the scientific community?Surely some of the scientists working today will make equally groundbreaking or insightful discoveries or develop innovative theories and thus can fairly be labeled “genius” or as having the same level of smarts? I think I have developed a stronger aptitude for language than for math and due to suffering from depression in high school and middle school I didn’t push myself nearly as much as I could and lost much of my motivation.

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