My goal is to become a mathematician. I am just starting to learn math on khan academy. I solve the problems but I do not understand how or why what I am doing works and I have a lot of questions. The answers seem to come to me intuitively. If I take time to think about it and search the answers to my questions I can understand things better but it's slower and I use up all my hours in the day. Should I take time to google a lot of questions learn proofs,history and philosophy of math or will I learn these things in school later on? How do I balance time spent understanding vs learning new things?


closed as off-topic by John B, Gibbs, Namaste, Paul Frost, ArsenBerk Nov 16 '18 at 0:04

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    $\begingroup$ I think you should try to understand deeply -- in particular, try to understand how to derive the formulas that you use rather than memorizing them. A good example is the quadratic formula: instead of just memorizing the formula, it's good to know how to derive it by completing the square. Another example is the Pythagorean theorem. Don't just memorize it, learn how to prove it. Time spent grokking fundamental math won't be wasted. $\endgroup$ – littleO Nov 15 '18 at 21:33
  • $\begingroup$ I think you should attempt to understand everything as you go along as much as possible. Although there are some exceptions to this. I also recommend reading books more than online videos and sources (but my recommendation might be wrong for you, I'm not sure). It's hard to give you specific advice without knowing more about what subjects you are learning and how deeply you are learning them. $\endgroup$ – Leonard Blackburn Nov 15 '18 at 21:43
  • $\begingroup$ Read the questions on MSE, try to work and help on the questions you understand, when you don't try to find what it means, and the perfect balance between practice and theory will show up naturally. $\endgroup$ – reuns Nov 15 '18 at 21:46
  • $\begingroup$ How old are you? What grade are you in, or what level are you studying at? This context matters with respect to how to answer your question. Understand as much as you can, but understanding deeply will only come much later when you have already developed the tools necessary to delve deeper. It's hard to answer this question because I would give different answers depending on level of mathematics one has mastered, and also depending on what is meant by "understanding deeply". $\endgroup$ – Namaste Nov 15 '18 at 23:29

It's very early in your life as a mathematician. As you learn, you will discover your own style - how much time to spend solving problems, practicing calculations, learning proofs, history and philosophy. For now, I suggest doing what you find the most fun. Actually, that would be my advice later too.

I like your ambitious choice of StackExchange username.

  • $\begingroup$ I respect OPs guts...I wouldn't dare call myself one. Also that pfp tho $\endgroup$ – Don Thousand Nov 15 '18 at 22:28

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