- #1

Kolmin

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I was reading the introduction of the book “A gentle introduction to the art of Mathematics” and I was wondering about what the authors wrote on whom the book is for. In particular he stated that the book is in particular for people who can easily solve exercises (i.e. computation) and want to make the next step, which is doing real maths in terms of proving stuff.

Now – and that’s not a rhetorical question, cause I really don’t know – if somebody is pretty good at math in terms of computations and usually he can solve problems easily, but at the same time he can get stuck by tough integrals and other tough computations, is it a problem or not?

Are making computations (like calculating integrals) and writing proofs related to the same skills?

Considering that there is a software like “Wolfram Mathematica” around that can do the computation for him, if doing tons of basic computational exercises is important in order to make somebody starts to think like a mathematician (without doing him/her a mathematician), if somebody has already that kind of mentality, but at the same time has some minor problems in terms of computations, can he skip the problem altogether and focus on proofs (and functional forms) instead of problematic exercises?

In other words: Is a necessary condition for writing proof doing every possible calculation without problems?

Looking forward to your opinions!

PS: I was not sure on which part of the forum this thread should be part of…I hope I didn’t make mistakes.