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As the title says, can anyone help me to find any book that shows how physical reasoning using concepts from classical/quantum mechanics and physics in general can enlighten us about mathematical problems/theorems? Second question,can you list some contemporary mathematician who subscribe to this view ,I know many russian mathematicians do like Vladimir Arnold, any others?

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A Primer of Infinitesimal Analysis, John L Bell. – mistermarko Jul 26 '14 at 6:25
Thanks.what's your review of it? – Daniel Faust Montana Jul 27 '14 at 4:45

The book you want is Mark Levi, The Mathematical Mechanic: Using Physical Reasoning to Solve Problems.

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@mixed, you are forgiven. I haven't read it all the way through. What I did read of it, I thought was pretty good. – Gerry Myerson Jul 26 '14 at 4:14
I already have it,didn't read it,anything else? – Daniel Faust Montana Jul 26 '14 at 4:26
I'll take that as your way of saying thanks, but it leaves me puzzled; you just want to find these books, you don't actually want to read them? In any event, can you edit into your question a list of all the books you have already found, so we don't waste our efforts finding them for you? – Gerry Myerson Jul 26 '14 at 4:30
Sorry ,Thank you for being a person who wants to help, and I meant that I haven't read yet ,I got it just last week. – Daniel Faust Montana Jul 26 '14 at 4:36
that's also the only book I know who does that . – Daniel Faust Montana Jul 26 '14 at 4:39

I recommend "The Geometrical Language of Continuum Mechanics" by Marcelo Epstein. I still have some way to go to understand everything this book says, but he makes a strong case that differential geometry and the mechanics of a continuum dovetail nearly perfectly with each other.

Epstein states (I quote) "...the presence of continuum mechanics as a materialization of many of the important geometric notions is of invaluable help."

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Thanks ,seems really interesting. – Daniel Faust Montana Jul 29 '14 at 19:48

A good one is Vladimir Arnold's Mathematical Understanding of Nature.

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