I picked up David Bessis' Mathematica on a whim. It focused on a discussion of what math truly was to one accomplished in it, and how the public’s understanding of what mathematicians do is wildly, grossly inaccurate. The book’s premise: language is a poor medium for transmission of intuition itself, whereas math and logical proofs are overkill but required to express it. Mathematics, he argues, is the art of intuition and imagination, not calculation, trying its best damndest to define it. But, since intuition is so beyond language, we have to invent new concepts and symbols in which to grasp it and communicate it.
I enjoyed it, and have certainly spent time thinking on its lessons, but wished it delved more into direct hands-on walkthroughs of intuition in which to further illustrate the separation of language and logic, or perhaps more solid advice on directly attacking the problem of intuition growth.
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