52 Books a Year: #27 - The Art of The Infinite

Posted by Brian Sun, 06 Dec 2009 23:31:58 GMT

The Art of the Infinite: The Pleasures of Mathematics
By Robert and Ellen Kaplan


Still on books picked up at the library sale, The Art of the Infinite has the aim of expressing the elegance of mathematics. Our educational system does an excellent job of destroying the creativity and beauty of true mathematics, focusing instead on mechanical calculation to pass standardized tests. Professional mathematicians do not consider this to be mathematics though.

The Kaplans elegantly mix complex mathematical problems with flowery prose. Some will be turned off by seeing this type of writing in a mathematics book, but I found it very refreshing. It fit in well with the concept of mathematical beauty that the book advances. You also get wonderful insights into the personalities of individual mathematicians and how conflicts between those personalities have driven development in the field. The explanations of various theorems and proofs are excellent as well. One that stood out is the beautiful mathematical explanation of sine and cosine.

The Art of the Infinite also tries to address the jumble of symbols that often scare people away from math. Unnecessary symbols are discouraged and new ones are only introduced after an explanation as to why they are being used. Another refreshing aspect was the hand-drawing of all diagrams. The authors felt that imperfect drawings would also help to discourage readers from studying for accuracy instead of the concepts they represent.

The imperfections are small. Some proofs are very long and it is difficult to remain focused to the end. This would have been helped by stopping at points and showing what we have done so far and how this relates to the original problem. There were cases where I forgot what we were even trying to prove by the end. Some of the proofs are also just difficult. It was very difficult for me to grasp the sections on perspective geometry and I lost my way at the end of the proof for Cantor’s set theory. However, in comparison to the positives the, negatives are negligible. The subject matter is difficult, but well worth the effort.


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