Sunday, August 15, 2021

99 Variations on a Proof

I picked up Philip Ording's aesthetic and amusing little book because I'm still trying to work some more math into the reading pile.  While I enjoyed his wit, the book wasn't quite what I expected.  Instead of mainly showing how many different areas of mathematics a simple polynomial equation can touch -- the proof is for the solution of a cubic equation -- Ording mainly shows us how many different styles a mathematical proof can be written in.  The two things are subtly different.  

Ording was inspired by Raymond Queneau's Exercises in Style, which retells the same simple story using 99 varieties of narrative technique.  So the focus here is literally on the style of each proof, with some reference to the history of that mathematical style, rather than directly on the mathematical content of the proof.   In fact, many of the proofs are mathematically equivalent, differing almost entirely in typesetting and wording.  And the ones that introduce (for me) new mathematics, for example like the one that uses group theory, are only really examined from the same stylistic and historical perspective, without delving much into how the math works.  In other words, while you can learn something about math from this book, you can't actually learn much math.  The author's implicit understanding is that you will either be able to read a proof without trouble, or you won't -- and that's fine, because it's not really the point.  There's not enough information provided within Ording's commentary on each proof to go from it not making sense to it making sense.  That would have been a different book.  And shorter. 

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