Sunday, December 4, 2016

How Not to Be Wrong by Jordan Ellenberg

Mathematics, at it's core, is the act of coming up with a set of rules and using those rules to make deductions that expand their reach. It can be applied to any other aspect of life because, unlike other sciences, mathematics is universal and incontrovertible. Once something has been set in stone in the mathematical world, there is little that can be done to undo it elsewhere. Conversely, a breakthrough in mathematics has often led to surprising developments elsewhere.

Jordan Ellenberg's How Not to Be Wrong is a wonderful look into how mathematics allows us to have a clear understanding of a variety of topics from genetics to lotteries to politics. Above all, it is a universal work, one that demands nothing more than a middle schooler's understanding of mathematics to feel enlightening and insightful.

Ellenberg's style is especially delightful. Experts in many fields take themselves too seriously and treat the reader like an ignorant child. Academic writing is full of obfuscation as researchers try to make their work seem more important and complicated than it really is. Ellenberg manages to reach out to all kinds of readers with prose that is succinct and clear headed. The illustrations are a highlight; one that I won't spoil for any would-be readers.

I have some background in mathematics (a Master of Science with a minor in applied math), so I wasn't really expecting How Not to Be Wrong to challenge me as much as it did. I had heard of Russell's paradox before but Ellenberg introduces the problem through its mathematical history and not as a singular event in time. As with many other science stories (Age of Wonder for one), the context of a discovery is often as important as the discovery itself.

Russell's paradox broadly states that any formal set of rules is bound to give rise to a contradiction. But the story only becomes memorable once you see it from the point of view George Cantor, a fellow mathematician, who had just finished his magnum opus on set theory, only to see his life's work wasted, as Bertrand Russell pointed out his shortcomings. The pressing of the book had to be stopped and an additional line added to it's first page that stated the inherent contradiction built into Cantor's theory. Mathematics would never be the same again.

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