Primes and Probability

At the suggestion of a colleague, I recently started reading Charles Wheelan’s Naked Statistics: Stripping the Dread from the Data. So far, it’s a fun, demystifying sort of book, the kind I hope my students will enjoy (watch out Lafayette Economics, I’m coming, and I will make you read). It rests on the twin ideas that statistics can be fun and statistics are incredibly useful to explain, to tell stories.

The book was high in my mind this morning when I read this deliciously accessible Slate piece by Wisconsin professor Jordan Ellenberg about an advance in prime numbers by a University of New Hampshire mathematician. Economists like to make lots of bad jokes about how they are failed physicists, who are in turn failed mathematicians, so while it interests me, I wasn’t expecting to really understand the discovery when someone riffed on twitter about primes.

What’s so wonderful about this really intense mathematical discovery, at least according to the mathematician author of this piece, is that it’s really about statistics, which I can totally get my head around. The theory goes that primes come in infinitely many ‘twin pairs,’ like 3 and 5 or 17 and 19, and the intuition lies in that we can think about primes as random numbers.

And a lot of twin primes is exactly what number theorists expect to find no matter how big the numbers get—not because we think there’s a deep, miraculous structure hidden in the primes, but precisely because we don’t think so. We expect the primes to be tossed around at random like dirt.

Zhang didn’t quite prove the twin pairs theorem, but he made an important step towards proving it, it seems, and understanding probability and statistics is key to getting there.

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2 thoughts on “Primes and Probability

  1. Jordan is a friend of mine and excellent as both a mathematician and an expositor. I’m excited that his article (and blog) are getting some good attention.

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