Tuesday, July 16, 2019

"Counting from Infinity": can a documentary about number theory be entertaining? Yes, if the professors are

Monday July 15, Maryland Public Television presented the film “Counting from Infinity: Yitang Zhang and the Twin Prime Conjecture” (2015) from Zalafilms, directed by George Paul Csicsery.

The controversy started with a lecture and paper from the University of New Hampshire in 2013 by the protagonist.

This refers to the existence of a minimum number for which there are infinite prime numbers less than that difference between them. The mathematical proofs (on computers) keep shrinking that minimum to a few hundred now.  The concept is counterintuitive;  you would expect this number to diverge but it does not.

This led to the involvement of the Polymath group at Berkeley, and some papers by young Oxford professor James Maynard from England.
I took number theory in my first semester of graduate school at the University of Kansas in 1966.  I can recall the (India-born) professor saying “Is it not?” all the time, not quite used to idiomatic English. I can remember hour examinations in grad school; you can’t solve four problems you haven’t seen before in that amount of time.  Final exams were much easier than hour tests.  (Some of the videos on Harvard student John Fish’s channel get into problem solving on exams.)

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