Jamesian Philosophy Refreshed

In yesterday's entry , I discussed a recent proof devised by a professor at the University of New Hampshire that there are "bounded gaps" between prime numbers. Specifically, Yitang Zhang has established that there are infinitely many pairs of primes that differ by 70 million or less. There are two fascinating things about this tidbit about which I wish to comment today. First, who the heck is Yitang Zhang? Second, infinity and size. Who the heck? One might naively expect the burning questions of a recondite field to be settled by the elites of the relevant expertise.  Andrew Wiles, the fellow who proved Fermat's Last Theorem correct (though in a way that can't "fit into a margin") was a Royal Society Research Professor at Oxford University, specializing in number theory. Before that, he had been a professor at Princeton University in the early 1980s and a Guggenheim Fellow at the Institut des Hautes Etudes Scientifiques in France in the late 1...

All right. Let's really put our geek hats on and talk about prime numbers. A little over a year ago I wrote about an enjoyable evening I spent watching the musical Fermat's Last Tango, a fictionalized (and lyrical) presentation of Andrew Wiles' successful effort to prove that Fermat was right about a certain famously generalized form of the Pythagorean theorem.  For purposes of the musical, Wiles is renamed Daniel Keane . Anyway, one of the conjectures that has acquired a good deal of importance in elite math-geek circles since Wiles' success is something called the " bounded gap conjecture" concerning prime numbers. As a refresher, a prime number is any number higher than 1 that can be divided only by 1 and itself. There are lots of prime numbers amongst the lowest counting numbers, but they thin out as one gets into the higher ones. 1 is by stipulation not a prime. Two and 3 are both primes. The first integer above 1 that isn't a prime, the...