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## Tuesday, May 14, 2013

### The Exhilaration of Math... (Zhang/primes)

"Math is a beautiful thang!" (I can't say that often enough)… or perhaps I should say, math is a beautiful Zhang!!

The words I've seen describing the newly-announced work of mathematician Yitang Zhang include not just "beautiful," but also "breakthrough," "incredible," "astounding," "stunning."

If you somehow missed the math buzz of the last 48 hours, Zhang claims to have proven that there are an infinite number of paired primes that are some given finite distance apart… and that distance apart is less than 70,000,000… that's right, I said 70 million digits apart!!  And, mathematicians are THRILLED! Thrilled because this is the first time someone has shown there to be an upper limit or boundary to what the gap between adjacent primes can be. This may be a first, sort of baby step, toward trying to prove the long-held (but unproven) 'twin-prime' conjecture (that there are an infinite number of paired primes with a gap of 2).
Yeah, sure, working down from 70,000,000 to 2 might require some work yet, but ya gotta start somewhere (and you have to understand that prior to Zhang the only boundary was infinity, so stepping us down from infinity to 70,000,000 is no minor accomplishment -- though it can be difficult for lay folks to comprehend how teeny a number like 70,000,000 is within mathematics).

The Zhang story began on the Web (so far as I'm aware) with Peter Woit's rumor report Monday on his "Not Even Wrong" blog, that a special seminar by Zhang, was about to take place at Harvard, related to “bounded gaps between primes.”
Following the seminar, and its positive reception, the story got picked up quickly, first by Nature, here:

http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

…and then by others, including these two pieces, also very accessible to the lay public:

http://io9.com/mathematician-makes-astounding-prime-numbers-breakthrou-505577996

http://www.newscientist.com/article/dn23535-proof-that-an-infinite-number-of-primes-are-paired.html

If you haven't followed the story, read some of the above links to catch up.
I won't try to re-cap what those articles tell you, but will simply comment on how fun it is to see mathematicians get excited over a piece of news (and also watch the press pick up on it). One suspects most of the public will merely scratch their heads in bemusement that mathematicians can be so enamored of a number like 70,000,000 when they are really aiming for 2! I wish, alas, we could translate the excitement and wonderment into some form that the general public might better fathom! I can only hope that those who don't grasp what all the fuss is about, might at least be fascinated that human minds exist which are subject to exhilaration by such findings!

(Having said all this, I should add that while the experts seem optimistic, Zhang's proof still must pass vigorous peer review.)

ADDENDUM (5/19/13): a very good follow-up to the story from the Simons Foundation here:

http://tinyurl.com/am5fvjp