How the Internet is accelerating mathematical progress, or, going beyond MOOCs...
There is a lovely story in Wired magazine that showed up on my FB page. http://www.wired.com/wiredscience/2013/11/prime/all/
People may recall that on April 17, an unknown lecture at U New Hampshire shocked the mathematical world by establishing that there is a number N <= 70 000 000 s.t. that there are infinitely many pairs of primes whose difference is N. This was the first proof that infinitely many primes come in pairs.
Terence Tao, a Field Medalist at UCLA, then proposed a polymath project, polymath8 (http://polymathprojects.org/2013/06/04/polymath-proposal-bounded-gaps-between-primes/#comments
) for mathematicians (and computer scientists!) from all over the world to collaborate on reducing this bound. In just five months, the bound was reduced to 4 680!
Just to establish that the Lone Mathematician still has a role to play, three days ago a post doctoral researcher from U Montreal sent in a preprint to arXiv reducing the number to 600!
The polymath idea is interesting! What is fascinating to me is that a whole lot of advanced mathematics is now happening collaboratively, in the open blogosphere, involving people who may not even have known about each other before they started collaborating online.
It seems that a new area of Massively Open Online Research has begun, at least in math. Wonder which other areas of research would be able to sustain this (without running afoul of credit / intellectual property / ....)