Razborov receives the prize for his paper "On the minimal density of triangles in graphs" (Combinatorics, Probability and Computing, 17 (2008), no. 4, 603-618), and for introducing flag algebras to solve problems in extremal combinatorics.
The full citation for this prize and additional information can be found in the massive Joint Mathematics Meetings Prize Booklet. Bloggers may like to read the response by John Baez to receiving the 2013 AMS Levi L. Conant Prize. (Presented annually, the Conant Prize recognizes the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years.) John writes:
I put a lot of energy into explaining math and physics online. Blogging is no substitute for more formal writing about academic subjects, but it fills a gap, especially for the millions who don’t live near a good research university. Socrates complained that “writing is unfortunately like painting, for the creations of the painter have the attitude of life, yet if you ask them a question they preserve a solemn silence.” This is no longer true with blogs: the author is there to answer your questions! So, I am hoping that eventually blogs will be taken seriously by academia and the AMS will have an award for the best mathematics blog. But I am very happy to receive this prize for a more traditional form of mathematics exposition.Congratulations to all the prize recipients and happy 2013 to everyone.