by Jonathan Kujawa
The big news in math this week was the opening of the quadrennial International Congress of Mathematicians (ICM) in Seoul. A number of prestigious awards are given at the ICM. Most famously this includes the Fields medal and the Nevanlinna prize (aka the Fields medal for computer science). Up to four winners of the Fields medal are announced along with the winner of the Nevanlinna prize. All the winners must be no older than 40.
I had the pleasure to attend the 2006 ICM in Madrid. This is the ICM famous for Grigori Perelman refusing to accept the Fields medal for his work in finishing the proof of the Poincaré conjecture. Perelman (or at least the media version of him) comes across as the stereotypical eccentric mathematician uninterested in worldly things. Fortunately for the PR folks, this year's winners all appear to be the sort you'd enjoy having over for dinner and drinks.
This year the Fields medal went to Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani. The Nevanlinna prize went to Subhash Khot. An excellent profile of each of the winners, including very nicely done videos, can be found on the Quanta website. The profiles are a bit short on the actual math of the winners. If you'd like a more meaty discussion of their work, former Fields medalist Terry Tao wrote blog posts here and here giving a more technical overview. Even better, former Fields medalist Timothy Gowers is blogging from the ICM itself! He's giving summaries of the main talks as well as his more general impressions while at the event. I can also recommend that you check out the excellent overviews of some of the winners' work on John Baez's Google+ page.
Rather than talk about the details of the winners' work [1], I wanted to point out a meta-mathematical common feature of their research. This is the idea of studying a collection of objects as a whole, rather than one by one.

