by Jonathan Kujawa
On March 26th it was announced that Yakov Sinai, a mathematician at Princeton University and the Landau Institute for Theoretical Physics, had won the 2014 Abel Prize. The Abel prize was established in 2001 by the government of Norway and was first given 2003. Unlike the more famous Fields Medal, which (in)famously can only be granted to those under the age of forty, the Abel prize recognizes an individual for the breadth and depth of their entire career. It has quickly become the highest award one can earn in mathematics. Indeed, the list of prizewinners over the past ten years reads like a who's who of influential mathematicians.
Dr. Sinai won the prize “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics”. Fortunately, I'm completely unqualified to tell you about Dr. Sinai's work. I say fortunately because Jordan Ellenberg already does an excellent job explaining Dr. Sinai's work in layman's terms as part of the announcement of the winner. You can watch the video here. Dr. Ellenberg gives a very nice twenty-minute overview of Dr. Sinai's work starting at the nine minute mark. Highly recommended!
I also say fortunately because it gives me the excuse to tell you about some cool math. A big part of Dr. Sinai's work is in the area of “Dynamical Systems.” This is a rare case where the name of a mathematical discipline actually tells you what the field is all about. Simply put, researchers in dynamical systems are interested in studying how a given system changes over time. The artist Tristan Perich explores the same territory by examining the upredictable dynamics of using computer code to draw in an unsheltered environment.
This is the sort of math you would be interested in if you want to model and predict the weather, the climate, the stock market, the reaction in the combustion chamber of an engine or in a nuclear explosion, etc. Of course these are all wildly difficult problems. Even with all our modern computing power it's hard to make progress. So here we'll instead think about much, much simpler examples which still exhibit some of the same interesting phenomena.