The recipients of this year's Abel Prize, the highest award in the field of mathematics, are Hillel Furstenberg and Gregory Margulis.
Dr. Furstenberg is retired after an academic career at the University of Minnesota and the Hebrew University of Jerusalem. Dr. Margulis is a professor at Yale University.
Their work that received the prize demonstrates the use of probability to find order in seemingly random data. It is based on the ergodic theory, (Greek: "the way it works") the branch of mathematics that studies statistics of deterministic dynamical systems. What does it mean? Deterministic dynamical systems are systems that change in a predictable way, without any random noise.
Ergodic theory studies the properties of the dynamics - changes, transformations - in such systems. It stipulates that if we took a certain measure of such a system, it would be preserved over time. For a very simplified example, if we threw a stone in a lake, the shape of the water surface would be changing over time as the stone bounces off, eventually returning to rest; but the density of the water in the lake at the beginning and the end of the temporary transformation will be the same. Mathematically, we would talk about the time average and the space average of a measure, which in an ergodic system would almost always be equal.
Confusing? Try it this way: when an ergodic system is affected by some sort of change, it goes through all possible states, which can be mathematized and analyzed. With this understanding, seemingly chaotic systems and randomness can be used to actually prove patterns.
An interview with Dr. Furstenberg can be watched here. Both scientists have been incredibly humble about their achievement.
