Maryam Mirzakhani, A Candle Illuminating The Dark

Paul Halpern in Forbes:

Abstract mathematics sometimes has surprisingly practical applications, to not only physics but other arenas as well. Take, for example, the work of extraordinarily innovative mathematician Maryam Mirzakhani, whose recent death at the age of 40 has been mourned around the world. One of the theorems she co-developed sheds light on several related longstanding physics quandaries having to do with ricocheting and diffusion—of light, billiards, the wind, and other entities. Undoubtedly, given its generality, it will find many uses in science, sports, and beyond, for years to come.

The class of problems Mirzakhani was interested in dates back more than a century. In 1912, Austrian statistical physicist Paul Ehrenfest and his wife, the Russian mathematician Tatjana Afanassjewa-Ehrenfest, proposed the ‘wind-tree’ model as a way of trying to understand how impediments in a system affect diffusion. (In this context, diffusion means the spreading out of particles, light, gases, etc., due to their natural motion.) They imagined a bounded forest that was empty except for regularly spaced trees—symbolized as rectangles forming a periodic pattern within a square lattice. Imagine the wind entering the forest from a certain direction and scattering off the various trees according to the law of reflection (incoming angle equals outgoing angle). How quickly, they wondered, would nearby streams of air particles separate from each other and spread throughout the entire forest?

More here.