One of the $3 million Breakthrough Prizes was awarded to Prof. Alex Eskin who co-proved the “magic wand theorem” with the late Iranian mathematician Maryam Mirzakhani. Eskin was cited for “revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials,” including the proof of the “magic wand theorem” with Mirzakhani.
Eskin teamed with Mirzakhani to prove a theorem about dynamics on moduli spaces. Their tour de force, published in 2013, has far-reaching consequences in the field of mathematics. It addressed a longstanding math problem: If a beam of light from a point source bounces around a mirrored room, will it eventually reach the entire room—or will some parts remain forever dark?
After translating the problem to a highly abstract, multi-dimensional setting, the two mathematicians were able to show that for polygonal rooms with angles which are fractions of whole numbers, only a finite number of points would remain unlit.
Eskin said he intends to donate part of the prize money to an International Mathematical Union fellowship to help graduate students pursuing doctorates in developing countries, following a tradition among winners of the prize.