

Mathematician paid $4.4 million for solving a highly complex problem

A mathematician has been handed A$4.4 million for proving a difficult concept dubbed the "magic wand theorem".
Alex Eskin received the Breakthrough Prize in Mathematics for "revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentia".
The 54-year-old American mathematician said the magic wand theorem is "useful in several different areas of mathematics" but was "not easy to explain". 
"It takes me hours and hours to explain to math Ph.Ds that work in different subfields," he told Live Science.
The prize was given for work including the "magic wand theorem"
The prize was given for work including the "magic wand theorem" (Getty)
Essentially the theorem is a litmus test for determining the orbital dynamics of systems given certain properties of the space housing them and any obstacles within – think of trying to perfectly predict the path of every billiard ball hit on a table filled with obstacles.
Eskin's work allows for the ability to calculate the diffusion rates of a wide range of systems instead of having to compute the individual trajectories
The mathematician said he first became interested in the concept while doing a series of proofs known as Ratner's theorems - a group of major theorems concerning unipotent flows on homogeneous spaces where every point is like every other point (the surface of a sphere).

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Eskin said his solution focused on whether Ratner's ideas could be carried forward into moduli spaces -  where not all the points are the same.
"I actually got obsessed with this problem," he said.
"I had to work on other things because I was young, and you have to publish [research] to get hired. But I was always thinking about this problem."
Eskin teamed up with mathematician Maryam Mirzakhani and over the next five years, the pair began working to prove the magic wand theorem.
"She's very much not interested in going after the low-hanging fruit. She wanted to work on the difficult problems. So, our projects got more and more ambitious," he said.
Eskin said eventually the pair verified the concept using a series of smaller proofs, with the results published in a 2013 paper mentioned by the judges of the prize.
The mathematician said he unsure what he will do with the prize money other than donating a small portion to an International Mathematical Union fellowship for graduate students pursuing doctorates in developing countries. 
"One of the things about working in math is that the highs are very high and the lows are very low," he said.
"It's very frustrating, because for a long time, you basically can make no progress. At some point, you've spent five years working on a project, and you never know if it's going to work or not.
"It's a big part of your life invested in this. There's always a big possibility you'll come out of it with nothing ... You need a lot of emotional stability to keep on going."
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