In 2003, Svetlana Jitomirskaya, who had spent years studying the almost-periodic function embedded in the Schrödinger equation, had just given up on her career-long goal of proving the ten martini conjecture. A year earlier, a competitor named Joaquim Puig(opens a new tab) had proved it for all but a few classes of irrational alpha values. What’s more, he’d used techniques she’d published earlier to do it. “I was kicking myself,” she said. “All the hard work was in my proof, and then here he comes with this beautiful argument.”
So she was surprised when a 24-year-old mathematician named Artur Avila visited her and suggested they work on the remaining values of alpha. “I told him it would be very difficult, very time consuming, and no one would care,” she said.
People did. Their proof, which they posted online in 2005(opens a new tab), was eventually published in the Annals of Mathematics(opens a new tab), the field’s most prestigious journal. Avila later won a Fields Medal in part for his work on the problem.