how bhargava and mirzakhani solved a problem

http://www.newyorker.com/tech/elements/maryam-mirzakhanis-pioneering-mathematical-legacy



Mirzakhani had first received news of the Fields Medal in an e-mail from the Duke mathematician Ingrid Daubechies, then president of the International Mathematics Union, which adjudicates and awards the prize. At first, Mirzakhani assumed someone was playing a joke; she ignored Daubechies’s note. When the two finally spoke, Mirzakhani was pleased, of course, but she was concerned that, having just undergone chemotherapy for breast cancer, she wouldn’t be well enough to attend. Plus, as the first female Fields medalist, she was wary of being hounded by the press. Once it became clear that Mirzakhani would come, Daubechies and a number of other distinguished women mathematicians devised a plan to insulate her. “There were six of us,” Daubechies told me. “We called ourselves the M.M. Shield.” Whenever Mirzakhani was in public, two women were always near; one would intercept any hovering journalists and offer herself as an interlocutor, and the other would facilitate Mirzakhani’s escape. “We felt, as a community, we should really help,” Daubechies said. “We wanted to help her celebrate. It was so unfair—here she was, and sick.”
Despite her illness, Bhargava said, Mirzakhani “was still producing some of her most amazing mathematics just these last few years.” She had an “uncanny intuition” about difficult geometric problems, even if they might require decades of work. Still, though she took the long view of mathematics, she wasn’t above more mundane and immediate concerns. When she and Bhargava brainstormed about their predicament in Seoul, they worked out that the easiest way to untangle the medals was for each of them to perform two trades. “Maryam and I exchanged our medals; then Maryam waited to run into Martin to exchange medals with him, while I waited to run into Artur to exchange medals with him,” Bhargava said. Then he offered a more mathy explanation for the solution to the four-medal mix-up:

A four-cycle cannot be expressed as the composition of fewer than three transpositions, or “swaps.” Therefore, since exchanging our medals resulted in a permutation that was the composition of two swaps, it was clearly making progress (two swaps is better than three); moreover, those last two swaps could now be carried out in parallel, making it better than any other possible solution. We had this amusing mathematical conversation very quickly, exchanged medals, and then ran off to our next obligations.

Mirzakhani stayed for a couple of days at the congress but, as she and Daubechies had planned, left before delivering her lecture, which was scheduled toward the end of the proceedings. That morning, Daubechies said, “people looked for her, but she was gone.”

Thanks for posting this.