Langlands Bridge Art — Daniel Castro Maia for Quanta Magazine

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

“It started to feel as if the program was within reach, so in the fall of 2016, to try to make further progress, [Ana] Caraiani and [Richard] Taylor organized what [Frank] Calegari called a ‘secret’ workshop at the Institute for Advanced Study. ‘We took over the lecture room — no one else was allowed in,’ Calegari said.

After a couple of days of expository talks, the workshop participants started realizing how to both polish off the second conjecture and sidestep the third conjecture. ‘Maybe within a day of having actually stated all the problems, they were all solved,’ said [Toby] Gee, another participant.

The participants spent the rest of the week elaborating various aspects of the proof, and over the next two years they wrote up their findings into a 10-author paper — an almost unheard-of number of authors for a number theory paper. Their paper essentially establishes the Langlands bridge for elliptic curves with coefficients drawn from any number system made up of rational numbers plus simple irrational and complex numbers.”