‘Grand unified theory of maths’ nets Abel Prize

‘Grand unified theory of maths’ nets Abel Prize

New bridges to maths’ ‘grand unified theory’

Two breakthroughs have established new bridges between apparently distant continents in the mathematical landscape. They are the most significant recent additions to the Langlands programme — a ‘grand unifying theory of maths’ that won its originator, Robert Langlands, the Abel Prize in 2018. The programme envisioned a correspondence between two classes of mathematical objects — one in the theory of tilings and the other in arithmetic. A preprint by ten authors — the result of a massive brainstorming session — has now extended the correspondence from rational to complex numbers. And another preprint created a new bridge using a class of geometric curves that previously seemed beyond reach of the Langlands programme. “People wanted to do this for a long time,” says mathematician Ana Caraiani, one of the authors of the first breakthrough paper. But, “we pretty much didn’t think it was possible.”

Quanta | 12 min read
Read more: Robert Langlands’s ‘grand unified theory of maths’ wins the Abel Prize (from 2018)Reference: arXiv preprint 1 and arXiv preprint 2