The Core of Fermat’s Last Theorem Just Got Superpowered
1 min read
Summary
A research team from the University of Chicago, Imperial College London, and the French National Center for Scientific Research have proven a conjecture that had been considered beyond the realms of possibility.
The group successfully extended the notion of “modularity” — a concept used in the proof of Fermat’s Last Theorem to tie elliptic curves to mathematical objects known as modular forms — to a higher-dimensional class of mathematical objects called abelian surfaces.
The proof, which the team posted online in February after almost a decade of work, opens up new lines of inquiry into a variety of previously intractable problems, including a major unsolved problem in number theory called the Birch and Swinnerton-Dyer conjecture.
The research builds on work in an area of mathematics known as the Langlands program, which aims to unify different areas of mathematics and which remains one of the most active areas of research in the field.
