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A ‘Grand Unified Theory’ of Math Just Got a Little Bit Closer
By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a unifying theory of mathematics.
If mathematicians want to understand something about an elliptic curve, Wiles and Taylor showed, they can move into the world of modular forms, find and study their object’s mirror image, then carry their conclusions back with them. The team— Frank Calegari of the University of Chicago, George Boxer and Toby Gee of Imperial College London, and Vincent Pilloni of the French National Center for Scientific Research—proved that every abelian surface belonging to a certain major class can always be associated to a modular form. All four mathematicians were involved in research on the Langlands program, and they wanted to prove one of these conjectures for “an object that actually turns up in real life, rather than some weird thing,” Calegari said.
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