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Mathematicians Bridge a Gap in Number Theory

Two mathematicians have proven an important result connecting elliptic curves to modular forms, extending a breakthrough achieved in the 1990s that led to the solution of Fermat’s Last Theorem. Ana Caraiani of Imperial College London and the University of Bonn, and James Newton of the University of Oxford announced in January that they had shown that elliptic curves are modular for certain imaginary quadratic fields. Their work builds on Andrew Wiles’ 1994 proof that elliptic curves are modular for rational numbers, meaning that for each elliptic curve, there exists a corresponding modular form — an object from analysis, a branch