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Arithmetic geometry of elliptic curves combines algebraic geometry and number theory to investigate cubic curves of genus one endowed with a distinguished rational point. Such curves admit a group law ...

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical ...

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world. The proof Wiles finally came up with (helped by Richard ...