Partition theory studies the ways in which a positive integer can be expressed as a sum of positive integers, without regard to order. Originating in the work of Euler, it has evolved through the ...

Iwasawa theory investigates the variation of arithmetic invariants—such as class groups and Selmer groups—along infinite towers of number fields, most classically the cyclotomic Z p-extension of the ...

In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last Theorem, a central problem in number theory that had remained open ...

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Let $\rho: G_\Q \rightarrow \GL_2(\Fpbar)$ be a continuous, odd, irreducible representation. The weight part of Serre's conjecture predicts the minimal weight k ...