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Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

Why do mathematicians enjoy proving the same results in different ways?

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.

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