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Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

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

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.