number theory – Quanta Magazine

Monumental Proof Settles Geometric Langlands Conjecture

Erica Klarreich — Fri, 19 Jul 2024 14:02:17 +0000

A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said Peter Scholze, a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.

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‘Sensational’ Proof Delivers New Insights Into Prime Numbers

Jordana Cepelewicz — Mon, 15 Jul 2024 13:55:18 +0000

Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a $1 million reward from the Clay Mathematics Institute. Its proof would give mathematicians much deeper certainty about how prime numbers are distributed, while also implying a host...

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A Rosetta Stone for Mathematics

Kevin Hartnett — Mon, 06 May 2024 14:23:30 +0000

In 1940, from a jailhouse in Rouen, France, André Weil wrote one of the most consequential letters of 20th-century mathematics. He was serving time for refusing to join the French army, and he filled his days in part by writing letters to his sister, Simone, an accomplished philosopher living in London. In a previous letter, Simone had asked André to tell her about his work. With war all around...

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Merging Fields, Mathematicians Go the Distance on Old Problem

Erica Klarreich — Mon, 01 Apr 2024 13:50:22 +0000

The change of plans came on a road trip. On a beautiful day last April, the mathematicians Rachel Greenfeld and Sarah Peluse set out from their home institution, the Institute for Advanced Study in Princeton, New Jersey, heading to Rochester, New York, where both were scheduled to give talks the next day. They had been struggling for nearly two years with an important conjecture in harmonic...

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Elliptic Curve ‘Murmurations’ Found With AI Take Flight

Lyndie Chiou — Tue, 05 Mar 2024 15:12:30 +0000

Elliptic curves are among the more beguiling objects in modern mathematics. They don’t seem complicated, but they form an expressway between the math that many people learn in high school and research mathematics at its most abstruse. They were central to Andrew Wiles’ celebrated proof of Fermat’s Last Theorem in the 1990s. They are key tools in modern cryptography. And in 2000...

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