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Mathematics

Incredible maths proof is so complex that almost no one can explain it

Mathematicians are celebrating a 1000-page proof of the geometric Langlands conjecture, a problem so complicated that even other mathematicians struggle to understand it. Despite that, it is hoped the proof can provide key insights across maths and physics

By Alex Wilkins

20 May 2024

The Langlands programme aims to link different areas of mathematics

Andrew Ostrovsky/iStockphoto/Getty Images

Mathematicians have proved a key building block of the Langlands programme, sometimes referred to as a “grand unified theory” of maths due to the deep links it proposes between seemingly distant disciplines within the field.

While the proof is the culmination of decades of work by dozens of mathematicians and is being hailed as a dazzling achievement, it is also so obscure and complex that it is “impossible to explain the significance of the…

Article amended on 20 May 2024

We have clarified the nature of the geometric Langlands conjecture

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