2018 Fields Medal and Nevanlinna Prize

Latest Articles

String Theory Inspires a Brilliant, Baffling New Math Proof

December 12, 2025

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.

Cryptographers Show That AI Protections Will Always Have Holes

December 10, 2025

Large language models such as ChatGPT come with filters to keep certain info from getting out. A new mathematical argument shows that systems like this can never be completely safe.

Why Is Ice Slippery? A New Hypothesis Slides Into the Chat.

December 8, 2025

A newly proposed explanation for the slipperiness of ice has revived a centuries-long debate.

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The Polyglot Neuroscientist Resolving How the Brain Parses Language

December 5, 2025

Is language core to thought, or a separate process? For 15 years, the neuroscientist Ev Fedorenko has gathered evidence of a language network in the human brain — and has found some parallels to LLMs.

What Are Lie Groups?

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.

‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard

December 1, 2025

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.

Particle Physicists Detect ‘Magic’ at the Large Hadron Collider

November 25, 2025

The supercollider is now being used to explore quantum phenomena, including a “magic” form of quantum entanglement.

A Cell So Minimal That It Challenges Definitions of Life

November 24, 2025

The newly described microbe represents a world of parasitic, intercellular biodiversity only beginning to be revealed by genome sequencing.

A New Bridge Links the Strange Math of Infinity to Computer Science

November 21, 2025

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.