DeepMind’s AlphaProof system solved four out of six problems at the 2024 International Mathematical Olympiad, generating formally verified proofs through reinforcement learning trained on millions of ...

Discrete mathematics is about precision in reasoning as much as it is about solving problems. Proof techniques like induction, contradiction, and direct reasoning are used to establish results in ...

Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance ...

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 ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? A 125-page proof posted to arXiv may represent a huge breakthrough in geometric ...

The verdict, it seems, is in: artificial intelligence is not about to replace mathematicians. That is the immediate takeaway from the “First Proof” challenge—perhaps the most robust test yet of the ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I examine an insightful AI research study ...