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 ...

When it comes to understanding the shape of bubble clusters, mathematicians have been playing catch-up to our physical intuitions for millennia. Soap bubble clusters in nature often seem to ...

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 ...

AI thrives on data but feeding it the right data is harder than it seems. As enterprises scale their AI initiatives, they face the challenge of managing diverse data pipelines, ensuring proximity to ...

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 ...

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 ...

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 ...

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 ...

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 ...