GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

Abstract: The paper is about formalization of Set Theory and Elementary Algebra theorems in mathematics and their proofs in a new programming language called LEAN 4 Theorem Prover. The paper describes ...

Researchers at Stanford and Caltech have found some critical reasoning failures in advanced AI models. LLMs are great at recognizing patterns, but they have trouble with basic logic, social reasoning, ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

Get set theory explained in a clear and complete way, covering everything you need to know from basic definitions to key operations and ideas. This video walks through sets, subsets, unions, ...

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. All of modern mathematics is built on ...

"We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity," says Dr. Faizal. "Therefore, no physically complete and ...

This post was updated Aug. 31 at 7:59 p.m. Warning: Spoilers for R.F. Kuang’s “Katabasis” ahead. “Katabasis” is an intriguing book for academics but possibly a challenging journey for casual readers.

Terence Tao, one of the world’s foremost mathematicians, who is often called the “Mozart of Math,” would rather not talk politics. Subscribe to read this story ad-free Get unlimited access to ad-free ...

Russell has a PhD in the history of medicine, violence, and colonialism. His research has explored topics including ethics, science governance, and medical involvement in violent contexts. Russell has ...