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OpenAI's AI helped overturn a longstanding math conjecture by finding a counterexample, highlighting a powerful new way to ...

At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications. In 1931, by turning logic on itself, Kurt Gödel proved a pair ...

Metamathematics investigates the structure and limitations of mathematical theories, with proof theory focusing on the nature of formal proofs and the principles that govern them. In the context of ...

This article is from Proof Positive, our friendly math newsletter that's delivered to your inbox every Tuesday afternoon. Sign up today and read it first. My friends and colleagues often ask me to ...

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 ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

In a new book, the mathematical epidemiologist Adam Kucharski explains how certainty, even in math, can be an illusion. Nonfiction In a new book, the mathematical epidemiologist Adam Kucharski ...

Ananyo Bhattacharya is chief science writer at the London Institute for Mathematical Sciences and the author of The Man from the Future: The Visionary Ideas of John von Neumann. One of the biggest ...