The original version of this story appeared in Quanta Magazine. In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was ...

LLMs have shown notable improvements in mathematical reasoning by extending through natural language, resulting in performance gains on benchmarks such as MATH and AIME. However, reinforcement ...

According to Jeff Dean on Twitter, mathematician Michel van Garrel highlighted how Google's latest Gemini Deep Think AI model successfully proved a mathematical conjecture using a novel methodology ...

One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of ...

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 ...

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 ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a decades-old mathematical puzzle believed to be true by leading experts in ...

Mathematics usually feels universal, certain, and free from drama. Numbers don’t pick sides, theories don’t hold grudges, and proofs don’t belong to nations, at least, that’s the idea. But math ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...