After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...

Turbulence is one of the least understood phenomena of the physical world. Long considered too hard to understand and predict mathematically, turbulence is the reason the Navier-Stokes equations, ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

There’s a curious contradiction at the heart of today’s most capable AI models that purport to “reason”: They can solve routine math problems with accuracy, yet when faced with formulating deeper ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

Suggested Citation: "3 Case Studies." National Academies of Sciences, Engineering, and Medicine. 2023. Artificial Intelligence to Assist Mathematical Reasoning ...

In the real world, probability is a tough thing to characterize. If I roll a die, what does it mean to say that it has a one-sixth chance of coming up 5? We say that the outcome is random because we ...