To come up with a result as weird as this, you need to be using some equally mind-bending math – and indeed, this paradox comes to us from the world of set theoretic geometry. If that’s not familiar ...

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?

For the last few years, chain-of-thought prompting has become the central method for reasoning in large language models. By encouraging models to “think aloud,” researchers found that step-by-step ...