OpenAI announced this week that one of its general-purpose reasoning models made a breakthrough that has grabbed the ...

Research in mathematics is a deeply imaginative and intuitive process. This might come as a surprise for those who are still recovering from high-school algebra. What does the world look like at the ...

In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...