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 ...

Math students may not blink at calculating probabilities, measuring the area beneath curves or evaluating matrices, yet they often find themselves at sea when first confronted with writing proofs. But ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...