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 ...

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 ...

If you’re a hacker you may well have a passing interest in math, and if you have an interest in math you might like to hear about the direction of mathematical research. In a talk on this topic [Kevin ...

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 ...

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 ...

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 ...

Using words like ‘factors,’ ‘denominators’ and ‘multiples’ may be part of a constellation of good math teaching practices ...

The International Mathematical Olympiad (IMO) is probably the most prestigious competition for preuniversity students. Every year students from around the world compete for its coveted bronze, silver ...

A mathematical proof is a sequence of statements that follow on logically from each other that shows that something is always true. Using letters to stand for numbers means that we can make statements ...