Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers. The change of plans came on a road trip. On a beautiful day last April, the ...

Since ancient Greece, researchers have tried to isolate special rational points on curves. Now they have the first ever formula that applies uniformly to all curves ...

Sometimes work in one discipline of pure mathematics has a completely unexpected payoff in another. Some of the famous mathematician Pierre de Fermat’s (1601–1665) work in number theory bears this out ...

Prime numbers are sometimes called math’s “atoms” because they can be divided by only themselves and 1. For two millennia, mathematicians have wondered if the prime numbers are truly random, or if ...

A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime numbers. The primes — numbers that are only divisible by themselves ...

Imagine spinning a top and then letting it come to rest. Is there a way for you to spin the top again so it ends up in the exact position it started, as if you had never spun it at all? Surprisingly, ...

AI tools developed by Google DeepMind are surprisingly effective at assisting mathematical research and could usher in a wave of AI-powered mathematical discovery at a previously unseen scale, say ...