A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.” Within a month, a loose collaboration verified it ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...

A basic feature of number theory, prime numbers are also a fundamental building block of computer science, from hashtables to cryptography. Everyone knows that a prime number is one that cannot be ...

The original version of this story appeared in Quanta Magazine. A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime ...

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 ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

Mathematicians sometimes think of their research as a garden and unsolved problems as seeds waiting to sprout. Some problems are analogous to tulip bulbs. As mathematicians work to solve them, they ...

Most people learn to count and do basic arithmetic at a young age and don’t give these skills a second thought. But numerosity or numeracy, the ability to think about and use numbers, is more than a ...