To make progress on one of number theory’s most elementary questions, two mathematicians turned to an unlikely source.

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 and 1 — are the most fundamental building blocks in math. They’re also the most mysterious. At first glance, they seem to be scattered at random across the number line. But of course, the primes aren’t random. They’re completely determined, and a closer look at them reveals all sorts of strange patterns, which mathematicians have spent centuries trying to unravel. A better understanding of how the primes are distributed would illuminate vast swaths of the mathematical universe.

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Now, two mathematicians — Ben Green of the University of Oxford and Mehtaab Sawhney of Columbia University — have proved just such a statement for a particularly challenging type of prime number. Their proof, which was posted online in October, doesn’t just sharpen mathematicians’ understanding of the primes. It also makes use of a set of tools from a very different area of mathematics, suggesting that those tools are far more powerful than mathematicians imagined, and potentially ripe for applications elsewhere.

“It’s terrific,” said John Friedlander of the University of Toronto. “It really surprised me that they did this.”

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