Welcome to Quantum Magazine's podcast.

Each episode, we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

A new proof has debunked a conspiracy that mathematicians feared might haunt the number line.

In doing so, it's given them another set of tools for

understanding arithmetic's fundamental building blocks, the prime numbers. That's next.

Quantum Magazine is an editorially independent online publication supported by the Simon's Foundation

to enhance public understanding of science.

In a paper posted last March, Harold Helfgott of the University of Göttingen in Germany and Maxim Radzwell of Caltech

presented an improved solution to a particular formulation of the Chowla conjecture.

That's a question about the relationships between integers.

The conjecture predicts that whether one integer has an even or odd number of prime

factors doesn't influence whether the next or previous integer also has an even or odd number

of prime factors. Basically, nearby numbers don't collude about some of their most basic

arithmetic properties.

That seemingly straightforward inquiry is intertwined with some of math's deepest unsolved questions

about the primes themselves. Terence Tao is a mathematician at UCLA.

This is sort of considered a warm-up or a stepping sort of towards

things like the true-app conjection. And yet for decades, that warm-up was a nearly impossible

task itself. It was only a few years ago that mathematicians made any progress. That's when

Tao proved an easier version of the problem called the logarithmic chowla conjecture.

The technique he used was heralded as innovative and exciting.

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