Welcome to Quantum Magazine's podcast.

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

I'm Susan Vallett.

Mathematician Ben Green of the University of Oxford has made a major stride toward understanding a nearly 100-year-old combinatorics problem.

He's shown that a well-known recent conjecture is not only wrong, but spectacularly wrong,

as Andrew Granville of the University of Montreal put it.

The new paper demonstrates how to create much longer

disordered strings of colored beads than mathematicians had thought possible. It extends a line of

work from the 1940s that's found applications in many areas of computer science. That's next. Explore math mysteries in the Quanta book, The Prime Number Conspiracy, published by the

MIT Press, available now at Amazon.com, Barnes & Noble.com, or your local bookstore.

Also, make sure to tell your friends about the

Quantum Magazine Science podcast and give us a positive review or follow where you listen. It helps

people find this podcast.

The conjecture formulated about 17 years ago by the late mathematician Ron Graham concerns how

many red and blue beads you can string together without creating any long sequences of

evenly spaced beads of a single color. You get to decide what long means for each color.

The problem is one of the oldest in Ramsey theory, which asks how large various mathematical

objects can grow before pockets of order must emerge.

The bead stringing question is easy to state, but deceptively difficult.

For long strings, there are just too many bead arrangements

to try one by one. Jacob Fox, a mathematician at Stanford University, says it's a tantalizing

problem. He says sometimes there's these very basic-looking questions where we really don't

...