Welcome to Quantum Magazine's podcast. Each episode, we bring you stories about developments in science and mathematics. I'm Susan Vallett. In the mid-1980s, mathematician Jean Bourgain thought up a simple question about high dimensional shapes, and

then he remained stuck on it.

For the rest of his life, it was one of the most important problems in high dimensional convex

geometry, and now a postdoctoral statistician has solved it.

That's next.

Explore more 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.

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Jean Borgon was one of the preeminent mathematicians of the modern era.

He died in 2018, having won most of the top awards in the field.

He was known as a problem solver extraordinaire, the kind of person you might talk to about

a problem you'd been working on for months,

only to have him solve it on the spot. Yet, Borgon could not answer his own question about

high-dimensional shapes. Sebastian Bubek is with Microsoft research in Redmond, Washington.

Borgain was one of the strongest mathematician of his generation,

or maybe the strongest of his generation, Phil's medalist, etc.

And Bourguin had said that he had worked on the hyperplane conjecture

more than any other topic, any other problem,

and he was stuck at end to the one force on the hyperplane conjecture.

In the years since Borgon formulated his problem, it's become what some mathematicians

have called the opening gate to understanding a wide range of questions about high

...