Welcome to Quantum Magazine's podcast.

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

I'm Susan Vallett.

After breakfast one morning last summer, UCLA mathematician Terence Tau opened an email from three physicists he didn't know. In it, a surprise.

In the email, the three physicists explained to Tao that they'd stumbled across a simple formula.

If true, it established an unexpected relationship between some of the most basic and important

objects in linear algebra.

Tao, who's a Fields Medalist and one of the world's leading mathematicians, remember seeing

that email.

And I looked at it, and it looked too good to be true. Like something this short and simple, it should have been in textbooks already. There'd be a name attached to it, you know, so-and-so's role or whatever. So my first thought was, no, this can't be true. Tell thought about it some more. I couldn't immediately see whether it wasn't. I tried a few examples, and it worked out. And then I got intrigued.

It was close enough to something that I had already done. There's another identity that I knew about relating these quantities or something else, which I could use as a starting point.

And then I spent the whole morning just working it out.

The physicists who sent the email were Stephen Park of Fermi National Accelerator Laboratory,

Sheeneng Zhang of the University of Chicago,

and Peter Denton of Brookhaven National Laboratory. They'd arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

Park says they discovered it when they were building up to a very big experiment at Fermilab.

Sending a beam of neutrinos from Fermilab to South Dakota into a detector in a mine in South

Dakota, which is 1,300 kilometers through the Earth.

So we were trying to understand what happens to neutrinos as they pass through the Earth.

They'd noticed that hard-to-compute terms called eigenvectors,

describing in this case the ways that neutrinos

propagate through matter were equal to combinations of terms called eigenvalues, which are

...