Usually the way things work is that mathematicians make math discoveries, and physicists borrow and adapt those ideas to explain the universe. But three physicists at the University of Chicago and two national laboratories have discovered a fundamental identity in linear algebra—based on studying particle physics.

Three theoretical physicists—Peter Denton, a scientist at Brookhaven National Laboratory and a scholar at Fermilab’s Neutrino Physics Center; Stephen Parke, theoretical physicist at the UChicago-affiliated Fermi National Accelerator Laboratory; and Xining Zhang, a University of Chicago graduate student working with Parke—were investigating the properties of neutrinos, a type of particle that interacts so rarely with matter that trillions of them zip through your body every day without you noticing.

As they travel, neutrinos flip back and forth between different types, or “flavors.” Scientists describe these oscillations using a type of mathematical expression called eigenvectors and eigenvalues.

Eigenvectors and eigenvalues are two important ways of reducing the properties of a matrix to their most basic components and have applications in many math, physics and real-world contexts. The eigenvectors identify the directions in which a transformation occurs, and the eigenvalues specify the amount of stretching or compressing that occurs.

Denton, Parke and Zhang’s formula, however, relates eigenvectors and eigenvalues in a direct way that hadn't been previously recognized.