In the field of harmonic analysis, there’s a constellation of questions about how the energy of a wave concentrates.

Earlier this year, a 17-year-old high school student named Hannah Cairo solved a 40-year-old mystery about how some of these waves behave, surprising and exciting mathematicians. Cairo has not yet obtained a high school or undergraduate degree, but she recently began a doctoral program at the University of Maryland to continue her already impressive career studying mathematics. In this week's episode, math editor Jordana Cepelewicz joins host Samir Patel to discuss the significance of Cairo's proof.

Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.