Audio Edition: ‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard

In 2018, using the Keck Observatory in Hawaiʻi, astronomers discovered the first known dark matter-deficient galaxy, DF2. It’s about the same size as the Milky Way, but way dimmer, with 200 times fewer stars. Since then, two more phantom galaxies (DF4 and DF9) have been spotted. All three of these strange galaxies exist along a line. Why? On this episode of The Quanta Podcast, host Samir Patel speaks with writer Robin George Andrews about this triplet of ‘ghostly’ galaxies and what they can tell us about the mystery of dark matter. This topic was covered in a recent story for Quanta Magazine.  Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

The uncertainty principle tells us that the more you know about where a quantum particle is, the less you can know about how fast it’s moving, and vice versa. In 2023, graduate student Alex Cohen stunned the math world when he posted a proof of the fractal uncertainty principle. The math, which combines chaos, quantum theory, and infinitely complex fractal structures, has been called a “foundational result.”On this episode of The Quanta Podcast, host Samir Patel speaks with writer Shalma Wegsman on this incredible breakthrough and how this principle has revealed a new deep way that quantum particles differ from classical ones.This topic was covered in a recent story for Quanta Magazine.  Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

Determination and effort propelled Jacob Tsimerman to the top of the math world. But now that he’s won a Fields Medal, he worries that the field is in jeopardy.The article Sometimes Being First Means Seeing the End Before Anyone Else first appeared on Quanta Magazine.

Turbulence is all around us: bumping our planes, roiling our rivers, swirling milk into our coffee. These systems quickly become extremely chaotic and complex. On this episode of The Quanta Podcast, host Samir Patel speaks with contributing writer Stephen Ornes about a recent study that used sea monkeys to complicate one of turbulence’s many mysteries. This topic was covered in a recent story for Quanta Magazine.  Each week on The Quanta Podcast, hear the people behind the award-winning publication navigate through some of the most important and mind-expanding questions in science and math.We've been nominated for a few Signal Awards, including Best Science Show, Best Host, and Best Show Artwork! Visit the links below to vote for us:https://vote.signalaward.com/PublicVoting#/2026/shows/genre/sciencehttps://vote.signalaward.com/PublicVoting#/2026/shows/craft/best-show-artworkhttps://vote.signalaward.com/PublicVoting#/2026/shows/craft/best-host

You might imagine that the DNA in your cells has a simple history. But that’s not the entire story. Nearly half of your genome is a wild drama, thanks to a genetic material called transposons that can clip itself out of the DNA sequence, float off, and paste itself somewhere else. While these “jumping genes” may seem pathological, they’re more than just junk. On this episode of The Quanta Podcast, host Hannah Waters speaks with writer Jake Buehler about these unruly genetic fragments and their connections to the evolution of everything from moths to wombs.This topic was covered in a recent story for Quanta Magazine.  The audio coda this week is a piece of music called Transposon. It's a musical sonification of transposable elements from the human genome by composer and sound artist Sam Nester. He created it in collaboration with genomicist Stéphane Boissinot as part of a year-long artist-in-residence at the Center for Genomics and Systems Biology at NYU Abu Dhabi.Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

Focus, commitment, and insight resulted in a “once in a century” proof. Hong Wang is now just the third woman to win a Fields Medal.The article Living Fully in the Math World Means Threading the Needle first appeared on Quanta Magazine.

When all you can see is a speck, it’s hard to tell what you’re looking at. Astronomers first argued that little red dots spotted by the James Webb Space Telescope in 2022 were distant galaxies on the cosmic horizon, mainly because of their brightness. Later, they concluded that little red dots look more like the supermassive black holes that sit at the heart of most galaxies. But in the spring of 2025, two teams of astronomers simultaneously announced observations of a pair of little red dots that were unlike all the rest. In fact, they were unlike any object ever seen.On this episode of The Quanta Podcast, host Samir Patel speaks with writer Charlie Wood to talk about the new celestial body that may have just dropped, what some astronomers are calling “black hole stars.”This topic was covered in a recent story for Quanta Magazine.  Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.This week's coda is a sonification of data from a device known as the NIRSpec integral field unit on NASA's Webb telescope. Here, the pitch of the sound represents the velocity of hydrogen gas moving around the black hole. The higher the pitch, the faster it is moving toward the telescope. This data enabled the first direct mass measurement of a black hole from the first billion years of the universe.Coda Credit - Sonification: NASA, ESA, CSA, STScI, Christopher Britt (STScI), Ralf Crawford (STScI), Alyssa Pagan (STScI), Margaret Carruthers (STScI); Science: Ignas Juodžbalis (Cambridge), Cosimo Marconcini (University of Florence), Roberto Maiolino (Cambridge), Francesco D'Eugenio (Cambridge), Hannah Übler (MPE)

In 1852, the mathematician Francis Guthrie was coloring in a map of English counties when he noticed that he needed only four colors. Was this always true, he wondered? The question captured the imagination of hobbyists and professionals alike — and in 1976, the mathematicians Kenneth Appel and Wolfgang Haken proved it, rather controversially using computers. Recently, mathematicians have revisited the four-color theorem and found a more efficient way to color maps with just four colors.On this episode of The Quanta Podcast, host Samir Patel speaks with writer Greg Barber about the “four-color disease,” its history of false starts and dashed hopes, and what modern mathematicians have learned about graphs by revisiting this famous problem.This topic was covered in a recent story for Quanta Magazine.  Each week on The Quanta Podcast, Quanta Magazine editor-in-chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.The article ‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard first appeared on Quanta Magazine.

In popular culture, computer science is practically synonymous with programming. There are obviously branches of computer science in which computer hardware and software are essential, such as in the design of operating systems or the study of memory management. But in the theoretical side of the field, researchers need not ever touch a real, physical computer. Do computers play an essential conceptual role in that kind of theoretical work? On this episode of The Quanta Podcast, host Samir Patel wades into an age-old debate with writer Ben Brubaker: If computer science isn’t about computers, then what is it about?This topic was covered in a recent story for Quanta Magazine.  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.The audio coda clip comes from the Computer History Museum. The use of this audio clip shall not be used to show or imply CHM endorsements of any commercial product or enterprise, or to indicate that the CHM concurs with the opinions expressed in the podcast.