The Shape That Can’t Pass Through Itself

Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s big enough for the other to slide through? It is — but what about other shapes? In a paper posted online in August, two researchers describe a shape with 90 vertices and 152 faces that they’ve named the Noperthedron, the first convex polyhedron that definitely cannot pass through itself. In this episode, Quanta contributor Erica Klarriech tells host Samir Patel about how the researchers discovered the shape, and how it solves a centuries-old geometric mystery. Audio coda courtesy of the Gemsmen Renaissance Consort.

Studies of neural metabolism reveal our brain’s effort to keep us alive and the evolutionary constraints that sculpted our most complex organ.The story How Much Energy Does It Take To Think? first appeared on Quanta Magazine.

Ask ChatGPT how to build a bomb, and it will flatly respond that it “can’t help with that.” But users have long played a cat-and-mouse game to try to trick language models into providing forbidden information. Just as quickly as these “jailbreaks” appear, AI companies patch them by simply filtering out forbidden prompts before they ever reach the model itself.Recently, cryptographers have shown how the defensive filters put around powerful language models can be subverted by well-studied cryptographic tools. In fact, they’ve shown how the very nature of this two-tier system — a filter that protects a powerful language model inside it — creates gaps in the defenses that can always be exploited. In this episode, Quanta executive editor Michael Moyer tells Samir Patel about the findings and implications of this new work.Audio coda courtesy of Banana Breakdown.

(This episode was first published in June 2025.)Changes in the number, shape, efficiency and interconnectedness of organelles in the cells of flight muscles provide extra energy for birds’ continent-spanning feats.This is the fifth episode of The Quanta Podcast. In each episode, Quanta Magazine editor in chief Samir Patel speaks with the minds behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

(This episode was first published in July 2025.) Where does gravity come from? In both general relativity and quantum mechanics, this question is a big problem. One controversial theory proposes that the force arises from the universe's tendency toward disorder, or entropy. In this episode, host Samir Patel speaks with contributing writer George Musser about the long-shot idea called "entropic gravity," which Musser covered in a recent story for Quanta Magazine.Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the minds behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.Audio coda provided by Cosmic Perspective.

By extending the scope of the key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a “grand unified theory” of math.The story The Core of Fermat’s Last Theorem Just Got Superpowered first appeared on Quanta Magazine.

We all know that hot coffee cools down. But quantum mechanics can enable heat to flow the “wrong” way, making hot objects hotter and cold objects colder. Now physicists think this might have an ingenious use. On this week’s episode, host Samir Patel speaks with writer Philip Ball about how a new "quantum demon” may allow information to be processed in ways that classical physics does not permit. 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.Audio coda by Forma, courtesy of Kranky. 

In math and science, knots do far more than keep shoes on feet. For more than a century, mathematicians have studied the properties of different knots and been rewarded by a wide range of useful applications across science. Classifying how some knots are different from others is an important part of this work. Earlier this year, two mathematicians found that a theory for how to differentiate between knots is false. In fact, they found infinitely many counterexamples that prove that this method for studying knots does not work the way it’s supposed to. In this episode, contributing writer Leila Sloman joins editor in chief Samir Patel to tell the story of how the unknotting number came unraveled.Audio coda courtesy of Zinadelphia.

When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science.The story How a Problem About Pigeons Powers Complexity Theory first appeared on Quanta Magazine.

Every summer since 1983, scientists at Crater Lake National Park have gathered data about the lake’s famous clarity. This past summer, Quanta contributing writer Rachel Nuwer journeyed with them as they conducted their annual tests. On this week’s episode, Nuwer and host Samir Patel discuss what gives the lake its vivid blue color, and what its data can tell us about the way water moves through a deep temperate lake.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.Audio coda recorded at Crater Lake National Park in July 2010 by the National Park Service Natural Sounds Program.