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.

How do sellers decide how to price their goods? Competition should keep prices down, while collusion can rig higher prices (and break the law). On this week’s episode, host Samir Patel speaks with staff writer Ben Brubaker about how computer scientists are using game theory to see how algorithms might result in high prices without shady backroom deals. 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.

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Audio coda from FDR Presidential Library & Museum.

At first glance, studying the math of waves seems like it should be smooth sailing. But the equations that describe even the gentlest rolling waves are a mathematical nightmare to solve. On this week’s episode, host Samir Patel speaks with math staff writer Joseph Howlett why waves are so elusive, even in a simplified world of equations. 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 is "The Merry Golden Tree" by Shovel Dance Collective.

Salvador Dalí, Thomas Edison and Edgar Allan Poe all took inspiration from the state between sleep and waking life. On this week’s episode, host Samir Patel speaks with biology staff writer Yasemin Saplakoglu about how brain systems dictate the strange transitions into and out of sleep. 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: Copyright in The Mike Wallace Interview with Salvador Dalí is owned by the University of Michigan Board of Regents and managed by Bentley Historical Library, University of Michigan. The Harry Ransom Center (HRC) at the University of Texas, Austin University Libraries, is the owner of the physical kinescope.