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.