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.