Exploring Turing Machines and the Halting Problem

The Busy Beaver Challenge, an open online collaboration, started in 2022 to finally solve a major problem in theoretical computer science. Over time, the online community grew to include more than 20 contributors from around the world, most of them without traditional academic credentials. In July 2024, the group announced that they finally solved the puzzle, bringing a conclusion to over 40 years of effort.

On this week’s episode of The Quanta Podcast, computer science staff writer Ben Brubaker explains the tantalizing Busy Beaver puzzle, which he covered in depth last year, in "With Fifth Busy Beaver, Researchers Approach Computation’s Limits."

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.