Can you fill in any map with just four colors? The so-called Four-Color theorem says that you can always do so in a way that neighboring regions never share the same color. But a proof eluded mathematicians for more than a century before Wolfgang Haken and Kenneth Appel controversially used a computer to show it must be true. This breakthrough forever changed mathematics.

Featuring David S. Richeson, Professor of Mathematics and the John J. & Ann Curley Faculty Chair in the Liberal Arts, Dickinson College

Read the full article at Quanta Magazine: https://www.quantamagazine.org/only-c...

Learn more about graph theory: https://www.quantamagazine.org/tag/gr...

00:00 What is the to the Four Color Problem
01:12 Historical origins of the map coloring theorem
01:49 Kempe's first proof techniques using planar graphs and unavoidable sets
04:49 Heawood finds a flaw in Kempe's proof
05:49 How Appel and Haken used a computer to verify their proof
08:15 Applications of the proof in the study of network theory

- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook:   / quantanews  
- FOLLOW us Twitter:   / quantamagazine  

Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/

#math #proof #computerscience