(Phys.org) —Sometimes mathematical theories have implications that extend far beyond their original purpose. This situation holds true for the four-color theorem, which was originally used by ...

Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...

Kenneth Appel, 80, who successfully brought the computer to bear on a celebrated mathematical problem that, in its capacity to perplex, tantalize and frustrate, conformed to a common view of ...

Kenneth Appel (1932-2013) together with Wolfgang Haken, proved the four color theorem and broke new ground in using a computer to complete the proof. For the first time a computer played a major role ...

This video explores why the Navier-Stokes equations are so difficult, what it means for their solutions to blow up, and how a new AI-assisted proof is reshaping one of mathematics’ most famous ...

Four Color Theorem,' which states that any map can be colored using only four colors, ensuring that no two adjacent regions are the same color. This proof also utilizes computers, but by focusing on a ...