(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 ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American Wrong in Public is a new, hopefully very ...

Mathematicians decided early on that strict rules must be imposed on mathematical proofs otherwise we may have a proof that does not match with the actual truth. The four color theorem is believed to ...

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 ...

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 ...

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 ...

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 ...

Imagine you're a mapmaker, ready to finish your masterpiece map of the world. The only thing left to do is add the colors. But how many colors do you need for the countries if you want to make sure no ...