Sunday, December 09, 2018

Today's interesting idea: 4 colour theorem

Today I learned about the 4 colour theorem: Namely, that no more than four colors are required to color the regions of a map so that no two adjacent regions have the same color.  This was a major breakthrough because it was proven by a computer during times when computers weren't the main way people computed numbers and math.

The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken, and it was commonly called the Appel-Haken theorem.  Haken was a mathmatician who specialized in topology, especially 3-manifolds. (Who knew such an interesting, nerdy thing existed as a speciality?)

The thereom, according to wikipedia, states that "in graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, "every planar graph is four-colorable"




It's interesting that a large amount of contreversy around the theorem had to do with the way it was produced, as it was one of the forumlas that was set out in the list of mathmatical problems of the 20th century by David Hilbert, who was an influential mathmatician in his own right.

It cannot be overstated how important some of the scientific discoveries of the early 20th century were.  A lot of very important math was done, often in reference to Hilbert's problems.  We've only known about the atom in its structure for about the last hundred years, and quantum physics is still in its infancy.

However, this problem is an interesting one, and one I wasn't expecting to discover while researching 20th century science.