Today is π-day (3/14) as well as Albert Einstein’s birthday. I was trying to get inspired to produce something pi related, so I scanned my bookshelves for the kind of fun recreational mathematics books that provide the raw grist for my geek mill. I found a copy of Peter Beckmann’s A History of Pi, which I remember cracking open a few times, but which I had not read in a while. I briefly flipped through the pages, looking for something interesting, and on page 113 found something that didn’t seem pi-related, but nevertheless caught my eye:
Even today there are many statements that are “true” by physical standards of experience, but that remain mathematically unproven. Two of the most famous are the Goldbach conjecture and the four color problem. … The other well known problem, the so-called four-color problem, is to prove that no matter how a plane is subdivided into non-overlapping regions, it is always possible to paint the regions with no more than four colors in such a way that no two adjacent regions have the same color. By experience, the trueth of the assertion is known to every printer of maps (common corners, like Colorado and Arizona, do not count as adjacent.) And no matter how one tries to dream up intertwining states on a fictitious map (see figure above), four colors always appear to be enough. But there is no proof.
That set me dashing to the front of the book to find out when it was published. It turns out it was 1971. But I remember reading the announcement of the proof of the four color theorem by Appel and Hacken in the pages of Scientific American as a young teen. In celebration of their achievement, the University of Illinois began using the postmark shown above (replacing their previous famous example declaring that 2^11213-1 is prime). The discovery was significant not just for it’s intrinsic value, but also because it was the first instance where computers assisted in proving a mathematical theorem. Very cool.
Beckman’s book is actually pretty interesting, but kind of fades out at the end when discussing computer attempts at computing pi. The record at that point stood at about 500,000 digits of so, although Beckmann said that “this record will, no doubt, eventually be broken”.
And it has. Not just broken, but obliterated.