For a recent episode of Numberphile, David Eisenbud explains the Collatz Conjecture, a math problem that is very easy to understand but has an entire book devoted to it and led famous mathematician Paul Erdős to say “this is a problem for which mathematics is perhaps not ready”.
The problem is easily stated: start with any positive integer and if it is even, divide it by 2 and if odd multiply it by 3 and add 1. Repeat the process indefinitely. Where do the numbers end up? Infinity? 1? Loneliness? Somewhere in-between? My favorite moment of the video:
16. Whoa, a very even number.
I love math and I love this video. (via df)