More often than I’d like to admit when reading XKCD, I don’t get the joke. Most of the time I understand the basic concept, but there’s clearly more to it that I don’t understand. Take for instance, this comic. Haha, funny right? Zombies are walking the earth, and he’s asking for a signature. Hilarious!

Except I’ve never heard of Paul Erdős, so really, I don’t get it.  Fortunately, when this happens, the answer can usually be found via a quick search on google or wikipedia.

For those of you in a similar predicament, here’s the relevent text from Paul Erdős Wikipedia entry:

Throughout his career, Erdős would offer small prizes for solutions to unresolved problems. These ranged from $25 for problems that he felt were just out of the reach of current mathematical thinking, to several thousand dollars for problems that were both difficult to attack and mathematically significant. There are thought to be at least a thousand such outstanding prizes, though there is no official or comprehensive list. These prizes are still active despite Erdős’ death – Ron Graham is the (informal) administrator of solutions. Winners can either get a check signed by Erdős (for framing only) or a cashable check from Graham.^[22]

Perhaps the most famous of these problems is the Erdős conjecture on arithmetic progressions:

If the sum of the reciprocals of a sequence of integers diverges, then the sequence contains arithmetic progressions of arbitrary length.

If true, it would solve several other open problems in number theory. The problem is currently worth US$5000.^[23]