Von Neumann also got the priviledge later in his life to work with Einstien and Kurt Gödel while in New Jersey.
The joke about infinite sums is one of Von Neumann's associates asked him
>"Two trains are 20 miles apart on the same track heading towards each other at 10 miles per hour, on a collision course. At the same time, a bee takes off from the nose of one train at 20 miles per hour, towards the other train. As soon as the bee reaches the other train, it bangs huwey and heads off at 20 miles per hour back towards the first train. It continues to do this until the trains collide, killing the bee.
>How far will the bee have traveled?"
This is called a mathematicians trap. And its similiar to XKCD 356 (Nerd Snipping) [2]. There is a simple eloquent algebraic way to solve the problem, but it requires some insite. And there is a complex way involving summing an infinite series. Normally mathematicians end up preforming a very vast complex infinite series sum. [1]
When Von Neumann was asked the question it took him about 10 seconds to respond.
The associate who asked him stated, "Oh you must have heard the joke before."
To which Von Neumann responded, "No I just solved for the sum of the infinite series."
[1] http://thesciencepundit.blogspot.com/2006/07/john-von-neuman...