Also known as conway: John von Neumann professor of math at Princeton. Really intelligent mathematician who sits around in his office all day and plays games. Discovered the surreal numbers (Donald Knuth wrote a great Alice and Bob dialogue on this) by watching Go. Nine in ten geeks have coded his Game of Life. Work is in combinatorics, knot theory, number theory, group theory, algebra, and logic.

John Conway also invented a mathematical notation, based on Donald Knuth's up arrow notation, called the chained up-arrow notation.

In the up-arrow notation, (a ↑ b) is to (a ^ b) as (a ^ b) is to (a * b), (a ↑↑ b) is to (a ↑ b) as (a ↑ b) is to (a ^ b), etc. Eventually, the ↑s get cumbersome, until you use the chained up-arrow notation.
For those of you with browsers that don't display the symbol properly, that ↑ is an upward-pointing arrow.

In the chained up-arrow notation, (a ↑ b) is written (a → b → 1), (a ↑↑ b) is written (a → b → 2), (a ↑↑↑ b) is written (a → b → 3), etc.
Those expressions with two terms have the ↑ up arrow symbol, the expressions with three terms have the → right arrow symbol.

(Extending this notation probably beyond what Conway intended, it could be argued that (a → b → 0) is (a ^ b), and (a → b → -1) is (a * b), and (a → b → -2) is (a + b).)