a combinatorial game is a two-player game with perfect information and no chance elements. the players take turns making moves under clearly defined rules, and the last player able to make a move wins the game. nim is one of the most well-known combinatorial games, and many people know that optimal play in nim involves an addition operation which is just an xor operation in disguise. nim has a richer structure than this, however, as there is also a multiplication operation, and some unexpected and delightful things pop up such as fermat powers (numbers of the form $2^{2^n}$). we'll explore nim fields -- finite fields of objects that aren't numbers, but nimbers, and really bizarre things happen -- even if i could convince you that 4 times 4 is 6, could you ever believe that the cube root of the nimber 2 is infinity? \vskip .1in \noindent refreshments will be served!