- A chess problem is genuine mathematics, but it is in some way ‘trivial’ mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better. [...] We may say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advance in mathematics itself and even in other sciences. No chess problem has ever affected the general development of scientific thought: Pythagoras, Newton, Einstein have in their times changed its whole direction.
- Is there a chess position with a finite number of pieces on the infinite chess board Z2 such that White to move has a forced win, but Black can stave off mate for at least n moves for every n?
1) Se gärna min uppsats Objective Truth versus Human Understanding in Mathematics and in Chess, publicerad 2007 i tidskriften med det charmerande namnet The Montana Mathematics Enthusiast, för andra synpunkter på förhållandet mellan schack och matematik.
2) Eller, med mer kortfattad matematikerjargong: Att svaret på Johans fråga måste vara nej följer av kompakthet.