We were discussing this on the train to work the other morning. Any definition of maths must include the process of determining relationships between entities. However I believe, as the banner on the home page of this website says, that the heart of mathematics consists of concrete examples. Therefore, I think I can show that the answer to the question "Is Sudoku maths?" is a resounding "Yes".

For a given puzzle, which the setter has declared to be solvable, there is no more information in a completed, "solved" grid than in the "unsolved" grid. Therefore for an experienced practioner there is nothing to be learnt from solving the puzzle. However they are exercising a concrete example and applying relationships they have learnt on previous puzzles. Therefore it is still maths.

For the novice, the answer is an even more emphatic yes. Very few people are able to infer all the rules and techniques which lead to a solution the first time they try a puzzle. Indeed, different puzzles often require different techniques (as witnessed by the varying levels of difficulty applied by the setters). Therefore with each new puzzle the novice is determining the relationships which lead to a solution, and in so doing they are undertaking the purest form of maths.

This website delights in new proofs of planar geometrical identities. Yet in a sense they are pointless - Euclid defined the propositions which define planar geometry, so why bother. The answer is that maths is all about new relationships and every true mathematician delights in finding out new relationships, particularly between ideas they thought they understood well. Why, then, would we want to deny that opportunity to the wider population?