>>12603200Ron Maimon copypasta:
There are things that are discovered, and things that are invented. The boundary is put at different places by different people. I put myself on the list and I believe that my position is objectively justifiable, and others are not.
>Definitely discovered: finite stuffBy probablistic considerations, I am sure that nobody in the history of the Earth has ever done the following multiplication: 9306781264114085423 x 39204667242145673 = ?
Then if I compute it, am I inventing it's value, or discovering the value? The meaning of the word "invent" and "discover" are a little unclear, but usually one says discover when there are certain properties: does the value have independent unique qualities that we know ahead of time (like being odd)? Is it possible to get two different answers and consider both correct? etc.
In this case, everyone would agree the value is discovered, since we actually can do the computation--- and not a single (sane) person thinks that the answer is made up nonsense, or that it wouldn't be the number of boxes in the rectangle with appropriate sides, etc.
There are many unsolved problems in this finite category, so it isn't trivial:
>Is chess won for white, won for black, or a draw, in perfect play?>What are the longest possible Piraha sentences with no proper names?>What is the length of the shortest proof in ZF of the Prime Number Theorem? Approximately?>What is the list of 50 crossing knots?You can go on forever, as most interesting mathematical problems are interesting in the finite domain too.