> Math has a very rigid and easily enumerable space of possibilities (strings of symbols), so we call it "discovery", while cooking has an enormous space of possibilities (countless pieces of meat and vegetables, each unique in its configuration of atoms, etc.), so we call it "invention".

I think you've made a good point here.

Although, to nitpick a bit: Both spaces (cooking and maths) are infinite, and for most fields of math, uncountably infinite. The difference is in the numbers we are dealing with. For cooking, it's mixtures of trillions of molecules. For maths, it's usually in the order of thousands of symbols (although those ellipses do some infinitely heavy lifting!).