What's the difference between deciding if a mathematical statement is true VS proving it? Isn't a statement only true if you can prove it?
Edit: To elaborate, when reading about foundations of math, there seems to be concepts of completeness and decidability that seems to suggest they are proving and deciding if true are different...

My opinion is that there is sometimes theorems that work everytime but we still don't have a specific reasonable proof for (and they are quite rare). Also there is something called axioms that are agreed on to be true with no proof, just by convention (I know this is a little it bit different than "deciding" if it is true or not, but I am just giving some ideas that may help)
