I would say the most important idea in math is logic. Of course, fix points do play an important role in logic as well. For example, Cantor's theorem means that

I would say the most important idea in math is logic. Of course, fix points do play an important role in logic as well. For example, Cantor's theorem means that it really makes no sense when studying a mathematical universe, to try to include all operators on that mathematical universe in the mathematical universe as well. Which is what all type theories are trying to do. Of course, it is impossible, so all that type theories are doing is cutting the mathematical universe into disjoint pieces.