I would disagree there are quick and easy answers to the question of whether math is man-made or discovered. What is the qualitative difference between discover

I would disagree there are quick and easy answers to the question of whether math is man-made or discovered. What is the qualitative difference between discovery and invention? Consider the product of no factors being equal to the multiplicative identity. Is that a discovery or a choice made because it is more useful? Is it a discovery because we 'discovered' it was more useful?