Longer than you or anyone else will live!
Thanks to Godel, there are statements about mathematical systems such that neither they, not their negation, can ever be proven to be true. This allows a whole new family of mathematical thinking to develop.
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mathematics is a hard subject and that's all
As far as I know, there is no difference. "Math" is just short for "Mathematics".
The German mathematician Carl Friedrich Gauss described mathematics one correctly as the quenn of all sciences. The German philosopher Immanuel Kant once remarked that one can only call a discipline a science as long as there is mathematics in it. Mathematics is the most basic science, because every other science (physics, chemistry, biology, geology, computer science) uses mathematical theorems to answer questions in this science. Mathematics does not depend on any other science. Mathematicians do mathematics for the sake of mathematics. That is why mathematics is the most fundamental science.
To bad those are all contributions to physics, not mathematics.
They are running businesses, so that can involve a lot of mathematics. The skills needed to cut hair, and even things like how much materials to use, how long to leave hair when cutting and so on, all involve mathematics.