I was reading Sturmfel's paper about how biology leads to math. He mentioned that " Many of the most exciting developments in current mathematics are a direct outgrowth of research in theoretical physics. Today’s geometry and topology are unthinkable without string theory, mirror symmetry and quantum field theory." What does he mean by "today math is unthinkable without physics?" Does he mean we can't do pure math at all without the help of physics?
Also, it seems that a field outside of math, be it physics or biology or any subject, provides motivation and insight for pure math rather than direct tools. Is it reasonable to think this way? (For example the theorems that Sturmfel outlined in the paper are still math theorems with motivation from biology rather than using a specific phenomenon/concept in biology to prove a math theorem.)