Well yes, but it takes a certain kind of instinct to take on that philosophical challenge, and again to guide your particular angles of attack on it. I took the

Well yes, but it takes a certain kind of instinct to take on that philosophical challenge, and again to guide your particular angles of attack on it. I took the question to be, within the framework of formalized math, how do people arrive at particular abstractions like groups? How do you pick the axioms and rules?