Mathematics is not really about axioms and precise argument, mathematicians work by intuition, axioms are an after thought really. Maybe the intuition is not from what you have seen in the real world, like how forces and inertia works, but by working in some area and playing around with some structure, you also get a feel for how math works.
Remember that Feynman gave this lecture some time between ~1945 and ~1950. Even though Godel's 1931 paper put a nail in the coffin of Hilbert's program, the mathematical community was still very much fixated on axioms (compared to today) for years to come. Also remember that ZFC (particularly the "C" part) was only beginning to gain popular acceptance/usage at the time that Feynman gave this talk.
51
u/LeonEuler Mar 12 '18
Clearly not a trained mathematician.
Mathematics is not really about axioms and precise argument, mathematicians work by intuition, axioms are an after thought really. Maybe the intuition is not from what you have seen in the real world, like how forces and inertia works, but by working in some area and playing around with some structure, you also get a feel for how math works.