Today in multivariable calculus, we had a discussion about this great article on The Paradox of Proof. I wish I had allotted more than 30 minutes for it. It brought up some interesting things and we could have talked about tons more things. I’m going to brainstorm some of them in case I ever do this again with a class!
Godel’s Incompleteness Theorem. If math is a social construct. The professional responsibility of being a mathematician (or in any profession). The proof (and controversy over the proof) of the four color theorem. The importance of clarity in math writing. Axioms. Andrew Wiles and Fermat’s Last Theorem. Gregori Perelman and the Poincare Conjecture. The Millennium Problems and Hilbert’s Problems. What makes a problem important? The trope of the madman/loner/crazy mathematician – in popular media and in films. If everyone in the world agrees about a mathematical statement, does it make it true? What if one person disagrees? What if all humankind were destroyed — would a proof still be true? When does a conjecture become a proof? Why do mathematicians do what they do — why do they devote their lives to doing math?