On Incompleteness

Simon is enchanted by Gödel’s incompleteness theorem (that he has learned about from Numberphile) and keeps talking about it:

“There’re problems that we just can’t solve. But if we prove that we can’t prove them, then we prove them! We can’t prove that we can’t prove that we can’t prove, and so on… Quirky! Standard math doesn’t really accept that because the statement goes on forever: you’ll just never get to what we can’t prove. What follows from Gödel’s incompleteness theorem is that that statement is actually true!”

The same evening, Simon is also bothered about the lies pupils are told in school. He repeatedly quotes James Grime that it’s a big lie that mathematics is about numbers. — “What is mathematics about? Mathematics is actually about proving! But there’s one more lie that even professional mathematicians don’t know. It’s that it’s about logic. Actually, mathematicians are a lot more creative!”