Friday, September 16, 2016

Mathematics without proof

My 11-year-old complained to me that his mathematics teacher tells them things without proof. This made me realize that the sorts of things that he mentioned as given without proof--say, the distributive law and maybe some facts about prime factorization (maybe the Fundamental Theorem of Arithmetic? I can't remember)--were things that somehow no one ever showed me a proof of, either, despite getting an undergraduate degree in mathematics and then a PhD. So I can't just say: "Hold on, one day they will give you the proof of this."


SMatthewStolte said...

Maybe, “One day, you will be given enough tools to be able to prove this for yourself or at least to follow a proof that you can find online somewhere”?

Alexander R Pruss said...

True, though several years down the road one might forget that one hasn't seen the proof yet, and hence fail to seek it out.

Alexander R Pruss said...

I did tell him that there are axiomatizations of arithmetic that make the distributive law an axiom. But he prefers axiomatizations that use simpler principles. He's got good taste .