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."

3 comments:

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 .