### What proofs are (split from amusing test answers)

Posted:

**Mon Nov 26, 2007 8:52 pm UTC**I split this off the other thread because, as was pointed out, it had kind of diverged from the original intent. I don't know if the discussion will continue now that oxoiron seems to have given up, but figured I'd make the new topic. - gm

As a kid, I barely scraped by with a passing grade in geometry because I refused to do proofs. The conversation leading up to this refusal went something like this:

Teacher: Prove [some really obvious theorem] is true.

Me: That's silly. Anybody can see that is true. Why prove something when I already know it is true?

Teacher: Not everybody can see it as easily as you.

Me: O.K. How do I prove it?

Teacher: Prove it using postulates, like I showed you.

Me: How do I know that the postulates are true?

Teacher: We just accept that they are.

Me: That's stupid. Why do we just accept them?

Teacher: Because they are obviously true.

Me: So is [some really obvious theorem]. Why should I prove something that is obviously true using something that I just have to accept as being true? Why I can't I just accept that [some really obvious theorem] is true, too? What's the difference?

Teacher: Postulates are true because [blah, blah, I don't really know, I never thought about it before]. That is why we use them to prove theorems.

Me: The theorem is just as obviously true as the postulate and I refuse to use something that is unproven to prove something else. If you expect me to just accept one as being true because it is obvious, I see no reason why I shouldn't accept the other as being true when it is just as obvious.

Teacher: If you don't learn how to do this, it will haunt you later when you do higher math.

That never happened.

As a kid, I barely scraped by with a passing grade in geometry because I refused to do proofs. The conversation leading up to this refusal went something like this:

Teacher: Prove [some really obvious theorem] is true.

Me: That's silly. Anybody can see that is true. Why prove something when I already know it is true?

Teacher: Not everybody can see it as easily as you.

Me: O.K. How do I prove it?

Teacher: Prove it using postulates, like I showed you.

Me: How do I know that the postulates are true?

Teacher: We just accept that they are.

Me: That's stupid. Why do we just accept them?

Teacher: Because they are obviously true.

Me: So is [some really obvious theorem]. Why should I prove something that is obviously true using something that I just have to accept as being true? Why I can't I just accept that [some really obvious theorem] is true, too? What's the difference?

Teacher: Postulates are true because [blah, blah, I don't really know, I never thought about it before]. That is why we use them to prove theorems.

Me: The theorem is just as obviously true as the postulate and I refuse to use something that is unproven to prove something else. If you expect me to just accept one as being true because it is obvious, I see no reason why I shouldn't accept the other as being true when it is just as obvious.

Teacher: If you don't learn how to do this, it will haunt you later when you do higher math.

That never happened.