I like the reframe. The part I best like is the removal of the illusion of certainty.
I don’t know if describing proofs as just evidence really captures it though. In many cases the point of a proof isn’t just to know that the statement is one you can rely on. It’s also to show you why you can rely on it. The process of understanding a proof can teach you something about how math works. The effect is stronger if you produce a proof.
Agreed! That’s definitely and important point, and one reason why it’s still interesting to try to prove P \neq NP. The point I was making here was only that when proofs are used for the “certainty” that they give, then strong evidence from other ways is also enough to rely on the proposition.
I like the reframe. The part I best like is the removal of the illusion of certainty.
I don’t know if describing proofs as just evidence really captures it though. In many cases the point of a proof isn’t just to know that the statement is one you can rely on. It’s also to show you why you can rely on it. The process of understanding a proof can teach you something about how math works. The effect is stronger if you produce a proof.
Agreed! That’s definitely and important point, and one reason why it’s still interesting to try to prove P \neq NP. The point I was making here was only that when proofs are used for the “certainty” that they give, then strong evidence from other ways is also enough to rely on the proposition.
Yep, agreed. I thought it was a very clever point!