[math-ias]

I believe knowing a proof exists will bring us closer to elegant human proofs.

I wanted to justify this with the “Roger Bannister Effect”. The thought is that we’re held back psychologically by the idea of the impossible. It takes one person to do it. And now everyone can do it, freed from the mind trap. But further reading shows we were incrementally approaching what Roger Bannister did first: the 4 minute mile. And the pause before that record was likely not psychological but physical with World War Two. [0] And this jives with the TFA when Mr. Wolfram writes about a quarter of a century not yielding a human interpretation of his computer’s output.

All I’m left with is my anecdotes. I had a math professor in college who assigned homework every class. Since it was his first time teaching, he came up with the questions live. I’d come to class red in the face after struggling with questions all night. Then the professor would sheepishly reveal some of his statements were false. That unknown sapped a lot of motivation. Dead ends felt more conclusive. Falsehood was an easy scapegoat.

[0] https://www.scienceofrunning.com/2017/05/the-roger-bannister...

[QuesnayJr]

I think there is something to this idea. There have been cases where person A was working on proving a result but struggled, then person B announced a proof of the result, and then person A was inspired to finish their proof. (Sadly, I don't remember the specifics.)