4 ms·
The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading: https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236 H
by BeetleB 2mo ago
The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading:
https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236
He wrote it in 1994.
He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field.
When he discovered this, he realized his error was that he was focusing on producing results, and not focusing on explaining his thought process. It's that thought process that is valuable in advancing the frontier - results alone won't do it. It didn't matter how many theorems he proved, if he was the only one who had the mental framework in mind on how to think about the whole field.
I'm sure we've come across abstruse books where every theorem has a rabbit being pulled out of a hat, whereas other readers find it intuitive. It's because the latter has developed a mental model for the discipline, and you haven't.
So he set about slowing down, and focusing on holding lots of seminars where he worked with other mathematicians to explain the thought process. Eventually others started publishing proofs of key theorems.
When people publish in a journal, they are not merely doing it to show the result. They are having a conversation with other mathematicians. If they cannot explain their own proof, they're not having a conversation.
This is why even decades after the Four Color Theorem was proved, plenty of mathematicians don't consider it "mathematics".
- a2ff6eeb0 2mo agoI don't understand why people are so fixated on the minds doing the mathematics being made out of meat. It seems obvious that soon, minds made of meat aren't going to be able to keep up. Useful thought, rather than hobbyist thought, seems destined to be the exclusive domain of silicon.
- BeetleB 2mo ago> I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. I don't follow - are you surprised that mathematicians have social rules on how they interact with others? You're definitely welcome to set up a journal that takes whatever types of papers you deem acceptable. It's not like they're preventing the dissemination of information by taking this stance. Personally, I wouldn't hire a SW engineer who only showcases output from LLMs, and can't explain the code it wrote.
- a2ff6eeb0 2mo agoWould you hire a SW engineer that only showcases output from compilers, and can't explain the assembly that it wrote? Since even the engineers that know what's going on aren't actually reading all of the AI output any more (or, if they are, they're not keeping up with their peer's output), why would you care? I don't think humans should waste time trying to understand their code, it's too slow and costly, and the understanding will be blown away the next time the AI changes it anyways. Software engineering is becoming pasting in vague-ish descriptions of what you want, and then manually testing that what the AI developed is close enough. It seems like math can go in the same direction too, with useful results that improve our technology getting put into a database for other AIs to consume. Removing humans from the loop can speed things up, especially as AI improves, especially when it reaches a self-improvement loop. As I keep saying, software is no longer skilled labor. Who knows, math may go in the same direction.
- addag 2mo ago[dead]
- demibabs 2mo ago> He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field. This is hilarious lmao