The problem of the proof was that we knew that FCT was true, but we had no idea why. A good/elegant proof teaches us something new about how that problem is related to other problems. It isn't just about getting a true/false answer to the conjecture.
Indeed, and the computer aided proof discouraged research into the insightful proof a lot of mathematicians think is probably out there to find. "Proved but not insightfully" is a problem status some mathematicians are starting to think of as closer to "open" than "closed", which is a good thing IMO. (I am not a mathematician, though)
Maybe the new heuristic auto tactics will lower the cost of finding the human proof of the four color theorem enough to be affordable in the current environment.
But people think it does, and it’s annoying. The past months I’ve often found mistakes and then heard the response along the lines of “oh Claude wrote that”.
It’s used as an excuse, and then the conversation just moves on. I don’t see a lot of accountability being taken. If anything, senior leadership sees it as a sign of adoption and accepts a certain level of risk.
The problem of the proof was that we knew that FCT was true, but we had no idea why. A good/elegant proof teaches us something new about how that problem is related to other problems. It isn't just about getting a true/false answer to the conjecture.
Indeed, and the computer aided proof discouraged research into the insightful proof a lot of mathematicians think is probably out there to find. "Proved but not insightfully" is a problem status some mathematicians are starting to think of as closer to "open" than "closed", which is a good thing IMO. (I am not a mathematician, though)
Maybe the new heuristic auto tactics will lower the cost of finding the human proof of the four color theorem enough to be affordable in the current environment.
> "The problem of the proof was that we knew that FCT was true"
Citation needed.
the title made me think of a much older machine that was used for calculating
https://en.wikipedia.org/wiki/Antikythera_mechanism
I think a lot of great ideas like tree-width were developed in hope of simplifying the proof.
I didn’t know we had invented time machines yet. ;)
I think the same happens now with AI generating code. Nobody will read every line. that's part of the process from now on.
The human who commits a bad change still takes the fall though. Automation doesn't absolve accountability.
But people think it does, and it’s annoying. The past months I’ve often found mistakes and then heard the response along the lines of “oh Claude wrote that”.
It’s used as an excuse, and then the conversation just moves on. I don’t see a lot of accountability being taken. If anything, senior leadership sees it as a sign of adoption and accepts a certain level of risk.