Earlier quoted context omitted.
Even if you use AI tools?
Yes. But you’ll spend more in tokens than you’ll get back from prize money.
Some people might be on the ChatGPT Pro subscription plan or consuming their employer’s tokens.
The Maxwell Conjecture Is False (GPT 5.6 Sol)
51–60 of 149 posts
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#52Earlier quoted context omitted.
I’m pretty sure “counterexample” is the wrong word here.
Isn't it a bit Catch 22 anyway? If someone finds a algorithm to reduce some NP task X to class P, then that just means X wasn't a true NP task and P!=NP is still undecided?
If it’s an NP-complete [0] problem like SAT, as many NP problems are, then we are done, because all NP problems can be reduced to it (in polynomial time).
[0] https://en.wikipedia.org/wiki/P_versus_NP_problem#NP-complet...
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#53Tip for smart science-y young people: think about a career in experimental physics. Experimental data is the complement of theoretical power. Since theory can be provided cheaply by LLMs, experimental ability is now the bottleneck for progress in physics. I expect to see frontier labs or startups hiring experimentalists to provide data for LLMs to analyze, pushing towards breakthroughs in areas like room-temperature…
Politely, absolutely not. Physics as a domain is a nightmare. Even the employment statistics are hard to understand because, like Philosophy, only the best of the best pursue it. I've had countless friends throughout my PhD studies tell me that their decision to pursue a PhD in Physics ruined their lives. (Which is an exageration, but you get the point.) The bottom line is that you should pusue Physics only if you st…
At least in europe you can do a 3 year Eng Phys BSc and if it doesn't pan out you can do a master in EE or MEng.
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#54Not to denigrate the moment (AI ingress into theory which this is a part of) or the result here, but these headlines are perhaps overstating the importance - some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important. Maxwell's name being invoked here for instance implies a hundred year old foundational problem like Fermat, but it's just a recent…
Yeah, the Jacobian conjecture counter-example was big news. In particular, it would have been news even if an AI hadn't done it. That's where the bar is now. Settling Erdős conjecture 7529 or whatever no longer qualifies as AI news.
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#55[dead]
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#56Earlier quoted context omitted.
Politely, absolutely not. Physics as a domain is a nightmare. Even the employment statistics are hard to understand because, like Philosophy, only the best of the best pursue it. I've had countless friends throughout my PhD studies tell me that their decision to pursue a PhD in Physics ruined their lives. (Which is an exageration, but you get the point.) The bottom line is that you should pusue Physics only if you st…
At least in europe you can do a 3 year Eng Phys BSc and if it doesn't pan out you can do a master in EE or MEng.
[deleted]
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#57Tip for smart science-y young people: think about a career in experimental physics. Experimental data is the complement of theoretical power. Since theory can be provided cheaply by LLMs, experimental ability is now the bottleneck for progress in physics. I expect to see frontier labs or startups hiring experimentalists to provide data for LLMs to analyze, pushing towards breakthroughs in areas like room-temperature…
Politely, absolutely not. Physics as a domain is a nightmare. Even the employment statistics are hard to understand because, like Philosophy, only the best of the best pursue it. I've had countless friends throughout my PhD studies tell me that their decision to pursue a PhD in Physics ruined their lives. (Which is an exageration, but you get the point.) The bottom line is that you should pusue Physics only if you st…
i would make a similar argument for entrepreneurship and most things: do it only if you can’t bear the thought and reality of doing something else.
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#58It is mathematical folklore that one should attempt to prove a conjecture by day, disprove it by night. Jordan Ellenberg recently popularized this in his 2014 book. He and I both heard this from Barry Mazur, but it dates at least to Bing, if not antiquity. What is the purpose of mathematics? To be the architect of new conventions by seeing clearly past the old? If so, believing that the entire point is proving statem…
Could you expend on what you mean? I don’t have a math background and don’t really understand your comment
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#59Tip for smart science-y young people: think about a career in experimental physics. Experimental data is the complement of theoretical power. Since theory can be provided cheaply by LLMs, experimental ability is now the bottleneck for progress in physics. I expect to see frontier labs or startups hiring experimentalists to provide data for LLMs to analyze, pushing towards breakthroughs in areas like room-temperature…
Only theory that is a convex combination of existing theory. Any paradigm shift is currently unreachable to LLMs and can be only obtained by luck with RL due to the curse of dimensionality.
Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)
#60Not to denigrate the moment (AI ingress into theory which this is a part of) or the result here, but these headlines are perhaps overstating the importance - some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important. Maxwell's name being invoked here for instance implies a hundred year old foundational problem like Fermat, but it's just a recent…
Yeah, the Jacobian conjecture counter-example was big news. In particular, it would have been news even if an AI hadn't done it. That's where the bar is now. Settling Erdős conjecture 7529 or whatever no longer qualifies as AI news.
Real talk.
AI solving these makes me feel like mathematicians put far more importance on their work than was actually there. Many solutions seems to be tautological games, and games of logic where conjecture puzzles that few work on or care can be solved by AI which doesn’t care what it works on.
It seems to always be some form of this:
Mathematician: “Propose conjecture a and conjecture b can’t be true simultaneously”
AI: “they can”
Everyone: “ok…”
I know this might be unfair or out of ignorance but it genuinely is how this field feels today. Games of games with self importance added in.
Edit: the point I should have made is, should we be using AI to figure out what proofs MATTER now vs games of proofs?