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The Maxwell Conjecture Is False (GPT 5.6 Sol)

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Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#71

Post by l33tman »

pdhborges wrote: post #53
ComputerPerson wrote: post #47

Earlier 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.

The engineering programs and their curriculums are very different from physics in the science faculties (which I guess was the context here)

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#72

Post by julianeon »

ashleyn wrote: post #43
mellosouls wrote: post #29

Not 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…

They might be low-hanging fruit but two things immediately come to mind: * As more of the small stuff is just proven for free, the more they can be used as a basis for other proofs. If you know something is true or false for certain, that can be a significant tailwind for the much harder, much more important problems. Fermat's last theorem looks deceptively simple and invited many failed amateur attempts at solving i…

Is the bar really higher? Those math PhD's can use GPT too; they benefit equally from AI assistance.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#74

Post by drob518 »

ComputerPerson wrote: post #47
d_burfoot wrote: post #25

Tip 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…

My university had a great Physics department (Nobel laureate level), but every year you’d have a bunch of junior year (year 3) physics students desperately trying to switch into engineering as they realized that making a go of a pure physics degree was going to be more difficult. It was a consistently repeating pattern.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#75

Post by piloto_ciego »

d_burfoot wrote: post #25

Tip 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…

ITT: people who think there’s going to be jobs.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#76

Post by qrios »

storus wrote: post #59
d_burfoot wrote: post #25

Tip 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.

The term “currently” is the sticking point here. As far as I know, there is still no one who can provide evidence as to why it should remain that way. And the "by luck with RL" is soon not by luck anymore. The more stupid and not so stupid ideas are discussed with the LLMs, the chances are growing that it is not a question about luck but by growing probability.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#77

Post by deeznuttynutz »

tsunamifury wrote: post #60
moomin wrote: post #54

Earlier quoted context omitted.

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 simultaneousl…

Don't do that...

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#78

Post by mmooss »

Syzygies wrote: post #34

It 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…

That is one of the more beautiful, insightful things I've read about mathematics. Thank you!

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#79

Post by chermi »

tsunamifury wrote: post #60
moomin wrote: post #54

Earlier quoted context omitted.

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 simultaneousl…

Very useful games, self-importance or no.

See pattern, conjecture generalization, test generalization. It's almost like empirical math. I like it and I also like mathematicians doing it the old way.

Re: The Maxwell Conjecture Is False (GPT 5.6 Sol)

#80

Post by jstanley »

tsunamifury wrote: post #60
moomin wrote: post #54

Earlier quoted context omitted.

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 simultaneousl…

We call a proof that is not tautological "wrong".
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