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The Maxwell Conjecture Is False (GPT 5.6 Sol)

arxiv.org

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

#41

Post by bre1010 »

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…

This sounds depressing. Imagine going to work every day and your boss is a computer telling you to do rote nonsense so it can barely-better-than-brute-force search for breakthroughs in whatever field. Then when it finds one we get another breathless news cycle like this while you get no credit at all. If you could understand what you were working on, you might be able to contribute more than a .csv of data, but the computer can't read you in because there is no understanding under the surface.

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

#42

Post by AlexErrant »

_jayhack_ wrote: post #21
pdonis wrote: post #15

Earlier quoted context omitted.

> most of the proofs I've looked at appear super messy and chaotic to me (while still being correct of course, so it doesn't matter) How do you know they're correct if they're super messy and chaotic?

formal verifiability e.g. vi Lean

Even Lean has bugs.

> AI "Proves" Collatz Conjecture with Lean 4 Bug

https://news.ycombinator.com/item?id=49101465

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

#43

Post by ashleyn »

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 it, but Wiles' proof drew on a diversity of seemingly-distant subfields within mathematics that were better understood.

* What are aspiring math Phd's supposed to do, now that the bar is much higher these days? The net effect of this appears to be that we'll see far fewer, but far more elite math Phd's, potentially discouraging many young people from the field.

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

#44

Post by SetTheorist »

Good4boothee wrote: post #38
layer8 wrote: post #35

Earlier 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?

AIUI if you have an (polynomial-time) algorithm to reduce some NP-complete task to P then you have indeed shown that P=NP.

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

#45

Post by Tyr42 »

Good4boothee wrote: post #38
layer8 wrote: post #35

Earlier 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?

You can prove something is in NP by providing a (polynomial) reduction from a known NP hard task, and vice versa. All the known NP problems (Knapsack, SAT, etc) are mutually reducable in this way, so solving one lets you solve the others. So if X was shown to be NP, then given a polynomial time solution to X, you can stack the polynomial time reduction from X to SAT to solve SAT in polynomial time too.

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

#46

Post by simianwords »

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…

How’s this different from just asking an llm to prompt you to perform experiments? You don’t need any expertise.

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

#47

Post by ComputerPerson »

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 still want to in the face of excessive media/reccomendations/statistics telling you not to.

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

#48

Post by alasano »

bre1010 wrote: post #41
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…

This sounds depressing. Imagine going to work every day and your boss is a computer telling you to do rote nonsense so it can barely-better-than-brute-force search for breakthroughs in whatever field. Then when it finds one we get another breathless news cycle like this while you get no credit at all. If you could understand what you were working on, you might be able to contribute more than a .csv of data, but the c…

Barely better than brute force (I can't believe it's not brute force!™) aside, presuming we get super intelligence it will all be depressing when it comes to intellectual pursuits like this.

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

#50

Post by js8 »

layer8 wrote: post #35
js8 wrote: post #30

Earlier quoted context omitted.

I agree, counterexample to P!=NP would be great. I tried but it's a mess.

I’m pretty sure “counterexample” is the wrong word here.

Why? A counterexample to P!=NP would be a polynomial algorithm for SAT. If it exists, it might be a constructible object.
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