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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)

#131

Post by subsistence234 »

paulpauper wrote: post #116
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…

some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important. The fact this has gone viral, shows otherwise. It is important to apparently enough people that the story went viral.

"AI solved another conjecture" is exciting for a lot of people who have otherwise no interest in math. So the fact that it goes viral may have very little connection to the mathematical importance of the result.

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

#132

Post by subsistence234 »

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?

NP doesn't mean "we don't know a polynomial time algorithm for it", it means "a proposed answer can be verified as correct in polynomial time"

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

#133

Post by subsistence234 »

windexh8er wrote: post #67
dcsommer wrote: post #6

Earlier quoted context omitted.

Sure they care about elegance, or at least brevity. Minimizing tokens out, or generally "token efficiency," is part of the objective function for these systems. It doesn't mean they are perfect at it though.

"They" don't "care" about anything. It is a stateless computational run across thousands of semiconductors. There is no objective this software has other than the computational function completing. To care would mean the model would have a level of discernment that goes along with sentience.

The supposed "magicality" of human consciousness is hard to reconcile with evolution -- where on that long path from amoeba to homo sapiens did God (PBUH) implant our connections to the soul realm?

Even evolution-deniers run into difficult-to-justify self-contradictions when trying to explain how the supposed supernatural part of our consciousness is both affecting the natural world and affected by the natural world, but not part of it.

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

#134

Post by tsunamifury »

lioeters wrote: post #126
tsunamifury wrote: post #93

Earlier quoted context omitted.

Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

> may never be useful at all Nobody is qualified to judge the usefulness of mathematical, scientific, artistic, or any other kind of research that people choose to dedicate their time doing. And the world is better for it. > or representative of reality This so-called "reality" you speak of is some arbitrary representation in your head. It's your theory and patterns of abstraction, as you call it. Who knows how far o…

This is nonsense. Its the shared based case we can all test against, the things you think are the abstraction.

So wildly goofy train of thought here.

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

#135

Post by tsunamifury »

fn-mote wrote: post #120
tsunamifury wrote: post #93

Earlier quoted context omitted.

Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

Parent seems to conflate “abstract” with “useless”. This comment addresses the “abstract” part only. > Math Theory are patterns of abstraction that may never be useful at all or representative of reality. This is a complete misunderstanding of (good) mathematical research. The results look abstract, but they are based on concepts that are real and have truth or falsehood. One example that comes to mind (sorry, techni…

Abstraction is useless until its proves use in test against a base case of reality.

its the defition of useless most of the time.

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

#136

Post by tsunamifury »

throw-the-towel wrote: post #84
tsunamifury wrote: post #60

Earlier quoted context omitted.

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…

To borrow a common wisdom about marketing, half of all mathematics is a waste of time, but you can't know which half.

But the issues is you have the ratios wrong. 99% of math theory is useless and maybe 1% has value.

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

#137

Post by tsunamifury »

chermi wrote: post #79
tsunamifury wrote: post #60

Earlier quoted context omitted.

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.

I feel like you should search through the thousands of papers that are generated nonsense math theory and laugh at how you cherry picked 3 things.

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

#138

Post by zarzavat »

CWuestefeld wrote: post #118
throwaway0123_5 wrote: post #68

Earlier quoted context omitted.

> 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. It seems plausible that the value of education will go down for the vast majority of fields and as a result less people will be getting degrees of all types. Not a good outcome I think for humanity to be less educated, even if people are provided for when they can'…

A large proportion of degrees awarded today are not useful for any practical application. But having a degree of some kind still serves as a signaling mechanism, demonstrating lots of things including the ability to "play the game". to follow instructions, and so forth.

If I were 18 I'd be sceptical about the value of degrees compared to the value of trades.

Yes degrees are a prerequisite for white collar jobs but if there is competition for ever fewer white collar jobs that's a life gamble perhaps not worth taking unless you are supremely confident in your abilities in a field.

If we're being honest, the value of a degree has been in decline for a long time. It was only being held up by STEM and even that is on shaky ground now. The days when an e.g. English degree would open doors are long over.

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

#139

Post by throw-the-towel »

tsunamifury wrote: post #136
throw-the-towel wrote: post #84

Earlier quoted context omitted.

To borrow a common wisdom about marketing, half of all mathematics is a waste of time, but you can't know which half.

But the issues is you have the ratios wrong. 99% of math theory is useless and maybe 1% has value.

Maybe so! My point was not about the exact percentages, just the fact that you can't predict which avenues of research will yield practical results.

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

#140

Post by hgoel »

fn-mote wrote: post #119
julianeon wrote: post #72

Earlier quoted context omitted.

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

This approach totally changes the game, in ways we are still discussing. The current consensus is that domain experts get the most out of using AI on problems. How will domain expertise develop when AI is doing the work? I’m not saying that there won’t be another approach that builds on the strengths of AI, but we have to look for that and develop it. There’s a lot to talk about.

A decent chunk of the work a student does during a PhD is stuff that their advisor would have done in much less time, but are intentionally delegating to the student to allow them to learn.

So, I don't think AI changes the way expertise is earned. It might change the cost tradeoffs depending on where AI costs eventually settle.

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