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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)

#141

Post by [deleted] »

tsunamifury wrote: post #134
lioeters wrote: post #126

Earlier quoted context omitted.

> 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.

[deleted]

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

#142

Post by card_zero »

tsunamifury wrote: post #134
lioeters wrote: post #126

Earlier quoted context omitted.

> 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.

I agree that rigorous logic shouldn't be assumed to get us closer to Ultimate Objective Truth than other forms of reasoning. It just gets us whatever peculiar oddments we can discover through rigorous logic, so far, here in our local, parochial patch of reality. Things that seem crucial powerful theories (theorems, whatever) to us here and now may not seem that way in the future, and arriving at them through logic doesn't provide a royal road to the Ultimate.

This means abstract mathematics is rooted in our current cultural concerns. I guess I'm saying that it isn't really useful or really abstract, but I also agree with the other poster that people can and should do what they like.

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

#143

Post by throwaway0123_5 »

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.

I agree somewhat, but for the most part the signal is that you can succeed in some kind of knowledge work. If AI replaces ~all knowledge work, that signal isn't actually going to be valuable I think. While I don't find it certain that AI will do that, it seems increasingly plausible with every model release. In that world, I don't think very many people are pursuing degrees.

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

#144

Post by cedws »

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.

I never understood why being able to “play the game” is considered a positive signal. Getting a degree is the safe path, it doesn’t require any risk taking, and not much initiative. It’s about having the money (or going into debt for most people) and sitting your ass in a chair until you’re told you’re worthy. That idea is repulsive to me.

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

#145

Post by altairprime »

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…

As a potential elite math Ph.D, though sadly I can't afford to complete studies in that direction yet, both before and after A.I. I have been interested in the field for synthesis of different fields of mathematics into novel outcomes. A.I. is, as with protein and antenna folding, excellent at constraint solving and optimization — but human creativity continues to excel at creating new frontiers that are not found within the 'local' maxima explored by algorithms. Consider that we have brute-force calculation tests that can be applied to an entire floating-point 2^32 space and I guarantee a lot of A.I. effort invested in finding more efficient storage methods, but there's still room for human invention of floating-point storage simply by a person making a leap between Field One and Field Two that hasn't been proven yet:

> We would like to stress that the key idea behind ALP is to design for vectorized execution; it led us to analyze and uncover unexploited opportunities from a vector perspective in a variety of datasets.

— doi.org/10.1145/3626717, via ALP: Adaptive lossless floating-point compression (6 days ago, 4 comments) https://news.ycombinator.com/item?id=49051355

Perhaps future mathematicians use A.I. to prove it, but that's still a human invention — and even if we brute force the entire space of mathematics, it's functionally useless without an ontology to help humans narrow an A.I. 'problem-solving' response from 'all possible solution spaces' to 'the interesting solution spaces', and even if that ontology is A.I. created, a human is still going to be evaluating 'interesting' through their own cognitive experiences, biases, and dissonances in order to identify novel connections for other humans to build with. Just because we can `echo 0..2^64-1 >> file.txt` doesn't mean that we're deriving value from it, even if it's indexed by number of digits or nearest power of two or whatever. OEIS exists, and cannot be easily replaced by an A.I., because it's not just a list of numbers indexed by sequence (which no doubt computerized proofs plus generative algorithms will eventually automate the generation of), it's a list of interesting to humans sequences, and that's something A.I. can't be substituted for.

> Director Cary Fukunaga mentioned a complex narrative structure in his 2018 big pharma miniseries Maniac being nixed because of the audience loss predicted by the data.

— via Bland, for fans of everything (11 months ago, 7 comments) https://news.ycombinator.com/item?id=45049412

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

#146

Post by Someone »

yreg wrote: post #12
Someone wrote: post #11

Earlier quoted context omitted.

> Minimizing tokens out, or generally "token efficiency," is part of the objective function for these systems. First time I heard that, and I doubt it. Don’t customers pay for output tokens? If so, why would a company specifically spend time training their LLM to generate fewer?

So they can charge more per token and decrease the pressure on their infra.

Even if you specifically train the model on producing shorter answers, I would think producing good short answers would require more resources just as it does for humans (https://quoteinvestigator.com/2012/04/28/shorter-letter/: “If I Had More Time, I Would Have Written a Shorter Letter”)

If so, charging per output token is the wrong incentive.

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

#147

Post by yreg »

Someone wrote: post #146
yreg wrote: post #12

Earlier quoted context omitted.

So they can charge more per token and decrease the pressure on their infra.

Even if you specifically train the model on producing shorter answers, I would think producing good short answers would require more resources just as it does for humans ( https://quoteinvestigator.com/2012/04/28/shorter-letter/ : “If I Had More Time, I Would Have Written a Shorter Letter”) If so, charging per output token is the wrong incentive.

What billing system would you suggest?

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

#148

Post by ConceptJunkie »

ndriscoll wrote: post #105
ashleyn wrote: post #43

Earlier quoted context omitted.

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…

The bar for math PhDs already ruled out like 99.9% of the population, so I don't see it having much effect on discouraging people. The gap between even a bright student who takes AP calculus or whatever and someone studying e.g. spectral sequences is already incomprehensibly large. Like you literally could not even convey to a smart young person how far away they are from the boundary of today's understanding. I don'…

I'll look at math papers on Arxiv, etc., and browsing the titles will find maybe one in a hundred where I even know what it's talking about. I've been a math enthusiast since I was a kid, but the field is so immense I can't even wrap my head around how big it is, leave alone the actual concepts.

Out of all the topics mentioned in the recent AI advances at finding counterexamples to conjectures, etc., about the only one I understood was the one where they've made advances in a bounds for kissing numbers in higher dimension, a topic I find fascinating even if I don't really know much about it.

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

#149

Post by ConceptJunkie »

zarzavat wrote: post #138
CWuestefeld wrote: post #118

Earlier quoted context omitted.

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…

There's going to be a huge realignment in white collar work in the next decade or two, and then there's the fact that college degrees themselves (except for maybe STEM), are becoming less and less valuable because higher education is so politicized and taken over by nonsense. My college education (Computer Science, 1987) served me very well over my career, but I don't know what I'd be doing if I were 18 now.
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