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Tao: Open math problems being non-renewably mined by AI

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Re: Tao: Open math problems being non-renewably mined by AI

#391

Post by bwfan123 »

Alien1Being wrote: post #252

Tao's central point seems to be : "In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. " I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.

> but at the cost of sustaining the ecosystem

John Naur said the same of coding eons ago [1]. That code is only as healthy as the human mental model of its maintainers. Code is not the artifact, it is the intuitions and insight and mental models of its human maintainers. For a project to sustain, it is vital that the human mental models are kept alive.

[1] Programming as Theory Building https://pages.cs.wisc.edu/~remzi/Naur.pdf

Re: Tao: Open math problems being non-renewably mined by AI

#392

Post by vouaobrasil »

pixl97 wrote: post #239
vouaobrasil wrote: post #46

Earlier quoted context omitted.

The reason is because the entirety of society, historically, has been based upon humans using their differential skills to further it, which in turn promotes societal cohesion. If most human endeavours are solved, then we will enter a period of abundance that paradoxically will erode the glue holding society together. In short, endless abundance of solutions and ideas cannot coexist with a healthy society. Only those…

I mean the past 10 to 20 years of social media have shown a lot of societies glue already breaking. A society can live just fine in a period of abundance. The societies that we currently have on earth do make it questionable of 'we' can right now. I mean I see people posting stuff like "I'd rather burn it all to the ground rather than see one cent more tax" kind of stuff when they have millions. That kind of person d…

Yes, the glue is already breaking and AI is the next stage in the process.

Re: Tao: Open math problems being non-renewably mined by AI

#394

Post by lanstin »

morpheos137 wrote: post #190
nafey wrote: post #76

Earlier quoted context omitted.

I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems. FWIW this is my understanding of his ar…

The sphere of human comprehensible mathematics is finite. Once everything is solve it is not necessary to advance the field. The recurring error her is to say ai is not the product of human effort but another agent. Ai is human. Ai may well be speeding up human comprehension of math to its limits in which case there is no further need to advance the field and mathematicians might need to get a job. Why is this a bad…

I have never heard this theory that mathematics is finishable before.

Re: Tao: Open math problems being non-renewably mined by AI

#395

Post by lanstin »

drusepth wrote: post #316
dgellow wrote: post #280

Earlier quoted context omitted.

The millennium problems is something done by a single institute to motivate progress on known open problems: https://en.wikipedia.org/wiki/Millennium_Prize_Problems

Yes, but why?

Because the mathematicians consulted 25 or so years ago believed their solutions would lead to the greatest amount of interesting new maths to explore, and because they had been validated as being hard by being attempted and not solved for a long time.

Re: Tao: Open math problems being non-renewably mined by AI

#396

Post by scruple »

kamaal wrote: post #351
nine_k wrote: post #223

Earlier quoted context omitted.

I'd say that a more appropriate reference from that time would be "The Nine Billion Names of God" by Arthur C. Clarke [1], which actually deals with the finiteness of the list of problems that a machine successfully exhausts. [1]: https://hex.ooo/library/nine_billion_names_of_god.html

>>which actually deals with the finiteness of the list of problems that a machine successfully exhausts. This is already the case with most DevOps jobs with Claude Code. There are only that many finite issues that need fixing in production, even for very large systems. So you don't need all that many people to run ops these days.

Well you see we need to migrate system A to B and X to Y and here's another new integration to look at and we need to finally get off of this EOL distro and... It'll never stop.

Re: Tao: Open math problems being non-renewably mined by AI

#397

Post by BeetleB »

adastra22 wrote: post #305
BeetleB wrote: post #246

Earlier quoted context omitted.

What is it, if not an art?

Truth.

What is truth if we are free to pick our axioms?

The universe is either Euclidean or not. If it were, how can theorems on non-Euclidean geometry be true?

Re: Tao: Open math problems being non-renewably mined by AI

#399

Post by kohllision »

matt3210 wrote: post #298
thymine_dimer wrote: post #80

Doesn't this just suggest that the next frontier for powerful AI models is to ask challenging questions, not simply solve them? Terry even says this: "In fact, it is now the identification of a promising problem which is the scarce and precious resource." The creativity and insight needed to ask a question that Terry gets excited about is the next step. Perhaps OpenAI should create a set of challenging questions and…

> ask challenging questions As far as I can tell, it's still not possible for an agent to reliably determine if a question is a good question. That means the test part of the loop cant be fulfilled.

That should be the easiest part of the loop. Frontier models are good judges of human preference and taste and should be excellent at prioritizing proposed questions. The generation part is much harder.

Re: Tao: Open math problems being non-renewably mined by AI

#400

Post by unrented7977 »

xigoi wrote: post #309
nullbio wrote: post #288

There's nothing that AI won't be able to mine and accomplish (aside from being literally human), it's only a matter of hardware and scale at this point. Generalized problem solving is a factor of search efficiency over the problem space. The actual software part is all figured out, the only open questions are how to do things efficiently and what the trade-offs are from a hardware perspective, but if hardware paradig…

> it's only a matter of hardware and scale at this point. The AI companies have already bought up the world’s entire supply of hardware. There won’t be any more.

Yes, clearly no more hardware will ever be produced. We've sold all hardware, it's over, everyone go home. Spin down the factories, we already sold all hardware we'll ever make.
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