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Comment by omnicognate

17 hours ago

> I suspect that this is in fact the source of much of the angst.

Why do you "suspect" this as if it's some hidden motivation when the very first paragraph of the advisory group's statement (linked from the OpenAI post) says:

> At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind. However, ideally, they would not do so. We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.

Tao and others in that group have been strongly and publicly pro AI from the start. They are not advocating "going back". They're objecting to the strip mining of open problems using proprietary technology.

OpenAI: At long last, we have created the Open Problem Strip Miner from classic Terence Tao tweet “Don't Create The Open Problem Strip Miner”.

I don't think the strip mining metaphor is appropriate. Mining is a zero-sum game; if I mine something, nobody else can go and mine the same resources I did. Mathematical problems don't go away when AI finds a Lean proof. They create new opportunities for humans to study the solutions, learn new techniques from them, identify promising directions for future research, discover alternative/more beautiful proofs, and write expositions for other humans.

  • Strip mining is very apt if you view the economics of the present system as "effort -> recognition -> career advancement". Even in strip mining, the resources that had been buried are now available for use in the broader economy. What's no longer available is the living that was to be had digging them out.

    • The problem isn't effort, though. All of the things I mentioned constitute effort and could be rewarded. The job economy was created by mathematicians incentivizing the proof of difficult theorems above all else and valuing all other work at approximately zero as far as career advancement was concerned. Now they're pulling a 180 and claiming that math was never really about proving theorems, but that's contradicted by their revealed preferences. The strip-mining problem only exists if they continue with the status quo ante.

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  • Strip mining is an extraordinarily appropriate metaphor.

    Imagine a mine has an unknown number of rare materials. And you know the general location of a few of the most valuable spots. But you don't know what may be valuable right next to it. If the pieces that we know are valuable are suddenly gone, the incentive to mine that particular area drops considerably, dropping the chance to discover potentially brand new materials that would have been found the normal way.

    • That's an empirical claim. I could equally well say that doing an automated search of the problem space and having a database of results and open problems will identify vastly more interesting and valuable areas. Again, the idea that math is some exhaustible material is a metaphor, not an established fact. I'm willing to change my view as new evidence comes in, but I think we're going to have to wait and see what the landscape looks like in a few years.

    • > the incentive to mine that particular area drops considerably, dropping the chance to discover potentially brand new materials that would have been found the normal way.

      FWIW, I think the metaphor breaks down with this framing. This isn't really a problem associated with strip mining, what's left behind is generally low or negative value (toxic). I'd suggest a different metaphor, from Wikipedia:

      > This process involves the removal of all ground vegetation in the area, which is a detriment to the environment.[19] Topsoil may be placed over the tailing along with planting trees and other vegetation. Another reclamation method involves filling in the hole with water to create an artificial lake. Large tailing piles left behind may contain heavy metals which can leach out acids such as lead and copper and enter into water systems.

      This feels very similar to the issues with algorithmic problem "mining". It has the potential to destroy the human ecosystems surrounding these problems, leaving barren wasteland behind where nothing can grow or flourish.

I hope sincerely hope they don't currently use "proprietary technology" like:

Wolfram Mathematica ($890/yr)

Magma ($2500/yr)

Maple ($680/yr)

COMSOL ($1500,yr)

Matlab ($500+/yr)

Seems like a very strange position to take, in my opinion.

Why does the field of mathematics suddenly now need to be "fair" and give everyone access to the same tools? Has that ever been the case in academics? It's always been a competition for name-recognition, grants, institutions, etc.

Macsyma / Maxima was an MIT developed CAS system back in the 60's that was proprietery until they sold it off to IBM for a tidy sum. Magma actually has free access if you're in the US, otherwise you pay. That's not to mention proprietary MATLAB toolboxes or specialized Stata modules.

Likewise, a lot of the above packages have pretty sweet site-wide deals with R1 universities. If you're at a smaller, foreign one, you're out of luck.

  • I was looking at those costs think wow, that is high.

    Then I realized I was spending 3600.00 USD for Anthropic and OpenAI per year.

> Tao and others in that group have been strongly and publicly pro AI from the start

Unfortunately being "pro AI" means relinquishing any control over what the AI, or more importantly the company running it, might be doing.

  • How is this different from literally any other part of the economy?

    We've relinquished control over just about everything we use or consume. We can't compete with larger enterprises for production of food, clothing, machinery, medicine, energy, services. Mathematics is just the latest thing to be industrialized.

    What keeps large companies under control is competition with other large companies. This competition causes the surplus value they produce to flow to consumers, not be hoarded via monopoly prices. Do we see strong moats that are going to cause monopoly in AI? I don't see it, and in particular I don't see it persisting if it exists transiently.

    • You're right, and that's a bad thing. AI is nothing fundamentally new, but its extremity is making many people aware of the truth that's been there all along. There's no contradiction in that.

      > Do we see strong moats that are going to cause monopoly in AI?

      Ownership of the capital assets used to train and inference new models. Yes, we may end up with more than one firm. But as we see with big tech today, a small number of fantastically wealthy firms in "competition" does not an open market make.

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  • No, it doesn’t. You can be in favor of something and opposed to a particular way of handling or implementing the thing. And the issue here isn’t what it’s being used for but who is able to use it.

  • "AI" is largely a marketing term for a particular type of computer program that uses a statistical language model.

    Computers and computer programs are tools. Humans always remain sovereign over their tools.

    • I am not sure how convinced I am by that argument. A gun is also a particular kind of tool, and it makes the person at the handle end sovereign, and the person at the pointy-shooty end subjugated.

Regarding the advisory group, OpenAI claims to “have drawn on their advice”, which would include not dumping a bunch of AI slop, with the footnote that if they do do that, at least fund the process of digesting it.

At the same time, there's a new note at the bottom of agmai.org stating how they've been in contact with OpenAI about this particular release, and they say that “we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully”.

So, what's going on there; is this British English for “they didn't follow anything at all”? Because from my perspective, it looks like they doubled down on the Navier–Stokes approach of trying to maximize PR gain while being as lazy as possible about actually contributing anything back to science, releasing only slop that may or may not be correct and may or may not be straight up plagiarism, as has been the case earlier.

If I were on the AGMAI board, I'd feel terribly exploited when reading that press release, yet their response is modest.

Hairer, if you're reading this: is there any indication whatsoever that AGMAI was anything but a cheap way for OpenAI to science-wash their press release?

  • > is this British English for “they didn't follow anything at all”?

    Yes, but the subtext is even stronger.

  • > AI slop,

    Now I know there are issues with the field and how just answering these questions may cause broader problems, but I feel like the posted results is far from slop. We can't just call any output slop, or it loses all meaning.

    If it was slop, it'd not be causing the issues the group are concerned about - they're not saying "the problem is we're getting loads of incorrect proofs thrown about that are nonsense".

    • When you blanket a set of things with a pejorative, and it turns out that some of the members of that set are demonstrably and definitively NOT covered by that pejorative, and that all the pejorative means at bottom is "I don't like", all you've accomplished in the long run is to call into question any future legitimate use of that pejorative. It is tempting, especially when heated, to stretch an invective, but it will ironically only lead to the death of its utility over time.

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    • They're not calling any output slop, they're calling indecipherable output slop. The management class responsible for hiring, firing, and paying people doesn't possess the domain knowledge to say for certain whether or not LLM output is optimal (which, in this context, means correct), but they will trust that it's good enough to justify further automation / fewer grant approvals / etc. So in that sense, slop can and will cause the economic issues people are concerned about.

      University boards want the prestige of successful research programs. Doing the hard work to get something demonstrably true is going to lose out economically in this paradigm, where we are all being conditioned to uncritically ooh and aah at the incantations being elicited from these magic boxes. The oracles even have legions of zealots who will berate you for not being sufficiently deferential and reverent, or worse, accuse you of blasphemy. If for no other reason, I agree with using the term to express all of the above succinctly, even if LLMs can be helpful tools generally.

    • I've read some of the results papers (the Einstein condensate one and the pi exponential one). I'm not an expert but it definitely wasn't AI slop. The introduction sections were particularly well framed and informative.

      Also you can see in the papers where an idea is introduced but in the bibliography you can see where the foundational idea comes from. So the narratives are not unmotivated as some claim (proof without intuition claims).

    • In the context of maths papers, the term has come to refer to papers having the shortcomings that are, for whatever reason, typical of LLM out, including things like using non-standard terminology all over the place, emphasizing easy steps while leaping over harder ones, having bizarre organisation, and, importantly, failing to properly cover existing work and as a result being hard to tell from plagiarism.

      The degree to which these issues feature will differ, but it is generally the case that converting the output to proper research requires significant effort, hence the AGMAI recommendations being what they are, and not performing that effort tends to come off as laziness or incompetence, so I can see how slop has become the popular term.

    • > We can't just call any output slop, or it loses all meaning.

      The term “ai slop” is not supposed to discriminate good ai output from bad, the entire purpose of the phrase is a blanket term that delegitimizes all ai output.

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Haven't been following this debate closely, but what's the issue with "strip mining open problems"? Surely the supply of interesting mathematical problems is (in theory) infinite?

  • You can find Tao’s arguments here: https://mathstodon.xyz/@tao/117237320796901560

    He argues that the supply nay be very large indeed but the interesting subset is not. Figuring out the interesting problems is difficult so strip mining the good known problems may lead to scarcity. I am not a mathematician myself, can not judge this accurately.

    • A Swedish proverb says, "a fool may ask more than ten wise may answer". This fool is reporting for duty! I'm glad I may have something to contribute after all (and I'm only halfway joking)

    • i'd be curious to hear why he thinks ai couldn't help make it easier to discover interesting problems, ie to make the interesting subset less scarce.

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    • That’s what we are doing with nature, seas (look up strip mining there, it’s a horrible practice), and now the industrial harvestors are strip mining problem spaces. How do we like our own medicine?

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  • These are a specific set of interesting, compelling, human-sized problems curated to motivate clever people to engage with math.

> stop testing advanced mathematical problems on proprietary models

I don't know but this phrasing comes off as gatekeeping.

  • It’s not. Intent matters.

    Imagine there's a very advanced crossword club where anybody can join and take a stab at these crosswords for the love of solving puzzles. Many of them are so difficult that no one's been able to solve them yet, but we know they're all solvable.

    One day, someone comes along with a super advanced crossword solver application, and it makes easy work of these crosswords. They run it on a few to prove how powerful it is, and then the community says, "Oh wow, that's cool, but please don't run it on any more of our advanced crosswords because they're very hard for us to come up with, and we really enjoy solving them by hand."

    That's really what this compares to. I wouldn't call that gatekeeping; just respect. Respect for the game, respect for people's desire to have these hard problems to continue to work on, solving by hand.

    If the company with the super advanced crossword solver then continues to use it and publish the results, they're effectively stealing the crosswords from this community. Soon, all the puzzles will be solved, leaving nothing left for the community to work on for fun.

    That doesn't sound like gatekeeping to me. That just sounds like someone asking "Please be respectful and leave the remaining puzzles for us to solve by hand.” A simple plea not to be an asshole.

    • This is a really confusing take.

      If someone can solve open problems in mathematics then they should do so, isn't it as simple as that?

      They should let the public use the models as well, but I guess they have no real moral imperative to do so.

      But asking them to stop solving problems is just weird.

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    • What is preventing these crossword solvers from not looking at the advanced crossword solutions?

      Mathematicians and academics in their ivory towers are forgetting that everything is getting automated. They want to carve out fun problem solving niches that's fine but who's going to fund that? If they want to be funded by the society/civilization their argument can't be leave advanced fun problems for their hobby.

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    • Its worth noting though that you are comparing a profession with a hobby.

      People go to said crossword group to enjoy the process of solving the puzzles. It doesn't actually matter if they have been solved yet or not, case in point the NY Times puzzles are enjoyed by more than just the first to solve them.

      Professional mathematicians are ultimately being paid to solve the problems for a (hopefully) practical reason. Its always excellent when a person enjoys the process of the work they are paid to do, but ultimately they are still paid to do the work. I really hope your argument isn't that we should collectively be funding mathematicians to solve problems simply doe the love of the game.

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    • Classic alignment problem.

      Despite nobody at openAI thinking of themselves as an asshole; despite society urging openAI not to be an asshole; despite the fact that being an asshole is entirely unnecessary even to accomplish whatever objective they are setting out to accomplish; despite everyone at openAI loudly declaring: we are not assholes!

      They are still assholes.

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    • This analogy is silly because (a) math is not primarily for entertainment, (b) we aren't going to run out of math proofs, and (c) results build on top of other results, having more results proven makes all math more powerful and useful.

    • Hmmm but in the case of math, while some of it is "just puzzles" there often turns out to be practical applications, even if they are not obvious at first. Number theory was considered the epitome of pure math with no practical applications for centuries, now our modern society is built on it (public key crypto).

    • If the crosswords were purely games that would be no problem. These crosswords seem to power physics, chemistry, engineering and science applications. These professions would not mind it too much.

    • Blah blah blah. They are free to do their own mathematics and/or spend time on polishing/reviewing proofs dumped by ai. But they don't get to make demands like don't test math on proprietary models. Idiots.

    • Math doesn't belong to academics. We don't pay them to work on problems for fun. They will just need to re-evaluate where the value their provide is. It won't be solving problems anymore. Hopefully it will be making them understandable by others at least till AI can't do that as well.

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    • I’m sorry; but if mathematicians are in it because puzzle club is fun, then they should go join the fucking puzzle club and stop impeding scientific progress.

      Science isn’t some passive busywork thing where you tie your hands behind your back because it isn’t fair on others to solve all the neat problems - or at least it shouldn’t be.

      If your idea of science is leather patches on tweed suits and the quiet ticking of a clock while you do crosswords, then this is an argument in favour of letting the AI do the work so you can focus on your sudoku book in your slippers.

  • Keeping the tech proprietary so that it can only be used on these problems by internal teams is the very definition of gatekeeping.

  • It's more like, "don't just casually destroy our hobby / career field", without letting us participate even a little.

    The picture I have in mind is OpenAI running their most advanced model in a loop over all the open mathematical problems they can find, just to verify that the model is indeed very smart. Neither the company nor the model actually care about the problems, it's just a cheap exercise machine for them, but the problems get solved and mathematicians don't even get to participate.

    Like, even those who accepted the "centaur" thinking, man + machine, won't benefit because by the time they get their hands on good enough models, everything is already done.

    It's an emotional thing first and foremost - people who care about the thing can't do the thing, because it's already been done by those who couldn't care less about it.

    And before someone goes "poor mathematicians", a food for thought: this is just an early instance of what looks like our shared destiny.

    I said here before: given the economics of progress in AI and robotics, it's obvious what the natural division of labor is: computers do the thinking, humans do the menial, manual labor. AI will do politics and philosophy, so you have more time to fold laundry and scrub the toilet.

    • So what is mathematics then? A fun hobby akin to chess or sudoku?

      Are we gonna get the same pushback from medical researchers if the models cure xyz diseases?

      I absolutely understand the emotional connection to their work and the heartbreak, but mathematics doesn't exist for their pleasure, it exists to provide tools to solve humanitie's problems.

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  • It's not like every disadvantaged kid now can solve a major problem just by sinking a hundred hours in their ChatGPT 8 instance.

  • Sure, and sometimes gates are needed. That's why we all run spamfilters, those are definitely gatekeepers.

    In this instance however, it's openAI and Anthropic that are pushing people out of the field by running secret models that take the interesting work away and leaves the persons having to review endless slop proofs.