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Mathematicians issue warning as AI rapidly gains ground

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Re: Mathematicians issue warning as AI rapidly gains ground

#201

Post by lovemenot »

turzmo wrote: post #48

Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…

>> At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.

This assumption may well turn out to be correct, but it is not self-evident.

Nearly everyone who has ever got interested in mathematics got discouraged at some point and they left the field. Mathematics is very hard. Those very few that remained certainly have talent, but they also have characteristics that are necessary for success in a competitive field, which are perhaps less valuable per se. Such characteristics as may be over-represented in males for instance. This is not a point about gender differences, but about the intrinsic merit of different success factors.

It seems equally possible that the above assumption will turn out to be diametrically incorrect. People that would have been discouraged before LLMs will now retain their curiosity longer. Democratisation is surely a possible outcome.

Arguably, chess has never been as popular and accessible. And that discipline fell to AI three decades ago.

Re: Mathematicians issue warning as AI rapidly gains ground

#202

Post by mswphd »

orangecat wrote: post #161
mswphd wrote: post #138

Earlier quoted context omitted.

for mathematicians, they do a form of fundamental research that is 1. (generally) incredibly cheap to fund, and 2. (occasionally) has extremely out-sized commercial impacts. This is to say that jobs programs for math (and more generally fundamental research) have lead to extremely positive ROI for society, which is the typical justification given for funding them.

This is to say that jobs programs for math (and more generally fundamental research) have lead to extremely positive ROI for society Which makes it not a "jobs program" as the term is generally used.

it arguably still is. The primary unit of production of the jobs of mathematicians is itself not particularly useful for society. In this sense funding them is a jobs program. It is also true that they occasionally produce things of great value, and more frequently the things they produce can be leveraged by other researchers to directly produce things of value. But neither of these are what the job of a mathematician is (either in a day-to-day sense, or even for many mathematician's careers).

To go back to the analogy of jobs programs for alcoholics, it is somewhat similar if there was a small chance every time an alcoholic defecated in public gold came out. This fact might be used to support a jobs program for alcoholics, on the basis of it being positive ROI to society. At the same time, the "job" any individual alcoholic is doing in this setup is not particularly useful to society, so one might still call it a jobs program.

Re: Mathematicians issue warning as AI rapidly gains ground

#203

Post by solid_fuel »

silveraxe93 wrote: post #5

> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

>> However, the declaration argues math is more than a machine for producing correct answers.

> There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

I can produce an infinite number of verifiably correct papers, if that's all that matters.

    1 + 1 = 2
    1 + 2 = 3
    1 + 3 = 4
    1 + 4 = 5
    1 + 5 = 6
Shall I continue? Or do you think that choosing which questions to answer might have some level of importance, in addition to getting correct answers?

Re: Mathematicians issue warning as AI rapidly gains ground

#204

Post by math_dandy »

overgard wrote: post #179
Spacecosmonaut wrote: post #24

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…

On the other hand, it could stall out at: good enough to take the easy problems, not good enough to take over the field, but damaging enough to erode the quality of new entrants. (Which incidentally is the scenario I think plays out for software)

I think the OpenAI model that resolved the Unit Distance Problem would be capable of solving a significant proportion of mathematics PhD thesis problems.

Re: Mathematicians issue warning as AI rapidly gains ground

#206

Post by pj_mukh »

Huntsecker wrote: post #163

Anyone else draw similarities with this and the artists and authors who complained when gen ai first came out. I think a lot of people don't realise the disruption ai will cause to many industries, until its directly impacting them, basically personal fable at scale ( https://en.wikipedia.org/wiki/Personal_fable ).

I'm not sure the similarities hold. The best comparison I've found is the construction unions in San Francisco. They frequently block housing that is factory built somewhere else in the Bay area even though that would make it possible to build tonnes of new housing in the city at a fraction of the cost.

"But Jobs" they scream and hijack the council to block new housing. I'm sorry folks, the point of housing isn't the jobs it creates, the point of housing is housing! New jobs ARE actually created, they are just higher leverage ones in the house factory.

Mathematicians are now facing the same... calculation (pun intended). And I think they are empowered to create a lot more leverage, and they shouldn't be afraid of it. A lot of them are catching on to this [1]

[1]: https://x.com/OpenAI/status/2060451757818601808

Re: Mathematicians issue warning as AI rapidly gains ground

#207

Post by rad_val »

par1970 wrote: post #195
rad_val wrote: post #190

Earlier quoted context omitted.

AI (in this form) will never be able to solve things we truly cannot solve yet. It might catch things that we didn't project properly or brute force things no human can , but it will never unify general relativity with quantum mechanics. It's amazing at finding hidden truths in large datasets, but won't win a Nobel unassisted.

> AI (in this form) will never be able to solve things we truly cannot solve yet. Argument?

The strongest argument for this is structural: what LLMs are.

In a brutal simplistic way: each token is represented in a high dimensional vector. LLMs operate on them. They are the true, underlying meaning of the token for the LLM. Think of it as 1000+ ways to think of that word/token. Those meanings are baked in at training time. So, LLMs might be able to cross-reference them and solve a class of problems that flew under our radar, but can't come up with revolutionary theories that were never in the training set.

Of course, they will help winning a Nobel in the years to come, no doubt, but can't speak mathematics we can't understand (beyond simple obfuscation) and won't discover anything substantial on their own.

Re: Mathematicians issue warning as AI rapidly gains ground

#208

Post by epistasis »

nyxtom wrote: post #192

For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.

A million monkeys at typewriters, but with momentary runs of extreme luck/brilliance.

Re: Mathematicians issue warning as AI rapidly gains ground

#209

Post by fc417fc802 »

bawolff wrote: post #139
datsci_est_2015 wrote: post #96

Earlier quoted context omitted.

No, it doesn’t sound like you get it. It has nothing to do with the properties of LLMs and everything to do with the complexity of mathematics. Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly. Without a human…

> Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly. > Without a human holding the reins, consider an LLM a rudderless superboat speeding erratically towards the horizon, finding and proving meaningless theorem…

Micromanagement wasn't the message I took from that. Rather the level of human involvement required which (it seems like) the two of you more or less agree on.

The meaning I took was how far it's possible to travel from the shore - ie the scope of the state space. The mathematics we're exposed to is all quite shallow compared to what will (presumably) be possible between digital formalization and massive ML models. But the latter probably can't ever be understood by regular biological humans.

Re: Mathematicians issue warning as AI rapidly gains ground

#210

Post by cout »

nyxtom wrote: post #192

For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.

Are you sure you aren't underestimating human capacity for stupidity?
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