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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#181

Post by margalabargala »

gritzko wrote: post #161
jimkleiber wrote: post #150

Earlier quoted context omitted.

I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more. That it makes life more ends and less means.

Let's take your argument one step further. Suppose that tomorrow we learn that AI just exploited a bug in Lean and the proof is, in fact, bullshit. Or suppose it is the case, but we never learn that. Where are "ends" and where are "means" here?

Well, given a proof of something then a system can be built that relies upon the inviolability of that thing.

Should the proof turn out to be bullshit, then that system will be revealed to be unreliable. Maybe.

Re: A misalignment of AI in mathematics

#182

Post by aswegs8 »

matherial wrote: post #120
yzydserd wrote: post #6

> solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. This is the effect of AI on most intellectual disciplines, and it’s a real worry.

Yeah. My other favorite example are books. Why do nonfiction books exist? There are some pathologies and corner cases, but fundamentally: to develop and share new ideas. Downstream from that, if it reads well and if you're lucky, you make some money. But now, LLMs can generate hundreds of books per hour. They make up 80-90% of new arrivals in many nonfiction categories on Amazon. They short-circuit the system, allowi…

Now you piqued my interest. Any good AI-written books out there? I thought it's all slop.

Re: A misalignment of AI in mathematics

#183

Post by malwrar »

jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

I feel a similar fate will befall engineers too. Your predictions anre quite interesting from that perspective.

Markets defined entirely by law have distorted our collective understanding of what can actually be built with the knowledge our species has accumulated thus far. How will traditional shields that have protected capital accumulation in tech to survive in a world where governments now realize control of technology is a national priority? Especially as we see its impact on modern warfare, and that such conflict looks like it’s only escalating over time.

Mathematicians appear to me (as an outsider) to exist in a field without such distortions, and I think offer engineers a preview of what’s to come. I certainly have completely ceased sharing original ideas online at this point.

Re: A misalignment of AI in mathematics

#184

Post by oytis »

sdeframond wrote: post #162
imdsm wrote: post #81

Earlier quoted context omitted.

I am on this track too. If AI leads to advancements, objectively that's a positive (depending on the advancement I guess) but it's only when mathematicians realise they'll get beaten to every thing now that they're outraged.

Say AI becomes the best at everything. Best at chess/go, best at maths, philosophy, economics, romantic advices ... and so on. Then what's the point of thinking by oneself? Of talking to one another? What's the point of being human if we dont do human things but entirely rely on AI? I believe this is more or less these mathematicians' argument.

It has been best at chess for quite a while. Yet everyone knows who is Magnus Carlsen, even though at no point of his career he was stronger than the machine

Re: A misalignment of AI in mathematics

#185

Post by pred_ »

tossandthrow wrote: post #51

On the contrary to what Tao believe, it seems like we need AI to move the needle on mathematics. > problems in many fields of mathematics Developing these different fields moves complexity from the field itself to the interactions of these fields. Getting too preoccupied with the established terminology risks us a local minima. Anf because the field overall has become so complex that we need to decompose into subfiel…

Tao is about as pro the usage of AI in maths as anyone will get. The point isn't about whether or not we can use AI in maths because clearly it can be useful; it's that the unscientific approach taken by AI companies is detrimental.

Re: A misalignment of AI in mathematics

#186

Post by bpodgursky »

grufkork wrote: post #47
boron1006 wrote: post #41

To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116 It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding. It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling sales…

Going to the gym and using a forklift

There is an implicit agreement that mathematics is funded, for the most part by the public, as a way to advance the state of knowledge and propagate (even if very indirectly) what has learned for the public good.

It was never about helping individual mathematicians demonstrate that they are individually good at math. It happened to work out that way, but it wasn't the goal.

Re: A misalignment of AI in mathematics

#187

Post by reasonableklout »

jrflo wrote: post #160
tmhn2 wrote: post #148

Earlier quoted context omitted.

At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.

I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.

Tao’s key point is that the way people are using AI today does disrupt that. Because people and companies are valuing the results over understanding. So we’re getting slop results rushed out that are automatically verified.

Moreover in the past, discussion and idea sharing would happen naturally to overcome the friction of the process. But now when OpenAI is stuck on a particular part of NS for example, they can just throw more capital & tokens at the problem.

Re: A misalignment of AI in mathematics

#188

Post by sigmar »

jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

>or there is a more deliberative approach to assigning credit than who was "first" to solve some problem

it feels like an unintended consequence of the millennium prize is that people view the [last contributor to the solution] as the only one to make progress on the problem. I've never viewed Poincaré as solved by one person and the objective of the prize was to encourage more people to make attempts and contribute towards progress.

this issue is independent, but in these circumstances perhaps interweaved, with the 'ai is taking over math' concerns

Re: A misalignment of AI in mathematics

#189

Post by 12qqtt »

Economist: "Are mathematicians talking their own book out of fear?"

The Economist, who recently used "moral panic" now stoops to Hacker News AI booster level and inverts arguments usually directed against the rich and investors. What is next? The Economist inverting Upton Sinclair's quote to serve its billionaire owners?

Look up the AI investments of the Agnelli family for example.

Re: A misalignment of AI in mathematics

#190

Post by rbtprograms »

andriy_koval wrote: post #29
rbtprograms wrote: post #8

Earlier quoted context omitted.

Tao basically reiterating "AI is making us dumber" a bit more eloquently and applied to math.

Its by choice. Mathematicians still can use AI to "achieve the primary goal of conceptual understanding and insight"

youre not wrong, but i think you are missing his base point. tao is saying that mathematics is a practice that the group collectively builds. students and new methods are built on top of what has previously been done, so its a community effort of research, experimentation, and knowledge sharing.

his core argument that is LLMs (and specifically LLMs owned and gated by corporations was my read), while able to solve problems, do not contribute to this practice of knowledge building. solving problems is just one piece, and the mathematics community ingests problems and new methods, iterates and thinks on them, and then produces new ideas, methods, etc. this is what he is defining as progress, and solving things like millenium problems are markers of this progress.

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