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The cultural divide between mathematics and AI

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Re: The cultural divide between mathematics and AI

#161

Post by Philpax »

piokoch wrote: post #137
nicf wrote: post #8

I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math world than the AI world, it's very natural for me to see this divide from the mathematicians' perspective, and I definitely agree that a lot of the people I've talked to on the other side of thi…

"I can imagine a future where some future model is better at proving theorems than any human mathematician" Please do not overestimate the power of the algorithm that is predicting next "token" (e.g. word) in a sequence of previously passed words (tokens). This algorithm will happily predict whatever it was fed with, just ask Chat GPT to write the review of non-existing camera, car or washing machine, you will receiv…

Luckily, we have ways of verifying mathematical results, and using that to improve our AI systems: https://deepmind.google/discover/blog/ai-solves-imo-problems...

Re: The cultural divide between mathematics and AI

#162

Post by recursive »

randomNumber7 wrote: post #145

Imo mathematicians want to be very smart, when a lot of ai is actually easy to undertand with good abstract and logic thinking and linear algebra.

I've known a few mathematicians, and none of them cared about being perceived as smart. They wanted to figure stuff out, which, incidentally, tended to actually make them smart.

Re: The cultural divide between mathematics and AI

#163

Post by ssivark »

nicf wrote: post #8

I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math world than the AI world, it's very natural for me to see this divide from the mathematicians' perspective, and I definitely agree that a lot of the people I've talked to on the other side of thi…

As Heidegger pointed out in _"The question concerning technology"_ the driving mindset behind industrial technology is to turn everything into a (fungible) standing resource -- instrumentalizing it and robbing it of any intrinsic meaning.

Maybe because CS is more engineering than science (at least as far as what drives the sociology), a lot of people approach AI from the same industrial perspective -- be it applications to math, science, art, coding, and whatever else. Ideas like _the bitter lesson_ only reinforce the zeitgeist.

Re: The cultural divide between mathematics and AI

#164

Post by int_19h »

tromp wrote: post #9
deadbabe wrote: post #7

Earlier quoted context omitted.

AI has been around since at least the 1970s.

Or 1949 if you consider the Turing Test, or 1912 if you consider Torres Quevedo's machine El Ajedrecista that plays rook endings. The illusion of AI dates back to 1770's The Turk.

"[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent." - Ada Lovelace, 1842

Re: The cultural divide between mathematics and AI

#165

Post by DeepSeaTortoise »

nicf wrote: post #8

I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math world than the AI world, it's very natural for me to see this divide from the mathematicians' perspective, and I definitely agree that a lot of the people I've talked to on the other side of thi…

TBH, I think you're worrying about a future that is likely to become much more fun than boring.

For actual research mathematics, there is no reason why an AI (maybe not current entirely statistical models) shouldn't be able to guide you through it exactly the way you prefer to. Then it's just a matter of becoming honest with your own desires.

But it'll also vastly blow up the field of recreational mathematics. Have the AI toss a problem your way you can solve in about a month. A problem involving some recent discoveries. A problem Franklin could have come up with. During a brothel visit. If he was on LSD.

Re: The cultural divide between mathematics and AI

#166

Post by alternatex »

whynotminot wrote: post #150
piokoch wrote: post #137

Earlier quoted context omitted.

"I can imagine a future where some future model is better at proving theorems than any human mathematician" Please do not overestimate the power of the algorithm that is predicting next "token" (e.g. word) in a sequence of previously passed words (tokens). This algorithm will happily predict whatever it was fed with, just ask Chat GPT to write the review of non-existing camera, car or washing machine, you will receiv…

I can also write you a review of a non-existent camera or washing machine. Or anything else you want a fake review of! Does that mean I’m not capable of reasoning?

If you are not capable of distinguishing between truth and lie, and not capable of reflection which is the drive behind learning from past mistakes - then yes.

Re: The cultural divide between mathematics and AI

#167

Post by losvedir »

crazygringo wrote: post #157
nicf wrote: post #8

I'm a former research mathematician who worked for a little while in AI research, and this article matched up very well with my own experience with this particular cultural divide. Since I've spent a lot more time in the math world than the AI world, it's very natural for me to see this divide from the mathematicians' perspective, and I definitely agree that a lot of the people I've talked to on the other side of thi…

> what it is that mathematicians want from math: that the primary aim isn't really to find out whether a result is true but why it's true. I really wish that had been my experience taking undergrad math courses. Instead, I remember linear algebra where the professor would prove a result by introducing an equation pulled out of thin air, plugging it in, showing that the result was true, and that was that. OK sure, the…

I guess, what university and what level of math was that?

I majored in math at MIT, and even at the undergraduate level it was more like what OP is describing and less like what you're saying. I actually took linear algebra twice since my first major was Economics before deciding to add on a math major, and the version of linear algebra for your average engineer or economist (i.e.: a bunch of plug and chug matrices-type stuff), which is what I assume you're referring to, was very different. Linear algebra for mathematicians was all about vector spaces and bases and such, and was very interesting and full of proofs. I don't think actually concretely multiplying matrices was even a topic!

So I guess linear algebra is one of those topics where the math side is interesting and very much what all the mathematicians here are describing, but where it turned out to be so useful for everything, that there's a non-mathematician version of it which is more like what it sounds like you experienced.

Re: The cultural divide between mathematics and AI

#168

Post by nybsjytm »

Xcelerate wrote: post #140
nybsjytm wrote: post #60

Earlier quoted context omitted.

> Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down. There is a major caveat here. Most 'serious math' in AI papers is wrong and/or irrelevant! It's even the case for famous papers. Each lemma in Kingma and Ba's ADAM optimization paper is wrong, the geometry in…

> Each lemma in Kingma and Ba's ADAM optimization paper is wrong Wrong in the strict formal sense or do you mean even wrong in “spirit”? Physicists are well-known for using “physicist math” that isn’t formally correct but can easily be made as such in a rigorous sense with the help of a mathematician. Are you saying the papers of the AI community aren’t even correct “in spirit”?

Much physicist math can't be made rigorous so easily! Which isn't to say that much of it doesn't still have great value.

However the math in AI papers is indeed different. For example, Kingma and Ba's paper self-presents as having a theorem with a rigorous proof via a couple of lemmas proved by a chain of inequalities. The key thing is that the mathematical details are purportedly all present, but are just wrong.

This isn't at all like what you see in physics papers, which might just openly lack detail, or might use mathematical objects whose existence or definition remain conjectural. There can be some legitimate problems with that, but at least in the best cases it can be very visionary. (Mirror symmetry is a standard example.) By contrast I'm not sure what 'spirit' is even possible in a detailed couple-page 'proof' that its authors probably don't even fully understand. In most cases, the 'theorem' isn't remotely interesting enough as pure mathematics and is also not of any serious relevance to the empirical problem at hand. It just adds an impressive-looking section to the paper.

I do think it's possible that in the future there will be very interesting pure mathematics inspired by AI. But it hasn't been found yet, and I'm very certain it won't come from reconsidering these kinds of badly-written theorems and proofs.

Re: The cultural divide between mathematics and AI

#169

Post by nybsjytm »

skinner_ wrote: post #106
nybsjytm wrote: post #60

Earlier quoted context omitted.

> Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down. There is a major caveat here. Most 'serious math' in AI papers is wrong and/or irrelevant! It's even the case for famous papers. Each lemma in Kingma and Ba's ADAM optimization paper is wrong, the geometry in…

Amazing! I looked into your ADAM claim, and it checks out. Thanks! Now I'm curious. I you have the time, could you please follow up with the 'etc...'?

There's a related section about 'mathiness' in section 3.3 of the article "Troubling Trends in Machine Learning Scholarship" https://arxiv.org/abs/1807.03341. I would say the situation has only gotten worse since that paper was written (2018).

However the discussion there is more about math which is unnecessary to a paper, not so much about the problem of math which is unintelligible or, if intelligible, then incorrect. I don't have other papers off the top of my head, although by now it's my default expectation when I see a math-centric AI paper. If you have any such papers in mind, I could tell you my thoughts on it.

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