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Terence Tao: Mathematics in the Age of AI [pdf]

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Re: Terence Tao: Mathematics in the Age of AI [pdf]

#31

Post by light_triad »

vouaobrasil wrote: post #26
light_triad wrote: post #18

This is the taste question applied to Mathematics in a similar way it's been applied to code. In an era of AI abundance, the question becomes what the goals are and what gets verified and digested (adopted by users). Goodhart’s law: the goal of producing code is not just about maximizing the number of tokens used, but the productivity gains and economic surplus. This could serve as the template for any field in the a…

This is the template any field should have in the face of AI: screw AI, forget it. If you're using it, it's a disrespect to the field. Let's continue without it. I think that's the only sane approach.

William Thurston's argument (from the quote) was that the point of math isn't to produce more math but to better understand the nature of reality, just like the point of code is not to generate more code but to increase user value.

AI is a tool that reshapes knowledge work but the ultimate goal remains about value.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#32

Post by yurimo »

I think it is important to divine what currently AI is good for and what it is not even in such verifiable environments like math. Current hyped announcements about breaking conjectures are notable and are a marker of how much improvement was made. But as I read them, and maybe I am wrong, I see it as a large model+ harness executing a broad brute force search and trying solutions until something sticks. There are lots of problems like that and they should be solved, as often they are perhaps less important or overlooked, or just a slog, any field of research has these, math even more so.

However, this is very different from inventing new mathematical machinery that allows to break old problems, I think it will be a while until AI will be able to do it if at all. For now I think we will be moving to a symbiosis where an AI cracking a problem and giving a solution, inspires a human to invent new techniques.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#33

Post by qw3127 »

vouaobrasil wrote: post #24
megaloblasto wrote: post #5

This is the thought process that I fail to see many people take (both here and other places). AI is changing many fields, ok what does that look like and how do we adapt? What can we do now that we couldn't before? What skills should I learn to adapt to this changing world? I think this is how we move forward. If you can get past the scary aspects of AI (not talking about datacenters or billionaires, that is a differ…

As a (sort of former) mathematician myself, I can say two things. First, one of the most exciting parts of mathematics is to see what other people can do with it and the results they obtain, and learning from them (and sharing with them in return). And second, I am completely uninterested in what AI has to offer. To me (and most normal people) knowledge pursuit is about inspiring others with discovery and the intelle…

People here don't want fun for others. The site is full of wannabe entrepreneurs whom daddy bought a startup and got VC friends to fund it.

They think they are better than you and me and everyone is just a human resource who has no right to enjoy anything.

That is why they hope for the industrialization of the sciences. The C students can feel equal to the A students.

Why Tao goes along? He is Chinese and they have an insatiable social pressure to be the first and best at "new" things. Since Yau tried to rip off Perelman, my view of the Chinese pressure cooker influence on Western academics has changed.

Especially since the results aren't the same as in the times when everything was more relaxed in academia and the stopwatch idiots hadn't taken over yet.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#34

Post by Syzygies »

I loved the appearance of Bill Thurston. He proved enough of what he saw to be considered one of our greatest mathematicians, but his brilliance was what he saw.

The obvious question Terry Tao seems not to address: AI mops up our unsolved problems? Whose unsolved problems? The architecture of mathematics will remain a human endeavor long after we replace human construction workers with machines.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#35

Post by knollimar »

2snakes wrote: post #12
Yokolos wrote: post #10

Earlier quoted context omitted.

Even as somebody who uses AI every day and has integrated it in useful ways, I don't see how the rise of the AI industry can be anything other than terrifying. It signals the rise of a new feudal system. Couple that with the rolling back of democracy across the globe and growing trend of authoritarianism, even in Europe, and I just can't be excited. In Germany particularly, it feels like every week there's some new i…

Open source intellectual power though. The promise of the personal computer.

Whats personal about a datacenter?

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#36

Post by goodmythical »

impendia wrote: post #29
andyjohnson0 wrote: post #21

A few predictions: 1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product. 2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we wil…

I'm an academic mathematician, and could you explain your second prediction? It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it. Of course, this culture could change under external pressure from AI tools. But, aside from cryptography and the applied fields, I'm finding it difficult to ima…

There could be a difference between academic mathematical research and commercial mathematical research, just as in the difference between FOSS and commercial code. Perhaps the difference lie between pure math and applied math with applied math having more incentive for secrecy given that large swaths of computing is just applied math in fancy wrappers.

If you can derive some special formula that prints money from accurate prediction of asset valuations if and only if you're the only one with the efficiency, you're incentivized to keep it quiet.

If you're a nation state that's cracked a simple method to decrypt modern "pre-quantum" encryption schemes with less compute/wall time using a development in mathematics, it is in your interest to keep this quiet so that the parties you surveil to not switch or adapt. Similarly if you've figured out a handy new form of encryption, you're incentivized to prevent leaking of details as it is harder to reverse such operations without details of the methodology.

Or you've designed some special optimizer that you then bundle in a subscription service. Your business now only profits while the algorithm is secret. e.g. The DVD Copy Control Association's CSS encryption was only a valuable thing that the company could charge for or entice clients with before DeCSS was published/became popular.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#37

Post by calf »

impendia wrote: post #29
andyjohnson0 wrote: post #21

A few predictions: 1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product. 2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we wil…

I'm an academic mathematician, and could you explain your second prediction? It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it. Of course, this culture could change under external pressure from AI tools. But, aside from cryptography and the applied fields, I'm finding it difficult to ima…

There are different levels of outcomes, but even Terence Tao essentially foresees this issue: look at his remark footnote 5 in this very talk. It complements the Balkanization point in the parent comment. Not a big leap or unfathomable to connect to broader issues.

Update: see also the later slide where he problematizes corporate secrets in relation to math culture.

Everyone should just read the slides, really

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#38

Post by fweimer »

impendia wrote: post #29
andyjohnson0 wrote: post #21

A few predictions: 1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product. 2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we wil…

I'm an academic mathematician, and could you explain your second prediction? It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it. Of course, this culture could change under external pressure from AI tools. But, aside from cryptography and the applied fields, I'm finding it difficult to ima…

I can see it happening if people start depending AI-generated proof libraries for the work they are interested in. Not because the libraries are proprietary, but because they are impenetrable. AI usage wouldn't result in this directly, but it could be a consequence of formal verification as a substitute for canonicalization in some cases.

(Disclaimer: I had quite a bit of formal training in mathematics at one point, but have worked in software for more than two decades now. I wasn't on the applied side, but I recall that MATLAB evoked similar concerns back in the day.)

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#39

Post by calf »

However, the writing often dwells at length on trivialities, while passing very briefly through (or even obscuring) the most interesting and novel portions of the argument.

This is consistently my experience chatting with LLMs. It's an very interesting anti-feature, what does it mean about them fundamentally, could more sophisticated machines one day surpass this, etc.

Chomsky for example took the position that LLMs will never be able to explain things and he thought this anti-property was fundamental to their model of computation. But that was years ago.

Re: Terence Tao: Mathematics in the Age of AI [pdf]

#40

Post by andyjohnson0 »

impendia wrote: post #29
andyjohnson0 wrote: post #21

A few predictions: 1. I fear that AI is about to change from being a human art to becoming something like a bulk-extruded, industrial product. 2. I also suspect that mathematics is about to become substantially less open. As the number of entities on the planet that are capable of top-level maths explodes, and because most of those entiries will have no interest in the validation that publishing papers brings, we wil…

I'm an academic mathematician, and could you explain your second prediction? It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it. Of course, this culture could change under external pressure from AI tools. But, aside from cryptography and the applied fields, I'm finding it difficult to ima…

I'm not a mathematician or any other kind of scientist. Just a toiler in the software mines, and an onlooker.

> It goes entirely against the culture of research mathematics to hoard secrets. If you've done something interesting, you want to share it, and it's in your best interest to share it.

You're describing an enviable human culture with a reward system suited to people. People publish papers etc. to enrich the human domain and to get recognition. AIs don't care about things - and neither, I'm asserting, will their owners. That culture will become a vestige.

Mathematics as the underpinning of science and technology that can be exploited for inter-state competition, including cryptography but not limited to that (image analysis, targeting algorithms, conflict modelling, whatever) won't see the light of day. The AIs that discover the mathematics will be paid for by the warfighting budgets of states, and by the corporations that feed on them.

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