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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]

#51

Post by hodgehog11 »

yurimo wrote: post #32

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 lo…

Agreed, AI is not capable at the moment of coming up with radical ideas to solve the tough problems. Sadly, I would argue many problems in math are likely to be found to be not actually tough in this sense, and those working in "comfortable" areas with fewer tough problems are having real crises of their own right now.

But even for the tough problems, it is good at executing on a particular idea with reasonable competency. It's also quite decent at verification now. That can radically speed up proof development overall, since those aspects can become quite tedious otherwise.

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

#52

Post by aurareturn »

andybak wrote: post #44
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…

> but the productivity gains and economic surplus. I think you might be missing out vast swathes of human experience here. Some things are about joy, or god help me - fun. (For the record I think AI has a role to play here as well)

I find AI a joy to use to build software. I was never the type of engineer who loved the code itself. I was always the type who wanted to see how users would react, how metrics change based on the feature, etc. The code was the most boring part for me generally.

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

#53

Post by Fordec »

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…

That's the current culture, but culture changes. Gauss, Onsager and Grothendieck hid their work. "Pauca sed matura".

Your best interest only means your current best interest. What makes for the best form of personal interest is evolutionary, not static.

Dresden Codak as a story has a concept of "Dark Science" where the world has the benefit doesn't come from publishing science, but from utilizing it. If you understand a piece of science when nobody else does, and integrate it into your technology, you have a strategic non-academic physical advantage. Trade secrets basically. And trade secrets used to be the norm prior to patent law. We could be in the pre-"AI patent" era where the government created incentive to share your AI findings isn't made strong enough yet.

Science is today built on the shoulders of giants, but what if an agent swarm makes your own tower of giants in a day? Why do you need an ecosystem of peer review, if you can discover your own science from first principles without meaningful effort? Yes, it's duplicated effort, but why does that matter if the monetary cost of effort trends to zero? The value of peer review is going to have to contend deeply with itself just like how open source developers have had to contend with the value and mechanisms of inbound AI generated PRs the last six months.

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

#55

Post by tackta »

Yokolos wrote: post #10
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…

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…

Compared to what though? When was this golden age when things were not scary or turbulent?

If you read about life in the 19th century, it was more turbulent than today with change.

We seem to frame these debates against some random week in spring 2017 that if it ever existed at all, was extremely fleeting.

I think the bigger issue is that social media doesn't exactly provide historical context. If anything it provides a type of ahistoric , hysterical context to the present moment.

Then if you have no social media, everyone feels more and more like a hysterical lunatic living in a reality that doesn't exist if you just go outside and put the phone away for 5 minutes.

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

#57

Post by knollimar »

2snakes wrote: post #49
knollimar wrote: post #35

Earlier quoted context omitted.

Whats personal about a datacenter?

You could have said the same thing about mainframes in the past? I am talking about smaller open source models not huge ones that need spaceships to run.

I thought the implication of the feudal system was that the spaceships create landed nobility

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

#58

Post by seanhunter »

qw3127 wrote: post #33
vouaobrasil wrote: post #24

Earlier quoted context omitted.

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 a…

Terry Tao isn’t Chinese, he was born Australian and has lived in the US for a long time.

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

#59

Post by madcaptenor »

jdm2212 wrote: post #45
layer8 wrote: post #42

Earlier quoted context omitted.

> Beamer Spotted the German guy. ;)

the software that generated the slides is called Beamer https://en.wikipedia.org/wiki/Beamer_(LaTeX)

I believe the software was written by a German.

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

#60

Post by vouaobrasil »

light_triad wrote: post #31
vouaobrasil wrote: post #26

Earlier quoted context omitted.

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.

I posit that one cannot decouple understanding from a healthy social environment in which to practise math. And AI destroys that.
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