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I didn't sign the Fields medallists' letter

18 pointsby 1h agogowers.wordpress.com
23 comments
42m agoHN ↗

With that interpretation, the issue becomes slightly different: is it more important that the collective understanding of the mathematical community should be as advanced as possible or that there should be answers to as many problems as possible? Or are those two aims valuable in different ways, so that there is no point in declaring one of them more important? Or are they so inextricably linked that it makes no sense to argue that one is more important than the other? And when we say “important”, for whom are we saying it is important: for mathematicians, or for society as a whole?

This is easy to me. Truth should be the North Star. If there is a fundamental truth that can be found via mathematics, then the shortest route to that truth should be preferred. While LLMs are definitely capable of solving problems in search of truth, I agree with Tao that instant "true/false" results threaten to short-circuit the traditional avenues we have used to escape local minima in the search for truth. Their products may be the junk food that provides immediate satiation in exchange for long-term health. Perhaps it's wrong, though.

31m agoHN ↗

The whole point of the letter was that if we adopt this gradient search strategy the humanity might get stuck in a local maximum forever.

28m agoHN ↗

Thing is, you can say that about any technology (not being here necessarily pro AI in math, but I think we need better arguments).

26m agoHN ↗

I mean sure? It's clear PLT and other applied CS fields are now as good as dead. You're never seeing new React or Python emerging ever again.

And unfortunately mathematics is much more fundamental to human endeavor than this.

14m agoHN ↗

I don't think that's true. Domain experts with the desire to create and experiment aren't going away any time soon.

9m agoHN ↗

Sure we are free to tinker, like the guys doing model railways. With about the same impact.

6m agoHN ↗

The letter is not incompatible with “pro AI in math” unless one thinks arguing against extreme behavior such as corporations using millions of dollars to scoop results makes one “anti AI”, which is not a reasonable stance in my opinion.

AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.

22m agoHN ↗

Then we develop ways of breaking out of local maxima.

Wherever we can recognise a problem we can solve it.

19m agoHN ↗

Nobody is going to recognize anything if the institutions of mathematics are torn down.

19m agoHN ↗

Tao's point is that we have a method already.

3m agoHN ↗

This isn’t true, as there are plenty of things proven beyond reach.

And plenty of things, eventually solvable, can create major problems that could both be avoided and the problem solved by taking a much better path.

Having technology and the ability to safely and sanely use the technology needs to progress together at a similar rate. The failure to do this is even a reasonable and common solution to the Great Filter. Jared Diamonds book “Collapse” has ample examples of cultures that wiped themselves completely out via not having this balance, so it’s not simply a theory.

14m agoHN ↗

This pattern of argument keeps repeating in every place.

Pro tech people: technology removes bottlenecks. Sometimes we use those bottlenecks as a side effect to build muscle and so on. But removing bottlenecks gives us much higher degrees of freedom. It is up to us to coordinate and make use of the technology.

Anti tech people: bottlenecks are fundamentally useful. They should remain and technology shouldn't remove those so easily. Humans cannot coordinate as well when the bottlenecks are removed, so lets not remove them so quickly.

12m agoHN ↗

I can only suggest reading the letter with open mind and literally, without uncharitable bias towards the authors or conspiracy mindset.

7m agoHN ↗

Its not a conspiracy. Its 25 fields medalists who think exactly like how I put it. Ideally, they can just take whatever the technology gives as soon as possible and use it. They don't want it because they don't think the community can rearrange and coordinate such that they can make use of the new found degrees of freedom.

That's literally all there is to it - they don't believe in the rearrangement.

11m agoHN ↗

Counterpoint: I'm not anti tech at all. In fact, I sell an AI harness for legal.

I think you've set up a false dichotomy. I'd propose to you the middle ground that a lot of us are concerned that VC-backed AI slop is "solving" problems in indigestible ways that hollow out the core. This applies in OSS as well as mathematics.

11m agoHN ↗

“Forever” is a long time. That’s quite the claim.

10m agoHN ↗

I think it is easy to just roll of a local maximum, however, you may get stuck in a local minimum.

I kid, of course, but I do wonder where the use of local "maximum" comes from, what is maximum there? Why do you not see this as a landscape of hills and valleys where marbles with certain energies may indeed get stuck in deep enough holes... Of course, I just assume and picture gravity pointing down in that landscape, but hey. I'm human, I feel it is expected of me.

9m agoHN ↗

Can't we get stuck in local maxima because of the lack of LLMs?

12m agoHN ↗

Siri, can you call the bicameral order, the captain has published again..

9m agoHN ↗

I thought one of the implicit points of the open letter was that unsolved problems are not something that falls out of the sky, they are a curated resource that people have spent time on and shared for the benefit of like-minded peers and humanity as a whole. And the AI companies treat them like they treat absolutely everything else: natural resources, literature, art, code etc. as something to be chucked into the ravening maw and pooped out the back as profit. They don't care if mathematics advances, they don't care if they strip-mine the available problems and damage the field. In fact, as with programming I think they see that as in their long-term interest - soon there will be no intelligence or creativity but the one that Sam Altman bills you for.

8m agoHN ↗

One way that might happen is that AI disrupts society so much, or even kills vast numbers of us, that the preservation of something like the current mathematical tradition ceases to be of any concern: all that will matter is the survival of the human race. But that again is a topic for a different blog post (which in fact I am in the middle of writing).