Comment by piker
1 day ago
> 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.
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.
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.
There's some interesting stuff in a book on Katathymic Imaginative Psychotherapy where patients are asked to picture a mountain. As far as I remember it's about using the process as diagnostic tool. What does the mountain look like? Is it a steep rising, rugged massif or a shallow hill. Are you looking up, do you picture yourself climbing it, or are you on it's top etc. While it said that it's always a contextual matter and in the conversation there was a suggestion of imagining to climb the steep massif, being potentially related to narcisim. Whenever I think of it i associatr that with casper david friedrichs painting.
Then we develop ways of breaking out of local maxima.
Wherever we can recognise a problem we can solve it.
Nobody is going to recognize anything if the institutions of mathematics are torn down.
Tao's point is that we have a method already.
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.
Can't we get stuck in local maxima because of the lack of LLMs?
The letter is not advocating not to use LLMs. It’s advocating to use them in ways which don’t erode human understanding.
as a society of researchers we've tended to cultivate pretty effective strategies for escaping local maxima. I think of it like ants, where you can see if you place an obstacle in between their nest and a foot source, they develop a path that loops around it. if you remove the obstacle, for some time they continue to follow the old looped path. However, some ants deviate and go around at random, exploring. eventually by chance one happens to find a quicker route. he gets a couple of his friends to follow him, by pheremone, and over time more and more take the quicker route, and they end up abandoning the old route
It works this way with research, with most following the current trends, and some curious souls searching around for other ideas, be they contrarians, dreamers, or just convinced of some strange truth. But if we're right, signs tend to slowly begin to point their way, and we can shift the whole hulking edifice of science towards their point of view.
The problem of llms is that while they may be able to find a shorter route, we can't follow them unless we understand the route. So the forces that slowly begin to change everyone's behavior are lost
“Forever” is a long time. That’s quite the claim.
Thing is, you can say that about any technology (not being here necessarily pro AI in math, but I think we need better arguments).
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.
You can say it about becoming collectively overdependent on any technology. And I think there's a good case to be made that a similar phenomenon is true for other technologies e.g. over-reliance on (normal) computers has done similar things in my opinion, at least in my field of physics, where you get a more precise result but much less insight.
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.
4 replies →
The way you get out of a local maximum is to force yourself to try something radically new every so often, even if what you were doing before was working just fine.
This is the 'stochastic' part of 'stochastic gradient descent,' and it's as important for human minds as it is for ANNs. These math wizards seem to be stuck in a rut of their own digging.
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.
I can only suggest reading the letter with open mind and literally, without uncharitable bias towards the authors or conspiracy mindset.
9 replies →
>It is up to us to coordinate and make use of the technology.
1) Coordination is hard, and 2) "us" is a hopelessly nebulous term that appears inclusive but is almost always exclusive.
I think people would have said the creation of social media platforms like Facebook was neither good or bad, but rather it was "up to us to coordinate and make use of".
But did our society really have a say over how Facebook and other social media sites were able to embed themselves in our everyday lives? I would argue the answer is no.
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.
23 replies →
What do you mean by "fundamental truth"? If LLMs produce a collection of proved facts this doesn't sound like what I would call fundamental. It may be the case that there is no such thing as "fundamental truth", that the world is just a blizzard of facts, but in that case we would need to give up on using it as a guiding star.