Comment by varjag

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.

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.

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

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.

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

>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.