Fields Medalists Warn AI Companies Are Destroying Mathematics

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding.

I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of these models being capable. Even without AI labs spending millions of dollars to solve millennium prize problems, there are plenty of other people who will use them to pick low hanging fruit. I don't think any social solution is going to make things go back to the way they were, where you could share your progress towards a famous open problem without risking someone "scooping" you within a couple of days.

I think that the most likely outcomes are either mathematics becomes more secretive, or there is a more deliberative approach to assigning credit than who was "first" to solve some problem. In the former case, this may slow down progress, and in the latter case, this could mean that credit would become more subjective, and be a continual source of controversy.

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0].

Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a painting could.

He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts.

Do you see some parallels as well?

[0] https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiq...

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It turns out having an oracle for the "right" answer in chess, even without an explanation, used properly, allows humans to develop broader, more accurate insights.

The argument here sounds similar. The fear, as I understand this statement to be saying, is that by being given the correct answer, in the form of a 100-page Lean proof, humans will be robbed of the chance to from insights about the structure of mathematics itself. I don't see any reason that humans can't continue to develop insights as they try to digest the 100-page Lean proof into something more manageable; but with more certainty and fewer false starts.

> We are witnessing a general threat to intellectual work

This is the crux of it and goes far beyond Mathematics or Computer Science. To get a bunch of humans to do anything, you have to motivate them. Kleos and Timē; renown and stuff. These AI companies threaten to rip this away from everyone but themselves, and this recent millennium prize is the perfect example.

Solving this problem as a human would have led to tremendous Kleos; my name would be written in the annals of mathematics, lecture tours of praise were mine to be had for the rest of my days. This one victory would have earned my recognition throughout history. The greatest a mortal may hope for. Ripped away.

It would also have given me great Timē. The prize money, the professorships, the book deals. Gone.

If all hope of “renown and stuff” in the intellectual realm is now taken by the AI companies, they will remove all human motivation to pursue these endeavours.

Perhaps the glory will come from slaying these fell beasts.

> solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.

This is the effect of AI on most intellectual disciplines, and it’s a real worry.

To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116

It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding.

It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling salesman” problems with a zoom meeting.

This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal. So this letter's message will fall on deaf ears.

Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction. They're knowingly risking the lives of every man, woman, and child to continue the work. The lives of their own sons and daughters. A person already rationalizing that isn't going to shed a tear for the careers of mathematicians. Just a bug on the windshield.

I understand this stance and where they are coming from, but I can't help but think this sounds very analogous to engineers' arguments against AI-assisted and vibe-coding, especially with regard to cognitive debt. Yet the software industry is plowing ahead, reportedly pushing mountains of unreviewed code to Prod, and the world hasn't ended.

Of course, nobody's really comfortable with it, so this is also a forcing function for the industry to adapt and figure out new techniques to manage complexity and trust. I think the same will happen with Mathematics.

But it is also possible we will end up with three forms of Mathematics: the one we understand, the one we don't, and the one we don't understand but can prove to work. Kind of like magic -- with all the positive and negative connotations of the word.

It is pretty evident that these models will soon exceed our cognitive capabilities. Is it right to hold them back just because we can't keep up? Many of those discoveries will be so beyond us that we can't do anything with them, but that also means they can't hurt us. On the other hand, there could be many discoveries that we can parlay into practically useful applications, even if we don't understand them.

Just like LLMs.

OpenAI: "Our mission is to ensure that artificial general intelligence benefits all of humanity."

- Except the mathematicians who we'll scoop and cause existential dread among their entire field.

- Except the software developers. They'll need to become plumbers or live on UBI.

- Except the people in countries that can't afford the cost of AI tokens to keep up with the rest of the world.

Just keep picking off groups of humans for the "benefits of all humanity"... while building larger and larger disparities been the have a lots and the just have enoughs.

We're going to build humans a utopia but along the way we'll leave a trail of destruction because that's not our problem.