As a mathematician maybe I am a little more optimistic than this declaration.

I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH.

Well, what is the result? In the Mochizuki case, it was a lot of skepticism, but it also generated conferences, papers, talks in the hallway, discussions with students, and so on--a flurry of exactly that kind of community process that the declaration says is the main driver of mathematics.

Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc).

Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.

The maths community is now in the antithesis phase, synthesis will take a while ;)

Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available.

But on the other hand, people learned a lot from chess engines. After decades of chess computers beating humans, there was still a renewed interest in watching Leela beat Stockfish, with many people trying to understand the strategy Leela used.

If your happiness comes from grinding on a problem and making progress, the prospect of having to dig through a corpus of AI-generated proofs might be hard to swallow. But if you're willing to do that, you will still find beautiful things that only so many people can truly appreciate.

Is this the scenario described in Ted Chiang's short story https://en.wikipedia.org/wiki/The_Evolution_of_Human_Science where scientists are "catching crumbs from the table" trying to decipher the results generated by superhuman intelligence?

>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.

Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI.

Title: Terence Tao - SAIR Competitions and the Future of Experimental Mathematics

https://www.youtube.com/watch?v=rB9YOi3lb7w

and this:

Daniel Litt - Working with LLMs to do high quality math

https://www.youtube.com/watch?v=0wL8NlhxXcU

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.

I don't like nuance here. I think progress is really measured by what humans are able to do and understand, not machines. It is significant if we find problems we struggle to solve. That tells us something. What does it take for humans to solve these problems is related.

The best analogy I can give is if you wanted to climb Mt. Everest you might ask someone for guidance. Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak? This is like the AI versus human gap to me. The helicopter is like using AI to generate a proof. The person who actually climbed Mt. Everest has firsthand knowledge of the experience. Same thing for a difficult proof. The struggle people have is actually valuable here. Likewise, we know people are actually capable of climbing Mt. Everest but if they had only ever rode a helicopter to the top, the knowledge of climbing it would not exist, and surely that is meaningful knowledge given the risks.

So if we rely on AI for proofs I think we lose a sense of what is difficult and why. We lose a sense of what human achievement is. Surely climbing Mt. Everest means more than taking a helicopter up? For students, why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? This would have the affect of destroying knowledge.

(please do not nitpick the analogy because it's the best but perhaps a clumsy way to describe my thoughts)

> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc).

This also sounds like a vector for trolling the community with complex putative proofs hiding a known flaw.

The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem.

> Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.

I think a better comparison is: mathematics just becomes like mining bitcoins.

Mochizuki's claimed proof of the abc conjecture was extremely unusual for the reason that nobody was able to extract a single useful idea from the argument. I was starting grad school when it came out, and my immediate visceral response was "if this is what number theory is going to look like in the future, then I will leave mathematics."

The current wave of AI slop mathematics might end up driving the next generation of mathematicians away from the subject for the same reason that Mochizuki would have convinced me to quit if his proof had been accepted by the community. Luckily, my professors had the taste to immediately recognize that it was garbage.

I really like this take, and while I hate math I value it. Your position sounds extremely plausible and it fits with the pattern we see in the community here. Regardless if it's ai slop or not we still debate the value and attempt to understand. In the process generating new insights and ideas. Life will go on.

It's not just the isolated dumping, it's the fast, isolated, possibly untraceable dumping, without long term support.

It'll basically become slop fatigue if OpenAI starts dumping out proofs faster than the community can keep up, and some turn out to be wrong, never formalize it, don't stay to support it, etc.

So it wasted everyone's time, thousands of hours of research trying to disprove something said very loudly. What OpenAI is doing is a DoS of the scientific community: wasting your time trying to check if they're not wrong, and claiming glory in the mean time.

Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain)

Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular.

AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity is growing while our human ability is stagnant.

meta-AI analysis cannot help. We (software professionals who use AI regularly) already know that if you run into a situation where a Fable/Astra-generated analysis reaches the limits of our comprehension/complexity due to their subjectivity, throwing more AI at the problem doesn't always converge.

There are many reasons to feel optimistic about AI, and ultimately its general ability to help science and mathematics.

I see no reason to feel optimistic about the future of mathematics and AI based on the current path of frontier labs, unless the misalignment Tao is writing about can be reconciled.

I get excited at the idea of a world in which advanced mathematical problems (and their solutions) become much more accessible to a much greater number of people. As a result, making mathematics much more loved at a societal level.

Imagine a world where these most complex mathematical problems are not accessible to a few hundred people, but a few hundred thousands people. ...Those original few hundred gifted mathematicians would have an even more prominent role, and their names and achievements would be known by orders of magnitude more people that they are now.

I've met a few Ph.D Mathematicians in Academia socially. My unfortunate experience was that they were insufferable,borderline hostile people. I tried to genuinely engage with them too. I've met one Ph.D Mathematician that left the industry whom was very enjoyable to talk to. I have a feeling that my experience was not unique and the Math world is mostly a bunch of too good for everyone on their high horse a-holes that are now being knocked down a peg. They don't like it obviously.

I'm not a fan of knocking down things that work, however I also find it hard to be against death of the gatekeeping old guard of any industry.

I think math is just gonna have to suck it up like every other industry now. Math productivity is longer out of reach of the average grad student. Like every other industry they are no longer untouchable and are gonna have to adjust to the new way of things or market forces will do what they always do which is refuse to fund ineffectiveness.

I've had to accept that tech/IT will never be the same. Just how it is. You can thrash against it all you want.