According to one of the linked articles, OpenAI is sinking money into funding seminars to entice mathematicians to look at some of the results.
But I was under the impression that LLMs are just doing the math of language to produce it. What word to use next is essentially a mathematical calculation. It’s not writing in the conventional sense, it’s doing math and then translating the result into words.
Am I getting that right?
Have you looked at the github repository in question? The AI-written “papers” are abysmally written. However, there are formal statements that anyone who cares about the results in question can check.
There is some stuff there formally written in the Lean programming language (certainly not mistakable for code a human would write, but it is all meant for automated verification anyway), and there is also stuff written in LLM-English.
And I’m told the two versions don’t match terribly well.
There was an article in the Times today about why all this AI doesn’t seem to be increasing productivity or letting companies get rid of people. The answer seems to be that everyone is spending their time checking and correcting the stuff the AI produces.
So you may have it right.
relevant YT vid (link = cued) from one of the best AI-channels:
interesting tidbid: among the 377 solved problems there seems to be one that stands out - and this is nicely addressed in the vid:
https://youtu.be/ C4Sq3Rot8FU?si=8kQEQkBry0oV6Cv-&t=941
link broken (take out the empty space)
I assume someone sat there working on the problems on the computer, that is, they were not generated automatically, in which case they should at least be quasi-interesting.
I would love to play with it myself to see what capabilities we are actually talking about, but I do not have access to tens of millions of dollars’ worth of computing time for free and access to secret models like Terence Tao. He is correct that AI is a useful research tool, but anyone could have told you that.
Not only in maths, but my collegues in the USA & Europe are reporting the same thing with AI-written computer code. This brings up the problem that once the AI have replaced the junior coders and mathematicians, and the older generation retire… who is going to have enough experience and knowledge to review the AI’s generated solution/hallucination?
FYI - There’s been some discussion of your point over here starting about when this year old thread was revived last week:
Proofs and Prompts* has a post called “100+ reactions to 100+ solutions” where they asked mathematicians to comment on the Open AI release. Well worth a browse.
- “A communal blog for mathematicians’ thoughts on how AI is changing what it means to do mathematics, from PhD students and professors, skeptics and enthusiasts alike.”
(bolding mine)
AI?
which brings up another interesting topic: cascades of AI agents …
- coding agent
- supervisor/code integration agent
- final code-QC agent
I have little doubt they will surpass us in this field, too
too late to edit:
Interesting that while we all know that we are just in the earliest of toddler years of AI, we - mentally - take what we see now and project it 1:1 into the future …
We being the brains, and the AI agents being our limbs/underlings/company-drones … and we tell AI what to do and approve its output …
Doing some critical thinking: do we really think this will be true in 3, 5 or 10 years from now? I have a hard time visualizing a human coder supervising like today - 10 coding-agents - which in a couple of years will probably be 100s or 1000s of coding agents - who will throw out solutions and results in mili-second-stakkatos …
I do not think all of this output will pass through that slow/lazy (doesn’t even work 24/7!) / low-bandwidth/mostly incompetent element called senior developer?
I don’t verifying proofs has a major impact on national productivity. No matter what the mathematicians think.
Back when I was in grad school the holy grail was proving software correct. There was a famous paper where the authors looked at a bunch of published proofs and found many had errors. Dijkstra came to our department to talk about this, my conclusion was that it would be possible if everyone was as smart as Dijkstra.
Now, could an AI - independently trained perhaps - figure out how to prove at least good-sized blocks correct? It seems plausible to me.
Bunch of bitter buggy-whip makers there…
But I think it’s important to focus on the big picture. If OpenAI wanted to destroy the mathematical community, this would be a great way to go about it. Open problems are a resource that the mathematical community developed over decades or even centuries. The value they have is the value we have given them. They provide structure, a yardstick for progress and long-term goals. The advent of AI was always going to be a seismic shock, but this huge dump of papers is a tsunami that we have no time to prepare for. It’s clear that OpenAI will happily wash away our community’s structures to further their financial interests.
“unsolved problems are a resource that we shouldn’t deplete” is certainly a unique argument. Imagine this applied to other fields. Let’s not cure diseases because it would harm the medical research industry by giving them fewer problems to solve. Though I suppose mathematics is a bit odd and different in that a lot of these problems don’t have much in the way of practical applications.
Yeah, to mathematicians, mathematics represents a sort of game. If, in one of our puzzle threads, a bot replied with the answer to every puzzle a minute after it was posed, the other posters wouldn’t be very happy about that, because it’d be spoiling their fun.
That said, though, the set of open mathematical problems is huge. These 377 proofs are only a drop in the bucket. It’d be kind of annoying to a mathematician who happened to be working on one of these specific problems, but then, it’d also be annoying if they got scooped by some human. But most mathematicians are working on many different problems at once, and it’s highly unlikely that there’s anyone for whom all of their work just got scooped.
lol
No, in real life, mathematicians try to solve problems, and computers are your friend.
Mathematicians like interesting problems. If you can just mindlessly throw a computer at a problem and solve it by brute force, it’s not a very interesting problem. But sometimes, you can take a problem so huge that it can’t be solved in that way, and find clever tricks to cut the problem enough down to size that a computer can handle what’s left. That is interesting.
Have you ever picked up a newspaper and discovered someone had already completed the crosssword, sudoku, word-search, and drawn a mustache on Mary Worth? That’s how mathematicians must feel.
Is it not the mathematicians who get to determine what are the interesting problems to solve in the first place? They are the ones writing the puzzle, not the ones finding an existing puzzle already filled in.