The research community is in uproar after OpenAI released a trove of more than 700 mathematical preprints entirely generated by AI on 6 October. The San Francisco, California-based maker of ChatGPT posted the preprints on the software repository Github.
Although some mathematicians celebrated the solution of longstanding problems, others took to social media to complain about being scooped. Some were incensed at what one physicist called a ‘slopocalypse’, even if the mathematical content could end up being formally correct.
Can someone please explain to a non-mathematician what the issue is specifically?
We all want the problems solved, right? Is there a wrong way to solve them? Or a process that people are supposed to follow not to “scoop” others? A honor system of sorts?
If a human dropped the same 700 solutions online, would it still be bad?
Solving a problem has no value if no one understands the solution.
Why would you work if someone else gets the salary?
There’s an onus now on those that care about math to check the proofs. If errors are found in one their might be similar errors in another. A serial release would have been cleaner and allowed commentary that might help improve the accuracy or perhaps even the way the model conveyed the data to make it more understandable / digestable.
Openai dug the problems up from somewhere. They could have collaborated with some of the people that defined the problems in the first place. This is just perpetuation of their culture of theft.
There are two issues really - one is a perception that they’re not vetting any of this output, just dumping it out on the internet and expecting real mathematicians to actually check it all, so yes if a human was doing the same thing it’d probably still be suspect.
The other is the widely held suspicion that much of the “breakthrough” mathematics here has been stolen from real researchers who’ve been using chatgpt to develop their theories by talking to it
I think a mathematician with no skin in the game should just make a big post saying “All 700 are wrong, no I am not going to show my work, if you disagree prove which one you think is right” put the ball back in OpenAI’s court.
Bold of you to assume OpenAI cares if they’re right.
They should care because if they don’t respond, everybody else stops caring and their PR stunt has little payoff.
I think that was just some rumor. In the end the accusation was that they basically brute-forced a solution using methods developed by someone else and claimed they solved it but those methods were public, not stolen because they used ChatGPT.
https://x.com/doomslide/status/2108121379660832930
I need an account to access that.
Managed to screengrab before the popup appeared
Thank you
I don’t have an account either. there’s a faint x on the top right. pressing it worked for me (Firefox on Android)
It is a lot of stuff from an unreliable source that basically vomits out stuff that looks correct but is often not and that is a ton of human work to verify that humans were already in the process of doing.
It is most likely just the stuff humans were close to finishing being scooped up and spit out and not reliably correct.
also the act of verifying is generally unpaid work. peer review was already having issues because people in the field don’t want to do it over their own research.
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A human still needs to verify the theorem statements at least.
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Maybe there should be: link to preprint stating that the Lean code doesn’t do what the papers claim (for Navier-Stokes)
I think there are three main issues (though I might be overlooking something):
However, it’s not entirely unprecedented for a computer to provide a proof that we don’t completely understand. I forgot the details (and I’ll edit them in if I can find it), but there was at least one problem that was solved using a computer and brute force trying millions of cases. That produces a proof much longer than any human could read in a lifetime, and iirc there where quite a few mathematicians unhappy about it at the time too.
I can add about your last paragraph(it’s literally the core of what I do). There is a field of computer assisted proofs, that is mathematical proofs that need a computer to be completed.
The first and most well known example is the four color theorem. How many colors do you need to color “a map”. Answer: 4. Proof: very very long. By hand it is possible to prove that there are only 1834 options, and a computer was used to color all these explicit options. At the time, it was a scandal. Nowadays, other computer assisted proofs are accepted, such as the ones relying on validated computing: if a computer (with some restrictions and guardrails) can show that a certain value is over/under a given threshold then something else is true.
Then, there is the validated proofs approach. This is where Lean comes into play, if you have heard about it. You can ask a computer to check your proof. This is helpful for confusing, long proofs (most of math). You input all the logical steps you took and Lean confirms that all is logically sound. Many AI proofs are “Lean verified”, but there is controversy if they are proving what they claim they are proving. It’s also a massive chunk of code that nobody can understand.
Have you looked at some of the problem solved? I’m way out of my depth here, so I’m having trouble understanding how much 700 is. If it is proven and understandable, how much of an advancement would this represent? Sorry if it’s a random question, but you seem more knowledgeable than most.
Just to give a comparison, a high-output mathematician publishes between 2 and 5 papers a year (depending on branch of math and dividing by co-authors).
Most are incremental work, so a little step towards solving a problem or a conjecture. A lot is just a “hey, look at this neat trick”. Solving “big problems” is usually the work of a decade or more, in which the mathematician is working on other stuff as well. So let’s roughly say that solving a big problem usually takes some 10 years of work and some 10-30 papers (assuming working roughly half time on it).
So on one hand, 1 paper per big problem is too little to actually understand what’s going on, on the other 700 papers are the output of more than a hundred mathematicians over a year. A math department in a university is around 50 mathematicians, I would say? So two medium-sized departments.
The other part of your comment. “If its proven and understandable”
At the moment, the preprints are assumed to be a shit sandwich. (Aka “would you eat a sandwich is there could be shit in it?” ). Using the results is just too risky without understanding if they are correct and how they are build.
The “understandable” bit is also really hard. I picked a random one in my field (nothing I directly worked on) and it was unreadable - mostly because of notation used without defining it and no explanation of what is going on, no overview or intuition. So to me it seems more shit than sandwich. As a reviewer, I would never accept such a paper.
Then finally, let is assume it’s all perfect and good. The goal of proving something in math is to develop understanding and a method to apply to other cases. So once all these papers are studied and understood, poop discarded, rest of the sandwich saved, ideally we will have new understandings of whole sections of math, new connection between items we’re weren’t aware of. What I think AI did in this context is to chain things that were already known, but there was no one whose knowledge spanned wide enough to know that all the pieces were already laid out. So it could be groundbreaking - once we remove the shit. How much shit there is is anyone’s guess.
Thanks! That really puts things into perspective. It’s less impressive than I first thought, especially since it seems like spaghetti that needs a lot of untangling. 700 struck me as a huge number at first.
Science is not mainly about solving problems (that would be engineering for example).
But more specifically to your question:
There are many wrong ways of doing scientific work, and what current AI does is one of them: reading it all, rephrasing it all a little and then already declare everything as done & good, even when it isn’t.
A scientist needs proof, and peer reviews, etc. before the work can be called good.
Never forget AI isn’t creating really new things, it can only chew up and spit out what has been there before. This is especially true in science.
I’d argue that it is capable of novel ideas.
I wouldn’t.