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.
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.