When our project was made public, a well-respected colleague wrote to one of us with some criticisms, which I paraphrase and summarise here:
- If AI solves a problem and one works on the presentation of it, should one be a named author of it?
- If grad students see senior academics publishing AI-generated proofs, modified or not, would they mimic such behaviour, thus affecting their mathematical development?
- When should one be an author of a piece of work? Presumably, this should bee the case if and only if such author comes up with the mathematical ideas for the work. This is a viewpoint that one would expect if instead of machines producing maths we were talking of other humans. Otherwise, people would misattribute the results to you in the future.
These criticisms look reasonable, but only if read unnuanced. In particular, the second point seems to be in contradiction with the third one. If a PhD student is only meant to put their name to papers where they are the sole creator of the ideas, there would be no need for the PhD supervisor (and most students would never graduate). If we allow them to do it, are we affecting their mathematical development? Clearly not. And what if they truly solve by themselves the problem their PhD supervisor (the ‘prompt giver’) gave them? Should the supervisor call themselves as such?
However, beyond internal consistencies of criticisms, let’s examine our own project. Some ideas may be good to solve a problem… But if nobody is able/willing to read them, few, if any, would understand them and, more importantly, we would never be able to know if the results are fully correct. When Vanya Cheltsov shared with us the output GPT Astra gave him, the reactions from project members went from “unreadable” to “difficult to read”. This said by experts who have written many papers in the same problem (different families). It quickly became apparent that for this result to ever be used/read, it would have to be changed in its presentation. This is not the firs time it happens in our research discipline, let me quote the beginning of the first proto-book on the Minimal Model Programme:
The existence of flips was first proved by [Mori88]. Recently a very different approach to a more general type of flipping problem (still in dimension three) was found by [Shokurov91] […]. Shokurov’s article contains many new ideas, but unfortunately it is very difficult to understand. Numerous parts required a truly joint effort of the participants and some details were understood only after several discussions with the author. Eventually we discovered an error in [ibid, 8.3]. Unfortunately, there was no opportunity to reconvene the seminar and study the new version [Shokurov92].
Was “Flips and abundance for algebraic threefolds” original? Some bits yes, others maybe not. But if the authors had decided to treat Shokurov’s paper like a Talmud that cannot be modified, development of the MMP would not have progressed as fast in the 1990s. PhD students would have found it very difficult to learn from this (take it from me, I tried when I was a Y2 student). The mistake would have also taken much longer to be discovered. To this day, we quote Kollar’s books to study MMP, not Shokurov’s “3-fold log flips”, because the goal is understanding, not claiming a territory as our own. Releasing the AI-generated texts without any intention of checking them would be irresponsible. Doing it having checked but not recognising the effort put in doing so is against basic labour principles. Checking them but not putting the utmost effort in ensuring readability and making it possible for the reader to understand as well as possible, would be unscholarly. At no point we have claimed any intention to produce a text hiding the seminal contribution of AI-contributed proofs. The process will be clearly explained in the text and if someone misattributes it, then it is their responsibility. Being the author of a document does not mean one is the author of every idea in it.
For us, this problem is important, among other things because of the effort many of us put in 2020/21 to see the initial solution for general element of each family. We want to see it through, we want to see it done. But if we had to manually find a working Abban-Zhuang flag for each remaining element, we would probably never finish and give up.