>Your article only mentions nameless mathematicians, without really giving credit.
I explicitly give credit to the papers the proof builds upon. Quoting from the article:
>The proof was only possible thanks to the many existing results from [References](https://gaearon.github.io/conway-refinement/#/references). In particular, [A factorisation theory for generalised power series and omnific integers](https://doi.org/10.1016/j.aim.2024.109513) by S. L’Innocente and V. Mantova has played a crucial role in the proof.
The project README (https://github.com/gaearon/conway-refinement) also states:
>Over the years, Berarducci, Pitteloud, Pommersheim and Shahriari, and L'Innocente and Mantova developed increasingly strong results about exactly that. This proof builds on all of that work and claims to finish the refinement conjecture.
It includes the same list of references: https://github.com/gaearon/conway-refinement#references
Regarding who I've talked to over email, I wasn't sure I want to "out" them explicitly in the article due to the article's likely polarizing nature, but, since he already engaged in this thread, I can confirm that this person was Prof. Mantova (who is a co-author of the primary paper that the result I published rests upon, and who I did explicitly credit in the text of the article and in the references).
You can read Prof. Mantova's own reflection here: https://news.ycombinator.com/item?id=49761718
I have not had an extended conversation with anyone else.
>Following your analogy it is not a very fair game if it allows winning for those having access to latest exploits. Playing against skiddies who bought the hack kind of ruins it.
You misunderstood the point of my analogy. The point was not that it is a game in which you "win" or "lose" and thus I have "won" or something like that.
The point was that "obtaining a true proof without understanding it" doesn't imply "understanding has no value" any more than "completing a game in an unintended way" implies "playing has no value". You stated a false implication. That false implication is what I am highlighting with the analogy. Understanding has a societal value; doing something weird for the fun of it has value to the person doing it; sometimes people do things with no value at all, and that's okay too. Each individual act is not a statement about what kinds of things have value.
Personally, I do not see mathematics as a game of "win" and "lose". If the broad value is primarily in understanding (which I think is correct), then my "contribution" doesn't make much dent in that. However, it might, as Prof. Mantova mentions, help show the way to an actually useful proof that improves collective understanding. That would please me beyond merely having had fun. In any case, I've enjoyed the experience of it in part due to the absurdity of it. Maybe it requires a certain kind of sense of humor.
Regarding the models, as far as I know, all of the models I have used are currently broadly available. Yes, they require subscriptions so access is not democratized yet. There's nothing I can do about that. I think it's unreasonable to require that someone playing around with LLM's must use the inferior free models.
I had not read the proof or any part of it because it is LLM generated. Most mortals won't for the same reason. It looked to me as if Prof. Mantova stepped from the crowd to get some credit which was not given. But maybe he did not care for it in the first place so you are right, it is not for me to judge.
And about the "value" I think we picked different meanings for this word:
For me for something to have value means it can be used for something else. In this sense you cannot pick what has value. There are people with deeper understanding of the subject than yours yet they were unable to use it to come up with a proof. You had no understanding but you had succeeded. Therefore understanding in this particular case had no value. You did not have to state it, it flows as a natural conclusion.
You can also say that being good at chess or catching all the pokemon has a value for you or for some society. This is true but it has to do with self-actualization rather than dealing with circumstances.
I also do not see how you can say you did not win anything. This proof will be a great addition to your portfolio which in turn will serve as a leverage while searching for your next job, even if it never comes up explicitly. It is a dream for some folks to be talked about on hacker-news. Good for you that you can treat is as if it was nothing, and I do not mean it as an irony.