In legal writing, an inline footnote begins with the word "see" in italics, e.g.,"football-related prayer in public schools is now permitted,see,Kennedy v. Bremerton School Dist., 597 U.S.507 (2022)." It's just as easy to make this a footnote but some judges have objected to "excessive" footnotes in legal submissions. Keeping them inline avoids this criticism.
ps On another note, AI legal hallucinations are a solved computing problem. Either a cite or case is contained in the closed universe of materials or it isn't--a simple binary question. Problem is, thos with control of the materials, starting with 1 Dallas (which predates the United States) won't share the list with AI companies.
pps This forum deletes unicode. The word see was gobbled from the original text.
I did not have the impression the proof uses a surprising and novel contribution of fields. I think the proof uses standard application techniques of algebraic number theory towards discrete geometry. If you have a quote substantiating what you said I would be curious.
I know these articles write that it used deep algebraic number theory techniques, which is true, but it may also just be the standard in the field.
You are believing a very unlikely scenario. I think the reason is that you have been convinced of a claim which is unlikely and indeed not true. That is:
>the model seems so capable at doing things like refuting fundamental theorems of mathematics
That is not true and a complete misrepresentation of recent progress of AI in math. It is therefore not necessary to believe the conspiracy theory you described in order to explain recent progress of AI in math.
You should believe that the proof works at least as much as any ither paper in mathematics. The proof has been scrutinized by experts and simplified and improved. If you don't believe that then I'm sorry but you are deluding yourself.
No it is not Leibniz/Euler/Galois. More like writing good papers that contribute to the broader understanding of a theory. I think if one evaluated a mathematicians research output and it consisted of mostly the kinds of problems AI has solved so far, it would give the impression that this person is somehow very good at picking accessible problems to target, but has not made a larger impact on the field.
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