Comment by dwrensha
20 days ago
I'm the maintainer of the linked website.
This morning, a mysterious user named "ranksunbounded" submitted the linked curve, which has rank at least thirty. This breaks the previous record of 29 found by Elkies and Klagsbrun in 2024.
Nobody knows whether it is possible to achieve arbitrarily high ranks.
I'm a research mathematician, and to me the biggest surprise is that the user didn't identify themselves or (yet) try to claim credit for their work.
Within academia, it is to your definite advantage to have your name associated with breakthroughs, for obvious reasons. Outside academia I don't have firsthand experience, but I'd have to imagine the same holds.
Update: the linked page has now been updated to say:
> it was Claude, with Levent Alpöge and Ava Howell!
Alpöge is the same guy who prompted Claude for a proof of the Jacobian conjecture.
He may have a penchant for unusual announcements. Making an "ranksunbounded" user and posting a 30 today, 31 tomorrow, and 32 the next wouldn't shock me.
It is also a sign of wisdom and maturity to not care so much, especially outside academia.
I know your reaction is the normal one these days, but I’d like to normalize the ones that don’t care about society petting them on the head and saying atta boy. They just deliver the work and retreat into the darkness. I find it highly inspiring. The alternative.. not so much.
Agreed. This is what real research looks like. Not publish or perish. Not going after a bunch of grants. Just doing the work and getting results. Sadly this is this antithesis of modern academia.
You might appreciate the first author on this paper, https://oeis.org/A180632/a180632.pdf
https://en.wikipedia.org/wiki/Superpermutation#Lower_bounds,...
Funny coincidence: I (who submitted this story) am the second author.
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If this work has an implication for cryptography they might want to be anonymous for any number of reasons.
Or a random amateur who got lucky with AI. This happened to someone I know and he doesn’t even know how to publish
ranksunbounded has added a comment on the curve: "it was Claude, with Levent Alpöge and Ava Howell!"
I just don't understand how Alpöge can get Claude to construct so many complex mathematical objects. He must already have some deep insight into the structure these things are likely to take. Naive prompting, or naive search would not have found pretty much any of the object he's found in the past month.
He has an AB in Math from Harvard with a senior thesis "The average elliptic curve has few integral points", and a PhD in Math from Princeton with thesis "Points on Curves", so it's fair to say he has some deep insight. (https://alpo.ge/cv.pdf)
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It wouldn't surprise me if he is given access to a more advanced model or more compute, since he is an Anthropic employee. Add to that the fact that this makes great PR and that he has not shown any of his prompts, it's more than likely in my opinion that this is the case.