theHigherGeometer

In case you weren't there, but are curious; the lecture notes are available here https://github.com/tomdjong/MGS-categorical-realizability/blob/main/MGS-categorical-realizability.pdf?raw=1

I need to learn more about the nitty-gritty of academic publishing practices in Germany in the 1880s. I have no idea where to start looking, and in any case, probably the place I need to look is in German. Need some historians to talk to!

A specific question I have is this: did publishers send […]

Disclaimer

I feel seen in that alt-text

https://xkcd.com/3126/

Disclaimer

I feel seen

https://xkcd.com/3126/

Blueberry Hill ChatGPT 5 was released today. ChatGPT-maker OpenAI has unveiled the long-awaited latest version of its artificial intelligence (AI) chatbot, GPT-5, saying it can provide PhD-level expertise. Billed as “smarter, faster, and more useful,” OpenAI co-founder and chief executive Sam Altman lauded the company’s new model as ushering in a new era of ChatGPT. “I think having something like GPT-5 would be pretty much unimaginable at any previous time in human history,” he said ahead of Thursday’s launch. GPT-5’s release and claims of its “PhD-level” abilities in areas such as coding and writing come as tech firms continue to compete to have the most advanced AI chatbot.

Oh, you....

https://kieranhealy.org/blog/archives/2025/08/07/blueberry-hill/

I think it would be nice if all of one's professional dealings were with other people in one's own continental range of time zones.

UK Royal Society adopts ‘subscribe to open’ publishing model Nature, Published online: 06 August 2025; doi:10.1038/d41586-025-02483-0 Eight of its journals will publish papers open-access each year they earn sufficient library revenue.

The Royal Society is committing to its values by choosing the fair and sustainable #SubscribeToOpen model for #OpenAccess publishing! More comments by me and my @ems_press colleague Laura Simonite in this Nature article https://www.nature.com/articles/d41586-025-02483-0 #s2o

Source: K. Buzzard, "The future of mathematics?" Jan 2020, https://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf
Quote from slide 22.

@xenaproject once wrote:

"Exhibit C: Gaitsgory–Rozenblyum.
Infinity categories are now a thing. They will only get more important over time. Scholze’s new ArXiv article relies on
them.
Lurie has written 1000+ pages on (∞, 1)-categories, and has included lots of details in his work […]

OK, so every Banach–Lie group (and hence every Hilbert–Lie group) is locally exponential. The problem is that there can be nontrivial, non-discrete closed subgroups where there every continuous path through the identity in the subgroup is constant.

The specific example I found via Alexander […]

Well, someone claimed on MathOverflow that the closed subgroup theorem can fail even for Hilbert Lie groups! But the reference talked mostly about Banach Lie groups, while mentioning just one that there can be a closed subgroup of a Hilbert Lie group that admitted no smooth curves in it (but […]

Oh, and he's listed at https://en.wikipedia.org/wiki/Morgan_Prize and https://en.wikipedia.org/wiki/Rollo_Davidson_Prize with redlinks, too.

And also:

https://www.math.columbia.edu/2022/10/19/amol-aggarwal-awarded-the-2022-packard-fellowships-in-science-and-engineering/ […]

arXiv in trouble? Since June 15, 2025 there have been 8 papers posted to arXiv with the phrase “Hodge conjecture” in the title or abstract. By my count 6 of them (75%!) are LLM-generated nonsense, replete with hallucinated references; as you might imagine the amount of correct mathematical content they contain is near-zero. I worry this issue will only get worse with time.

I've seen the papers that @littmath mentions here:

https://www.daniellitt.com/blog/2025/7/17/arxiv-in-trouble

and they are baad.

Ideally the @arXiv can come up with a solution....

Today we started on the actual proof of the closed subgroup theorem, and, what with things like needing the exponential map to be a diffeomorphism near the identity, choosing a complementary subspace of what will be the subalgebra of the Lie algebra, estimates and whatnot, I was really wondering […]

@xenaproject I suspect the blog post by Google was silently changed, but it does reference and link to the "we got gold at IMO2025" announcement twice.

Apropos your latest blog post @xenaproject, already inaccurate claims of AI solving "years-old unproved conjectures" are surfacing.

Reddit post: "Google Deepmind claims to have solved a previously unproven conjecture with Gemini 2.5 deepthink" https://blog.google/products/gemini/gemini-2-5-deep-think/ Seems interesting but they don't actually show what the conjecture was as far as I can tell?"

TeX source for the conjecture as seen Google's announcement video, in the Gemini interface: "Fix an integer $d \geq 1$. Then we have \[ \sum_{(d_1,\ldots,d_r) \vdash d} \dfrac{2^{r-1} \cdot d^{r-2}}{\#\! \operatorname {Aut}(d_1,\ldots,d_r)} \prod_{i=1}^r \dfrac{(-1)^{d_i-1}}{d_i} {3d_i \choose d_i} = \dfrac{1}{d^2} {4d-1 \choose d} \] where the sum is over strictly positive unordered partitions of $d$ (of any length)."

User on Reddit having scraped the TeX source and compiled it.

Exact match for the conjecture, in v1 of a 2023 preprint https://arxiv.org/abs/2310.06058v1, "Gromov-Witten theory of bicyclic pairs", by Michel van Garrel, Navid Nabijou, Yannik Schuler. It has a proof of the conjecture.

Claims of AI proving "previously unproven mathematical conjecture" are exaggerated. The conjecture had been proved in 2023, see Theorem 3.10 in:

https://arxiv.org/abs/2310.06058v1

https://bsky.app/profile/dangaristo.bsky.social/post/3lvc7ldavhk2o

🤯

I found this paper because the main offender here cited a paper of mine in a non-arXiv preprint and I got a Google Scholar alert about it. Nice to know that LLMs have absorbed stuff I have written, and are now promoting it...

I will let you find this paper and the gem hidden in its Appendix B, and the other preprint cited there. Actually a rather worrying sign, though...

Sure sign of an LLM-generated paper: it starts devolving into reflective dialogue about the content. For example:

"But T here is in the scaled units relative to something? [...] Our approach is essentially an extremely heavy smoothing, meaning we might not need T to grow with x as a power at […]

Likewise, Ivan Angiono, Tim Austin, Uri Bader, Benjamin Bakker, Afonso Bandeira, Pierre Berger, Itaï Ben Yaacov, Anton Bernshteyn, Jacob Bernstein, Massimiliano Berti (red link at https://en.wikipedia.org/wiki/Vinti_Prize), Valentin Blomer (redlink at […]

Well, Amol Aggarwal needs a Wikipedia page, now he's an invited speaker to the ICM, and also a red link as a prize-winner at

https://en.wikipedia.org/wiki/International_Association_of_Mathematical_Physics#IAMP_Early_Career_Award

cc @11011110

And of course, I personally know nothing about what will be awarded to whom at the next ICM.

Now the plenary/invited/etc speaker list has been announced for #ICM2026, people who are curious might feel the need compile the subsset of people on this page

https://www.icm2026.org/event/ac193975-5d24-4628-8c30-ddb23de19a8b/speakers

who are under 40 😉

Click through for the video of it being held by a human...

https://www.abc.net.au/news/2025-07-31/giant-stick-insect-acrophylla-alta-wet-tropics-discovery/105596666

#straya #FNQ

Well, now I noticed a double space. Not going to edit again!

I can't believe I had to edit this three times to fix everything. Muphry's law indeed.

MathOverflow is now future-proofed against the closure of Google's immanent shuttering of the legacy goo.gl link-shortening service.
As far as is possible, all such links have been replaced by working links, or even the broken link targets, except in a very few cases where the target link was so […]