theHigherGeometer

rimcræftiga |
bespoke constructions in categorified geometry since 2010 |
dude

Public Key

npub1p2q4c7sn2jgtj3w7g9syy5zjldxd8e5ruknf99g8y636ls8vx8esq5c0lr

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highergeometer@mathstodon-xyz.mostr.pub

Profile Code

nprofile1qqsq4q2u0gf4fy9egh0yzczz2pf0knxnu6p7tf5jj5rjdga0crkrrucpz3mhxue69uhhyetvv9ujuerpd46hxtnfduqs6amnwvaz7tmwdaejumr0ds3sepf8

Publishing to

relay.damus.io

nos.lol

Author Public Key

npub1p2q4c7sn2jgtj3w7g9syy5zjldxd8e5ruknf99g8y636ls8vx8esq5c0lr

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Last Notes

2026-02-08 23:19:41 UTC

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@nprofile…4257 How much of this is down to a lucky scramble? In other words, how many moves did it take? (perhaps this is answered in the video, sorry)

2026-02-08 09:44:07 UTC

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@nprofile…lfhd @nprofile…gpz3 Sure, but you have to establish the required radius of convergence to know that π is something that be extracted. I was interested in an elementary-as-possible approach.
[Lárusson's short lecture notes on real analysis book (which I once formally reviewed) does it by establishing that the zero-set of $\sin$, defined by a power series is a discrete additive subgroup of the reals, but this is not early in the book!]

2026-02-08 03:44:41 UTC

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@nprofile…gpz3 I can't remember!

2026-02-07 12:08:45 UTC

Having taught first-year calculus, including things like geometrically deriving $\tfrac{d}{dx}\sin(x)$, and estimates on errors from Taylor polynomials, and also liking the kind of foundational subtleties in analysis that can be broken down to understandable chunks, I agree that Archimedes' argument involving more than one round of estimates (post 2/3 in the below mentions $256/153 < \sqrt{3} < 151/78$ as going into the process of calculating the bounds for π. Once my colleague Raymond Vozzo and I tried to work out what was the clearest/simplest way to completely rigorously define π or 𝑒, in the sense of analysis. It's not trivial!

2026-01-29 22:23:19 UTC

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@nprofile…lfhd On the sentence "Cet exposé fait suite à celui d’il y a deux ans (25 janvier 2024)," the link on celui is broken!
https://webusers.imj-prg.fr/~antoine.chambert-loir/exposes/tb-20240125.pdf

2026-01-28 10:16:34 UTC

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@nprofile…fws0 Thanks :-) now that things are in full swing, are participants likely to make their slides available on the conference site?

2026-01-12 11:28:36 UTC

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@nprofile…lfhd The slides link on your site is broken! https://webusers.imj-prg.fr/~antoine.chambert-loir/exposes/20260111-cpp2026

2026-01-10 08:28:36 UTC

https://doi.org/10.1112/jlms.70374
Not every day someone's paper gets a review 30 years later by a leading figure in the same (top-notch) journal. Michael invented the main definition in his now-classic paper while waiting for Brylinski's then-recent book on gerbes to be shipped to Australia, based on the tiny blurb in a publisher's ad for it.

2026-01-07 05:18:45 UTC

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The first proof in the paper says to pick four cardinal parameters to be the specific values $\aleph_6,\aleph_5,\aleph_2$ and $\aleph_0$ and then apply a more complex main theorem.
I mean, this is the guy who proved
\[2^{\aleph_\omega} < \aleph_{\omega_4}\] which never ceases to boggle my mind.

2026-01-07 05:10:44 UTC

"This is publication number 1258 on Saharon Shelah’s list"
Of course it is 🫠
https://arxiv.org/abs/2601.02923

2025-12-25 08:40:49 UTC

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@nprofile…dand @nprofile…fdxu there's a bunch of stuff and I don't know how deep it is, nor how much the IA's Wayback Machine will save. Also I want copies myself, to get rid of the current formatting fluff.

2025-12-25 06:53:36 UTC

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If there is anyone reading this will skills in crawling websites and capturing complete webpages, I would be very grateful if this happened....

2025-12-25 06:52:39 UTC

"Dear all,
I am writing this to inform you that the Institute for Geometry and its Applications (IGA) is coming to an end. As the IGA does not meet the requirements to be a University Research Centre it can no longer continue, even in name. Consequently the IGA webpage will disappear along with the University of Adelaide website early in the new year."
This is the website:
https://set.adelaide.edu.au/geometry-applications/
it contains a record of 30 years of research seminars and workshops, 17 years of member's publications and postgraduate students. If it's not saved, these will vanish into the ether as no one has said the university will try to save this information.
I've not been explicit about the university name in posts about the merger, but "it can no longer continue, even in name" is just ridiculous. Apparently there can be only research centers that are linked with external (i.e. industry) money.

2025-12-24 04:59:11 UTC

OK, I have a noob question about fields: Let ι : k->k' be an arbitrary extension, and i,j : k'->K arbitrary embeddings to some other field that agree on k. Suppose I have x\in k' such that i(x)=j(x). It seems to me like one can easily have such a setup where x doesn't come from the subfield k, namely take i=j.
Asking that given x,i,j as stated, then x = ι(y), is, I think, the sheaf condition for the forgetful functor U : Field -> Set that gives the underlying set, and the coverage (not a pretopology) on Field^op that takes arbitrary field inclusions as covers. I may have made a mistake, but doesn't any morphism of fields k->k' induce an fpqc cover Spec(k')->Spec(k)?
So surely U is not a sheaf for this coverage? It's easily seen to be a separated presheaf. Though it's been suggested to me that U, despite being the restriction of Waterhouse's non-sheafifiable presheaf along Field^op -> Aff, *does* have a sheafification.
First I'd like to know if I'm thinking about this correctly. If so, one can then think about how one might try to calculate the sheafifiation. Since for any ι : k->k', the identity on k' fills the square, this feels like a bunch of simplifications can be made.

2025-12-19 06:34:01 UTC

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The video references this page: https://ncatlab.org/nlab/show/trigonometric+identity

2025-12-19 03:21:10 UTC

I love seeing my logo in the wild
https://www.youtube.com/watch?v=59XrCDmXiCc

2025-12-16 01:29:10 UTC

Wow.
"By 1974, Garfield’s citation tools had become influential enough that a conference was convened at the Center for Advanced Study in the Behavioral Sciences to assess their implications.[9] Merton attended, and he warned Garfield directly: “I’d like to get on the record the problem of goal displacement as it might work with citation analysis.” But Merton didn’t only warn. He sat on ISI’s board of advisors. He gave Garfield strategic advice about how to position the company. And when Garfield worried about evaluative misuse of citation data, Merton reassured him that massive use for appointments and promotions was “not in the cards.”[10] He was wrong, and some part of him knew it. A footnote in a 1972 paper Merton co-authored with Harriet Zuckerman had already conceded the problem: using citation analysis for appointments and promotions would, they wrote, “invalidate them as measures altogether.” [11]"
That last footnote:
"[11] Harriet Zuckerman and Robert K. Merton, “Patterns of Evaluation in Science: Institutionalisation, Structure and Functions of the Referee System,” Minerva (1971). The warning, in footnote 18, reads: “Through the process of socially induced displacement of goals, this value of open communication would eventually become transformed for appreciable numbers of scholars and scientists into an urge to publish in periodicals, all apart from the worth of what was being submitted for publication. This development would in turn reinforce a concern within the community of scholars for the sifting, sorting and accrediting of manuscripts by some version of a referee-system.”"
https://artificialbureaucracy.substack.com/p/context-widows

2025-12-15 21:52:44 UTC

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@nprofile…fdxu @nprofile…8eua ok, the paper has obvious signs of LLM-generation that the author hasn't proof-read and fixed. There's Markdown syntax mixed into the TeX in the image.... on MO this would be a fast close.
https://media.mathstodon.xyz/media_attachments/files/115/725/791/615/015/010/original/4e40df22ce7d3123.jpg

2025-12-15 21:39:36 UTC

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@nprofile…fdxu @nprofile…8eua I wrote originally "if you mean Huawei, then note that they also fund research into topos theory and do things like this: https://www.ihes.fr/en/laurent-lafforgue-en/"
But it's not. That's not to make any judgement call on the paper (or the company) either way.

2025-12-15 07:07:17 UTC

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@nprofile…63jn I replied to the email confirming submission, as it seemed to invite. Otherwise I don't know who the handling editor is (did I pick one? I can't recall) and cold emailing an EiC or managing editor feels a bit too much

2025-12-15 07:06:04 UTC

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@nprofile…63jn I'm really hoping it's the first

2025-12-15 01:56:09 UTC

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Like this:
https://media.mathstodon.xyz/media_attachments/files/115/721/088/596/635/484/original/b94f03a4273fe1ce.png

2025-12-15 01:52:06 UTC

OK, submission to Comptes Rendus Mathématique is now nearing 6 months. Has anyone here published anything in that journal in the past couple of years? I'm thinking of emailing an editor, since the editorial platform claims the review stage is "not initiated".

2025-12-14 09:42:44 UTC

For all those classical music nerds to spot all the composers and their stolen pieces
https://www.youtube.com/watch?v=5FEUbrFgfc8

2025-12-09 23:25:21 UTC

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@nprofile…9s72 FWIW here's an old talk on it https://www.youtube.com/watch?v=9seDf_HrBYg

2025-12-09 04:24:04 UTC

Want some eyeballs on this: https://meta.stackexchange.com/a/415282/
Curious to know thoughts of people on the situation.

2025-12-05 09:53:00 UTC

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@nprofile…9s72 Ta. I found the publisher page in the end.

2025-12-05 01:37:40 UTC

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@nprofile…9s72 Link?

2025-11-29 01:09:02 UTC

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@nprofile…p3nn your two books made me think of this one that I saw in the school library: https://www.goodreads.com/book/show/207003952-capital-ideology

2025-11-25 07:01:50 UTC

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@nprofile…u5vz Hmm, this is interesting. The first condition puts an upper bound on how fine the topology of X \times Y can be, and the second puts a lower bound.
Part of the way to check this really is the product topology is to consider *any* topology \tau satisfying these two conditions (and symmetrically for the projection to Y and the subspaces X \times {y}), and a function F = (F_1,F_2) \colon Z \to X\times Y such that F_1 and F_2 are continuous. Is F continuous for \tau?
Note that you always have a continuous bijection (X\times Y, \tau) \to (X\times Y,prod), so that tau is no coarser than the product topology. You just need to check the inverse bijection (X\times Y,prod)\to (X\times Y, \tau) is continuous, which is the case of Z=(X\times Y,prod) in the above.
So take an open X\times Y \supseteq U in \tau. All you know about it is that pr_1(U) and pr_2(U) are open, and for all (x,y)\in X\times Y, the intersections with {x}\times Y and X\times {y} are open. Does this tell us that U is open in the product topology?

2025-11-24 00:43:48 UTC

Riemann Hypothesis proof claimers: here's my proof bro, all the mathematicians didn't see it because it's simple and they are blinded by BiG mAtH. It only took 5 pages!!
Actual analytic number theorist who proved the weak Goldbach conjecture: here's an explicit estimate that uses zeroes of the zeta function...
https://media.mathstodon.xyz/media_attachments/files/115/601/887/390/133/278/original/21b4c9bd16d00538.png

2025-11-19 19:29:24 UTC

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@nprofile…kgh3 well....
https://arxiv.org/abs/2110.00239
@nprofile…99up

2025-11-19 11:14:36 UTC

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@nprofile…99up @nprofile…kgh3 I was really wondering if there are any in substructural logics, for instance bunched logics, relevance logics; in light of your synthetic computability example could one have a really impoverished type theory and still land a fixed point result, using a substructural version of the FPT as I considered?

2025-11-18 23:53:20 UTC

Thanks to @nprofile…dand for this fun game :-)
https://thehighergeometer.wordpress.com/2025/11/19/a-game-strategy-that-depends-on-the-continuum-hypothesis/

2025-11-18 11:43:23 UTC

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@nprofile…dand aha, so it's really a statement about Eve being given three ordinals, and there's a winning strategy iff they are all (known in advance to be?) countable?

2025-11-18 11:01:24 UTC

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@nprofile…dand I'm aware of determinacy shenanigans 😉 but I'm not sure I'd count trying to guess a nearly arbitrary real number as "recreational"

2025-11-18 07:57:56 UTC

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@nprofile…63jn Only for those specific types of articles (generic overview/review articles), which are trivial to generate by AI and require no actual hard thinking. The sort of literature review you'd set as an undergrad essay task. From memory, the justification was that this really isn't research and that the (CS) arXiv is for research papers.
@nprofile…6fuz @nprofile…hcpk

2025-11-18 04:53:05 UTC

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@nprofile…hcpk Standards for the computer sciences section or the mathematics section? The former has cracked down on review articles, which apparently were always kinda off-topic there, but perhaps tolerated. Mathematics is different as far as I know. Also, When people of the stature of Atiyah, Mac Lane, et al, or Thurston, write opinion pieces about mathematics, I think that this is clearly not AI slop. Suppose Scholze or Tao or Yau or Uhlenbeck (!) or .... today posted something to math.HO about the nature and practice of mathematics that was going to be published in the Bulletin AMS. I don't think the arXiv would say no.

2025-11-17 23:52:26 UTC

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Source: https://arxiv.org/abs/math/9404229
I think in today's increasingly AI-saturated landscape, these short pieces responding to the famous/notorious Jaffe–Quinn article should be required reading, along with Thurston's https://arxiv.org/abs/math/9404236 also written in response to Jaffe–Quinn.

2025-11-17 23:47:24 UTC

"On occasion, some leading journals (The Annals of Mathematics) have
been sometimes careless in not checking for errors in papers on fashionable subjects. Moreover, when error is discovered, the journal should publish a retraction, so that all workers may know."
—Saunders Mac Lane
Don't leave it to experts to know among themselves which unacknowledged errors are critical!

2025-11-17 00:46:26 UTC

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@nprofile…dand Well, foundations don't make me uneasy. I was putting my philosophical hat on, and also not trying to be precise.
I'm not sure that mathematicians *consciously* avoid independence phenomena. For instance, arithmetic geometers somehow seem to make great headway with their subject without suddenly having to worry about Diophantine equations having solutions or not depending on what model of set theory they are in.
The only person I know in that area that puts very careful foundational fences around their work is Scholze, who does care about not assuming the existence of inaccessible cardinals, eg dealing with condensed mathematics (contra Barwick and Haine, who did) And I think the work is richer for it.

2025-11-08 23:26:33 UTC

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This is a terribly fuzzy thought, but you can see vague shades of this in MacIntyre's chapter "The Impact of Gödel's Incompleteness Theorems on Mathematics" in the 2011 book Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. He argues, as I recall, that much of the actual ('generic', I would call it) mathematics that is done and where the biggest results are, falls in the realm where one doesn't run afoul of incompleteness phenomena.

2025-11-08 23:11:35 UTC

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We still keep things like plane geometry because of Tarski's theorem that says the theory of real-closed fields is complete and decidable, but we treat these as synthetic.

2025-11-08 23:01:41 UTC

Here's a radical thought: can one make sense of a mathematico-philosophical position that takes as 'real' only those parts of mathematics that aren't subject to independence phenomena? This is vaguely cousin to ultrafinitism, except that instead of bounding the raw stuff of mathematics by size, it is more of a complexity bound. The upper limit is vague, with definite known points where eg Hilbert's 10th Problem fails, and I guess a known region where things are OK (to continue the example, "small" Diophantine problems are provably not undecideable).

2025-11-05 23:30:53 UTC

Mathematics publishing can be sloow
"Received by editor(s): March 7, 2022
Received by editor(s) in revised form: March 2, 2023, December 31, 2023, September 5, 2024, April 3, 2025, and June 4, 2025
Published electronically: August 29, 2025"
And one of the authors even died in 2018, so it took a while to get to submitting this paper, too....

2025-11-04 06:29:08 UTC

David Mumford, a past president of the International Mathematical Union, once wrote, in a piece on the history of mathematics publishing:
"More recently Springer realized that even books out of copyright could generate new revenue and offered authors the “benefit” of keeping their books in print indefinitely by voluntarily extending copyright to infinity. Actually, you can get nearly all math books free online at the rogue Russian “Genesis Library,” with websites libgen.in and gen.lib.rec.ec (most of my books are there – help yourself). Which do you prefer: lunch money royalties once a year or wider free distribution of your books?"

2025-11-04 02:04:55 UTC

*Brunerie meme* 🙃
https://youtu.be/UNBfyeB9u1s?si=X7xArp_odHgt8-nr&t=3282
https://media.mathstodon.xyz/media_attachments/files/115/488/961/702/386/878/original/cd95b654170cdf4d.png

2025-11-03 07:53:23 UTC

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Oh, wait: there's a third option: the infinite dim'l separable Hilbert space itself...

2025-11-03 07:49:58 UTC

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Hmm, maybe separable LF-spaces will work. There is a very short list if you consider them up to *homeomorphism*, namely, the finite-dimensional vector spaces, then two non-homeomorphic infinite-dimensional ones, if I'm not mistaken, by
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/52/2/100372/on-topological-lipschitz-and-uniform-classification-of-lf-spaces
1. The union of all the R^n's, i.e. eventually zero sequences of real numbers
2. The space of eventually zero sequences in the separable infinite-dimensional Hilbert space.

2025-11-02 22:02:56 UTC

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OK, this isn't going to actually work for what I want. I need more general model spaces, but also want control on the size of the site...

2025-11-02 02:11:08 UTC

OK, so I am going to invent a new site, to replace Cart, the site with objects the Euclidean spaces and all smooth maps, where covers are families jointly-surjective open embeddings: I'm going to use something like nuclear Fréchet spaces instead. Then have a type of generalised smooth space that is a concrete sheaf on this small site.

2025-10-23 22:53:14 UTC

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@nprofile…p3nn Indeed:
"Is this LLM-generated? "
"I'm not sure if this is real, but the abstract says machine-verified."
"It seems a pretty serious attempt though- it’s not just some random crank paper."
"The fact that they have formalized the proof should mean it will be quicker to verify whether or not this is indeed it."
@nprofile…8eua

2025-10-23 21:47:37 UTC

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@nprofile…p3nn @nprofile…8eua Oh dear, some people there don't seem to realise just how trash this is.

2025-10-23 06:16:39 UTC

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I'm reliably told that it is indeed a first printing of the first edition.

2025-10-23 00:14:03 UTC

https://doi.org/10.1038/d41586-025-03340-w
(forgot who I saw there this here, sorry!)

2025-10-22 09:43:50 UTC

An image caption on a BBC article (about Philip Pullman and his comments on AI ingestion of authors' works):
"Dafne Keen, with her daemon Pan, played Lyra in the BBC's His Dark Materials series, which ran from 2019 to 2022"
I guess they do not really mean that Dafne Keen has a real-life daemon and together they played the character Lyra 🤣

2025-10-22 04:36:47 UTC

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@nprofile…w8t5 "Someone needs to make an observation about what I was just talking about: something you notice or wonder"
Doesn't need to be a question!

2025-10-22 04:32:47 UTC

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@nprofile…g95x A Springer journal? I suspect that company is using AI to speed up (read: perform more cheaply) the production process.

2025-10-22 04:21:45 UTC

Oh dear. AI-generated Lean code and a document saturated with bullet-point lists
https://arxiv.org/abs/2510.17829
Don't bother. Cross-listed to math.CT, but should be in math.GM.

2025-10-21 08:06:21 UTC

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@nprofile…nx65 in the positive characteristic case, one might want coefficients that are related to divided powers

2025-10-21 04:48:46 UTC

TIL that there are some fields for which you can define the exponential map, but it has a finite radius of convergence.... o.O

2025-10-21 02:17:00 UTC

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@nprofile…dtfl One would guess the guitars wail while getting whaled...

2025-10-20 22:17:42 UTC

"...with the box office just having eeked past $100 million"
*eked 🤓

2025-10-20 04:59:40 UTC

Has anyone ever seen "A Categorification of Quandle Coloring Numbers by Anafunctors" by John Armstrong? My only leads are the blog post https://unapologetic.wordpress.com/2007/05/21/ and the arXiv paper https://arxiv.org/abs/0803.1642, which doesn't mention anafunctors. Section 5 of that paper is vaguely evocative, but without sitting down and trying to really understand it, matters are not clear to me.

2025-10-20 01:04:15 UTC

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Hmm, what I want also might turn up under the name "coalgebroid". I think this is what Schäppi calls them. I guess I want one that is nice, for instance flat (?) or better, étale.

2025-10-20 00:10:35 UTC

In honour of the passing of Chen-Ning (Frank) Yang, here is the "dictionary" that he published with Tai Tsun Wu, that is an absolute foundation stone for the area of mathematical physics that I work adjacent to:
https://en.wikipedia.org/wiki/Wu%E2%80%93Yang_dictionary

2025-10-19 22:37:26 UTC

Does anyone know of an interesting (commutative) bialgebroid from either algebraic geometry of algebraic topology that isn't a Hopf algebroid, not just a bialgebra?

2025-10-19 22:30:20 UTC

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@nprofile…huu7 👉 @nprofile…maev
@nprofile…w8t5

2025-10-17 06:05:14 UTC

Also, I was thinking a bit more last night about random finite $T_0$ topological spaces, and if I have $\mathbb{S}^n$, for $\mathbb{S}$ the Sierpinski space, then I should sample from this a set of points smaller than $2^{n-1}$, possibly empty, then take its complement, and take the subspace topology on that. This gives a random topological space of size between $2^{n-1}+1$ and $2^n$. So if I pick a natural number from a suitable distribution, then do the above procedure, it will sample finite topological spaces. Exactly what the distribution looks like is mysterious!

2025-10-17 05:56:21 UTC

For various reasons, earlier in the year I was wondering if (finite, say) regular CW-complexes could be identified among posets by combinatorial properties. Recall that these are CW-complexes where the attaching maps are injective (and hence embeddings). The naive definition depends on that point-set notion, particularly knowing that the image of the attaching map (which is a sub-complex) is a cellular decomposition of a sphere.
Not pleasant!
But today I managed to find some literature that gives a purely poset-theoretic description of those posets that arise from regular CW-complexes! 🎉
Note that regularity is needed here, because the unit disk and $\mathbb{RP}^2$ have CW-decompositions with isomorphic (graded) face posets, and so the face poset doesn't determine the topology without extra assumptions.
I'm not sure exactly how I'm going to use this yet, but it's just nice to know these things....

2025-10-16 01:20:00 UTC

In this video Jesús De Loera mentions getting a bunch of grad students in a room for months just grinding out by hand the algorithm that was used to prove the four-colour theorem:
https://www.youtube.com/watch?v=17hiB2j4FB8
I've also thought that it might be an interesting exercise, a kind of mathematical performance art on par with how @nprofile…maev organises laborious group exercises to do hand-computation of π. If this happens, there should be a documentary made, about the background to the problem, to the organisation of the effort, documenting the effort, and getting reactions from people who might have interesting things to say.

2025-10-15 20:58:02 UTC

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I should say this was in a bibliography item. It didn't happen on the next entry, also by us, whose title had the same first word.

2025-10-15 06:12:09 UTC

My coauthor's surname was replaced by the first word in the title of the paper listed under our names, and that word was dropped from the title.
Thanks, Springer's possibly AI-using typesetting company...

2025-10-14 20:27:33 UTC

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@nprofile…nslg @nprofile…8pq6 it works even better in an non-rhotic accent with "t flapping", where the t sounds the same as a d.

2025-10-13 23:10:53 UTC

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@nprofile…63jn Ah, that one makes me really wish for a movie about Galois in the same style. That that scene is a mere three days after Galois's funeral is never far from my mind.
Having the Elephant in the background was a nice reference to the book, I think.

2025-10-13 02:34:43 UTC

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Here's the list of all his papers: https://www.pnas.org/authored-by/Ono/Ken

2025-10-13 02:34:12 UTC

TIL that not only does Ken Ono have 14 number theory papers in the Proceedings of the National Academy of Sciences (!), he has had two of them feature on the cover!
https://doi.org/10.1073/pnas.191488598
https://doi.org/10.1073/pnas.1902572116
https://media.mathstodon.xyz/media_attachments/files/115/364/491/001/098/108/original/d913feb1aac0d6af.png
https://media.mathstodon.xyz/media_attachments/files/115/364/501/801/485/978/original/f34cd2d5953aba65.png

2025-10-13 02:01:01 UTC

I almost fell for thinking they were actually by the same person, posting again after it got closed the first time, but apparently not?
https://media.mathstodon.xyz/media_attachments/files/115/364/380/572/090/160/original/3fd7832cdf52e9b7.jpg

2025-10-11 21:04:35 UTC

"The ability of z to freely roam the plane unleashed in us a degree of visual imagination that had to remain dormant so long as we could only watch the real number x forlornly pacing its one-dimensional prison."
—Tristan Needham, Visual Complex Analysis
via r/math

2025-10-11 07:37:36 UTC

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@nprofile…dgud math.stackexchange.com or Reddit.com/r/askmath ?

2025-10-10 06:52:52 UTC

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@nprofile…4yyd Link?

2025-10-10 02:29:46 UTC

Ross Street is going to get a present for his 80th birthday!
"Dear Colleagues,
In honor of the 80th birthday of Professor Ross Howard Street, we are pleased to announce a special issue of Journal of Pure and Applied Algebra dedicated to celebrating his remarkable contributions to category theory and mathematics in general.
Topics of interest include (but are not limited to) all areas of pure and applied category theory.
The Guest Editors are:
Jiří Adámek
Maria Manuel Clementino
Marino Gran
George Janelidze
Stephen Lack
We are sending this message now so that you can begin to plan for possible submissions. The deadline will be 31 July 2026, and we will write again with further information about submissions once the journal’s website is ready.
George Janelidze, on behalf of the Guest Editors"
Sadly, it's in JPAA, published by Elsevier, otherwise I'd submit something.

2025-10-10 00:36:58 UTC

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@nprofile…ta23 Yes, with domain-specific axioms.
But note you can also do analytic coordinate geometry with axioms, say using those of the real numbers as a Dedekind complete ordered field. So "axiomatically" is not a unique specifier.

2025-10-09 22:43:05 UTC

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@nprofile…ta23 Synthetic as in Euclidean axiomatic geometry vs doing it all with coordinates in the plane (=analytic).

2025-10-09 22:40:56 UTC

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@nprofile…39gf You could try copying the construction of the Long Line [1] except replace the ordinal $\omega_1$ by an ordinal that is bigger than size continuum. Assuming appropriate well-orderability, you could take a well-ordering on $P(\mathbb{R})$, call this $\alpha$ and then do the $\alpha$-Long Line. I've not seen this explicitly done, but I can't immediately see why it wouldn't.
[1] https://en.wikipedia.org/wiki/Long_line_(topology)

2025-10-08 02:15:26 UTC

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@nprofile…jev0 I agree that would be helpful!
@nprofile…fa4k

2025-10-07 21:09:14 UTC

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@nprofile…fa4k Regarding the projective plane/incidence geometry stuff, the condition analogous to Pappian and Desarguesian that gets you a Moufang plane (https://en.wikipedia.org/wiki/Moufang_plane, OP^2 is the prototypical example, I believe) is "little-Desarguesian". This holds iff the planar ternary ring is an "alternative division ring" (of which the octonions are an example).
Axiomatic/synthetic projective *lines* are less easy, and you get more exotic examples
https://ncatlab.org/nlab/show/projective+line#synthetic_projective_lines
analogous to how you get non-Desarguesian planes, but no non-"Desarguesian" projective n-space for n≥3.
I think Buekenhout's definition of projective line is instructive to consider for lines isomorphic to OP^1.
@nprofile…jev0

2025-10-07 03:54:08 UTC

"The Graduations Office will now turn its attention to the University of [redacted]’s final graduation ceremonies, scheduled for March 2026. These events have been moved to March, away from the traditional May timeframe, to align with the University’s disestablishment. This will mean both staff and students will be working to a tight and compressed timeline."
[Press F to pay respects]

2025-10-07 02:08:03 UTC

Thank you to @nprofile…lu35 for the coffees!
https://buymeacoffee.com/highergeometer/c/15658089

2025-10-06 05:17:25 UTC

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@nprofile…qmju I want to also emphasise for people reading that this is rather far from the typical way in which people try to use AI to answer questions on MO, and that there is going to be a serious discussion on meta (thank you for opening that) about how MO will adapt to serious use of appropriate use of AI assistance: https://meta.mathoverflow.net/q/6285/4177
(MO Moderators had already realised this meta discussion was going to have to happen, and while we were discussing the linked MO answer/project in real time over emails, Terry put up the linked post.)

2025-10-05 22:29:41 UTC

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@nprofile…rrr0 Also, English is ok? Otherwise translation might be in order.

2025-10-05 22:28:51 UTC

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@nprofile…rrr0 I was wondering if writing an email to someone in France who could print it off and put it in a local postbox would be reasonable. Airmail is expensive and slow.
@nprofile…4yyd

2025-10-05 22:25:45 UTC

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@nprofile…rrr0 It's been on the backburner. Trying to finish off a joint paper in geometry first, then I said I need to break from that and work on some solo papers.
I really need to write that letter. Didn't hear back from AC, but that's perhaps not surprising.
@nprofile…4yyd

2025-10-05 21:00:14 UTC

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@nprofile…4yyd Ah, well, that's still very cool.

2025-10-05 05:57:31 UTC

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@nprofile…hszg @nprofile…6kk0 I'm also intrigued

2025-10-04 06:38:01 UTC

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@nprofile…jev0 I have no expectations! The argument that one shouldn't expect such a bundle from the screenshot seems to me insufficient: it just points out the elements of OP^2 aren't literally O-lines, so no obvious analogue of the canonical bundle on say CP^2 falls out immediately. But this isn't a proof that no nontrivial O-line bundle exists on OP^2!
The obvious thing to try to start is classify rank‐4 complex vector bundles on OP^2, which surely is possible, say by obstruction theory using the known cell-structure of the Cayley plane.
@nprofile…fa4k

2025-10-03 22:41:54 UTC

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@nprofile…hu2s Absolutely: he varies the pattern just enough that it's not boring. Also it separates the people from the things, and he further splits up the clauses with commas, into further more specific categories of things: large human constructs, legacy, artistic creations, transient arts/joy, knowledge.

2025-10-03 12:47:03 UTC

Is there a rank-8 real vector bundle (or rank 2 quaternionic vector bundle) on the octonionic projective plane, with any additional structure that makes it "octonionic"?
Cc @nprofile…fa4k @nprofile…jev0

2025-10-03 05:38:08 UTC

English teachers: don't use the word "and" too many times in a sentence.
Tolkien: I think I'll write a sentence that uses "and" 20 times.
#Akallabeth #Tolkien
https://media.mathstodon.xyz/media_attachments/files/115/308/594/513/022/175/original/e8bda1caa2ccdb85.png

2025-10-03 05:37:12 UTC

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@nprofile…zven The one I know that really was (eventually) lost and then rediscovered, and wasn't preserved by translation to Arabic was the Archimedes Palimpsest, which survived in a 10thC Byzantine transcription of a copy of a 6thC edition of Archimedes.