theHigherGeometer

rimcræftiga |
bespoke constructions in categorified geometry since 2010 |
dude

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npub1p2q4c7sn2jgtj3w7g9syy5zjldxd8e5ruknf99g8y636ls8vx8esq5c0lr

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highergeometer@mathstodon-xyz.mostr.pub

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nprofile1qqsq4q2u0gf4fy9egh0yzczz2pf0knxnu6p7tf5jj5rjdga0crkrrucpz3mhxue69uhhyetvv9ujuerpd46hxtnfduqs6amnwvaz7tmwdaejumr0ds3sepf8

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relay.damus.io

nos.lol

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npub1p2q4c7sn2jgtj3w7g9syy5zjldxd8e5ruknf99g8y636ls8vx8esq5c0lr

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Last Notes

2026-02-10 01:26:52 UTC

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@nprofile…7md8 That recording booth looks like the one that @nprofile…fh5u used, IIRC!

2026-02-10 01:24:42 UTC

I wish that some internet trolls were this level of "barely literate" when complaining about how certain authors' works are adapted.
Or for that matter, billionaires who like cool invented names and steal them for their companies, ignoring the context, the ethos, and the themes....

2026-02-09 07:28:37 UTC

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@nprofile…4257 Sure. Obviously people aren't solving in anything like just 20 moves, but I can certainly imagine that perhaps the scramble happened to produce a state such that his preferred algorithm resulted in a rather-shorter-than-average move sequence.

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

2026-01-29 03:26:11 UTC

From Sergei Artemov, talking next at the the NYC CT seminar. The best bit is in the last paragraph.
-----
Abstract: Non-compact proofs are used in mathematics but overlooked in the analysis of (un)provability of consistency. We focus on arithmetical proofs of universal statements (*) "for any natural number n, F(n)." A proof of (*) is compact if all proofs of F(n)'s for n=0,1,2,... fit into some finitely axiomatized fragment of Peano Arithmetic PA. An example of non-compact reasoning is the standard proof of Mostowski's 1952 reflexivity theorem: PA proves the consistency of its finite fragments.
It turns out that Gödel's Second Incompleteness Theorem, G2, prohibits compact proofs but does not rule out non-compact proofs of PA-consistency formalizable in PA. This explains why and how the recent proofs of PA-consistency in PA work: they essentially formalize in PA the explicit version of Mostowski's non-compact proof and use Gödelian provable explicit reflection to rid redundant provability operators.
These findings yield a new foundational reading of G2: "the consistency of PA is not provable within a finite fragment of PA," complemented with the positive message: "the consistency of PA is provable within the whole PA." This perspective suggests that Gödel's theorem does not represent a failure of the system to "know" its own consistency, but rather a structural limit on how that knowledge can be packaged into a single finite string.

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?

2026-01-28 10:02:19 UTC

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@nprofile…fws0 How's this morning's talk on Chevalley?
I ask because Serre once answered a question of mine, and noted of him "c'était le plus puriste des membres de Bourbaki."

2026-01-26 08:24:00 UTC

I say the following reluctantly, since I leave the online discussion of politics to others better versed and placed to do so. My voice is not that strong, and does not count for much, but I do wish the IMU would publicly address what is going to happen to the ICM this year. The leadership would, I hope, either make a hard call sooner rather than later to shift venues, or explain why not. Or, at absolute minimum, let everyone know if there are ongoing discussions the outcomes of which will be announced in due course. I cannot imagine such discussions aren't happening.
#ICM2026

2026-01-21 03:26:21 UTC

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@nprofile…4hp5 No, he's opening up his book by description of natural numbers and then different kinds of numbers that arise in solving problems (squares, 'roots' etc)
https://archive.org/details/algebraofmohamme00khuwuoft/page/5/mode/1up

2026-01-21 03:08:21 UTC

"When I consider what people generally want in calculating, I found that it always is a number."
—Abu Ja'far Muhammad ibn Musa Al-Khwarizmi, https://en.wikipedia.org/wiki/Al-Jabr ca.820
TIL this is the opening sentence of the book proper (after the author's preface).

2026-01-20 02:11:40 UTC

@nprofile…fws0 sorry to be a pain, but the link that says 'abstracts' on https://conferences.cirm-math.fr/3523.html points instead to a differently-formatted version of the schedule instead. Is this intentional?

2026-01-13 07:08:15 UTC

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@nprofile…sqfw The publisher seems a little niche (speaking generously) but the paper seems serious.

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.

2026-01-10 06:02:22 UTC

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@nprofile…r0xq no, that is mentioned higher up:
"A correction is needed to the Section on the Phragmen-Brouwer Property and the details are in Brouwer correction, 6 pages. arXiv: 0948151"

2026-01-07 22:57:37 UTC

Oh dear: an erratum file for Ronnie Brown's book 'Topology and Groupoids' at the end of this page is missing (no Wayback Machine capture!)
https://groupoids.org.uk/topologygpdserrata.html
does anyone have a copy, or know how to get in touch with Taras Kolomatski to try to get one?

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

2025-12-30 05:47:39 UTC

https://www.chronicle.com/article/the-crisis-of-the-humanities-is-over-thats-not-a-good-thing
#icanhazpdf ?

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

2025-12-17 11:16:02 UTC

Oh, this is fun. Read the abstracts in order.

2025-12-16 07:40:36 UTC

Hmm, Professor Tolkien, what *is* this unnamed "large 'work'" that occupied your time leading up to 1955? Pray tell....
(The introduction to https://en.wikipedia.org/wiki/English_and_Welsh)
https://media.mathstodon.xyz/media_attachments/files/115/728/101/888/470/290/original/139c8522e8008e55.png

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".

2025-12-15 00:02:58 UTC

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@nprofile…atf6 The point of the article is purely about the use of metrics to evaluate people for workload allocations, promotions and jobs, and in fact completely ignoring the content of their work: reducing a project to a single number of suspiciously high precision (IF1.234 vs IF1.324 is basically meaningless) attached to the container in which is was finally published.
The IF was originally designed for librarians to know which journals were being cited a lot, hence presumably read a lot, and the window of citations was chosen as 2 years, because it's about current reading trends and purchasing. The use of it to signal quality of research is spurious and not backed up by evidence.

2025-12-14 23:01:22 UTC

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"In this article we show that this index [the Impact Factor] and the ordering criterion obtained by using it are highly unstable in the case of mathematics, to the extent that sometimes no reliability can be assigned to its use."

2025-12-14 22:13:34 UTC

To steal from myself elsewhere
Antonia Ferrer-Sapena, Enrique A. Sánchez-Pérez, Fernanda Peset, Luis-Millán González, Rafael Aleixandre-Benavent, "The Impact Factor as a measuring tool of the prestige of the journals in research assessment in mathematics", Research Evaluation 25 Issue 3 (2016) pp 306–314, https://doi.org/10.1093/reseval/rvv041

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?

2025-12-01 23:47:39 UTC

Spicy 🌶️ but also 🤯
"Almost half of Allen Hatcher's papers are very significantly wrong according to his own website (and there are issues with some of his papers that are not listed there). "
—Now-deleted Reddit account
https://pi.math.cornell.edu/~hatcher/Papers/publist.html
The comments here by Hatcher span 35 years of papers:
"(The proof has a mistake -- see below.)"
"There is a mistake (actually two closely related mistakes) in Part II of this volume, ... A corrected version of the theorem was published in a paper by Kiyoshi Igusa
"The mistake in the preceding paper affects this one as well, but this was a dead-end paper so it doesn't much matter." [A paper in Inventiones!!!]
"This paper is well-known to have serious flaws ... More fundamentally, the whole paper is far too sketchy on technical details, and these are not easy to fill in." [A paper in the Annals!!!]
"Some of the calculational statements need to be modified in view of the errors in my earlier papers."
"A revised version is available on my main webpage."
"There are several errors in the tables at the end of this paper, "
"See my main webpage for a revised version."
"Another paper with a mistake, in fact two mistakes, one major and the other minor"
"The original Lemma 2.3 in the published version of this paper was wrong"
"Another paper with an error, but this time there are two authors to share the blame. (Corrections have been published.)"
"The comment for the preceding paper applies here too."

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

2025-11-26 02:08:55 UTC

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@nprofile…6fuz Does the department you are in have an admin phone number? If forced you could add that.

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

2025-11-20 13:28:26 UTC

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Hmmm. That 2005 paper has this citation:
Бикчентаев А. М. О представлении линейных операторов в гильбертовом пространстве в виде конечных сумм произведений проекторов // Докл. РАН.. 2003. Т. 393, № 4. С. 444–447.
https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dan&paperid=1659&option_lang=eng
which *is* the citation in the Paseka–Vetterlein paper. It's listed as being in MathSciNet, but not @nprofile…t8gv
Annoyingly, you can't get a pdf!
@nprofile…8eua

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?

2025-11-19 06:48:22 UTC

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@nprofile…v64a Suppose the two countable ordinals were \(\omega+\omega\) and a finite one...

2025-11-19 06:35:04 UTC

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It was from approximately the time when I presented some work on this in an online seminar. Possibly Ross told me then; he was watching my talk, and thinks he told me about it. I clearly didn't remember!

2025-11-19 00:11:19 UTC

Ross Street wrote a nice little note on Lawvere's fixed point/Cantor's diagonal argument, which I just discovered!
http://science.mq.edu.au/~street/LawvereDiagArg.pdf

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.

2025-11-15 10:48:22 UTC

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@nprofile…rrqe Are you saying mathstodon is like LotF? 😛 Or senior academics are joining some random instance that is much less scholarly?

2025-11-12 06:56:38 UTC

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@nprofile…nx65 Thanks for the correction, I had fixed it locally, but not in the version I pasted here.
I think that the hierarchy is somewhat similar to the Bourbaki notion of "echelon" from their set-theoretic structures.
One naive interpretation of the notion of "canonical" here is that an element of the hierachy is canonical if for every automorphism of S, that element is fixed under the induced automorphism of hS. (I notice more copying/transcription errors!)

2025-11-12 05:53:50 UTC

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Here's the extracted version of the definition:
"Let \(S\) and \(K\) be sets, \(S \subseteq K\), such that no element of \(S\) is a subset of \(K\). The *hierarchy* of \(S\) is defined to be the minimal set \(hS\) such that: (1) \(S \subseteq hS \subseteq K\), (2) if \(A \subseteq hS\) and \(B \subseteq hS\), then \(P(A) \subseteq hS\). Denote by \(A : B\) the set of all functions mapping \(A\) into \(B\). Then to each \(f \in A : B\) there corresponds a unique function \(f \in A : hB\), the maximal canonical extension of \(f\). An element \(e\) of \(hS\) is said to be canonical if \(f(e) = e\) for every \(f\) which is a one-to-one mapping of \(S\) onto \(S\)."
Ignoring the condition about elements of \(S\) and subsets of \(K\), which can probably be arranged by changing things via any handy bijection of the latter not changing the former, what is the definition of \(hS\) even trying to say?

2025-11-12 04:00:12 UTC

Here's one for @nprofile…vp0v : a 1949 definition of "canonical" by R.C. Buck
"It is then shown that a large body of familiar structures, some of which are termed "natural" in the Eilenberg-MacLane theory, are, in the present sense, canonical elements, mappings, or equivalences"
331t Canonical mappings and algebraic structures. I
332t Canonical mappings and algebraic structures. II
https://doi.org/10.1090/S0002-9904-1949-09248-0
https://media.mathstodon.xyz/media_attachments/files/115/534/717/465/241/500/original/161023d2a00eea62.png

2025-11-11 01:25:08 UTC

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@nprofile…356e Bravo!

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).

2025-11-07 02:27:04 UTC

This Annals paper apparently makes claims that haven't ever been substantiated:
http://doi.org/10.4007/annals.2007.165.843
See details here
https://mathoverflow.net/q/234778/4177

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 19:47:39 UTC

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@nprofile…sjny https://www.dam.brown.edu/people/mumford/BlogBook2.pdf it's called "Wake up!"

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 03:00:22 UTC

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@nprofile…8eua @nprofile…dnqz @nprofile…n7dy @nprofile…ral2 A different paper sharing two authors states the classification up to iso like this:
"Recall that two surfaces are isomorphic if there exists an element in the collineation group of PG(3,q) which maps one surface to the other."
so yes, it's counting embeddings up to automorphisms of the ambient projective 3-space.

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.

2025-10-30 00:59:28 UTC

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@nprofile…atf6 Any you'd recommend?
@nprofile…9s72

2025-10-28 23:55:01 UTC

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@nprofile…6fuz Oh, cool! How do you think this would go when applied to things like dependency graphs for (previous results needed for) theorems? The standard layout you get in eg the Blueprint software that people formalising things use can be a little annoying.

2025-10-25 21:10:40 UTC

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@nprofile…xnhe Hmm, I seem to recall I _might_ have, but you can't tell from the replies there, and I can't remember where it would be
🤷‍♂️

2025-10-25 00:10:13 UTC

Hello everyone. If you haven't ever interacted with me, say hello!
What's something you notice or wonder about my activity here?

2025-10-24 00:56:54 UTC

On the excision of the chapter "The Scouring of the Shire" from adaptations:
"Yet there is a depressing Hollywood logic to the decision. The battle of Helm’s Deep, a slim handful of pages in the novel, takes up 40 minutes in Jackson’s The Two Towers. The necessity of peace and restoration, the hard work they require, are left to the cutting floor, while hour-long scenes of heroic violence take more and more space in each subsequent film. Though the films’ pastoral sequences have warmth and joy to them, they lack the bitter, beautiful edge that Tolkien’s prose grants them. That’s the cost of cutting Return Of The King‘s most crucial chapter"
https://www.avclub.com/return-of-the-king-70th-anniversary-scouring-of-the-shire

2025-10-23 23:24:54 UTC

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@nprofile…uqlt And why not?
https://euromathsoc.org/magazine/articles/18

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 20:16:29 UTC

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@nprofile…8eua if it was on the actual site it's gone now, as far as I can tell.

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 00:35:09 UTC

I'm not envious....
https://www.abc.net.au/news/2025-10-22/tasmanian-woman-op-shop-selling-jrr-tolkien-the-hobbit/105921072

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