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highergeometer.mathstodon.xyz.ap.brid.gy
theHigherGeometer
@highergeometer.mathstodon.xyz.ap.brid.gy
250 followers 0 following 930 posts
rimcræftiga |
bespoke constructions in categorified geometry since 2010 |
dude

[bridged from https://mathstodon.xyz/@highergeometer on the fediverse by https://fed.brid.gy/ ]
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highergeometer.mathstodon.xyz.ap.brid.gy
*Brunerie meme* 🙃

https://youtu.be/UNBfyeB9u1s?si=X7xArp_odHgt8-nr&t=3282
Screenshot of slide from presentation: "So what about computations? - So now that this has been formalised, this means that we can plug any fixed \pi_n(S^m) into Agda and compute a list of integers (r_0, r_1, ... r_k) s.t. \pi_n(S^m) = Z^{r_0} \times \prod_{1\leq i\leq k}(Z/m_{r_i}Z) - *Insert meme with Guillaume Brunerie* - Haven't even been able to get the number of generators of \pi_2(S^2)"
November 4, 2025 at 2:09 AM
highergeometer.mathstodon.xyz.ap.brid.gy
*This* is how you avoid creating paradoxes, by doing category theory properly.
Screenshots of a Theorem from Scholze's notes that "The infinity-1-category Pr-L-kappa is itself kappa-presentable, i.e. Pr^L_\kappa \in Pr^L_\kappa." and the proof that in fact uses clever encoding tricks and Gabriel–Ulmer duality. The page is headed "Lecture II: A category of categories that contains itself".
October 31, 2025 at 12:50 AM
highergeometer.mathstodon.xyz.ap.brid.gy
"I was never sure if I would succeed in academia, so my plan B was always to become a high school teacher."
—Peter Scholze, Fields Medallist (became the youngest full professor in Germany when he was 24)
October 27, 2025 at 12:14 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Whee! I'm officially internet famous!
Screenshot of notification on MathOverflow showing a gold badge, "Famous Question", awarded for a question with 10,000 views.
October 23, 2025 at 9:40 AM
highergeometer.mathstodon.xyz.ap.brid.gy
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
Cover of the May 21 2019 issue of the Proceedings of the National Academy of Sciences, showing a picture of an ammonite ("Ammonite in Amber"), but with one of the other items, "Hyperbolicity of Jensen polynomials" highlighted with an added red box and arrow pointing to it. Cover of the November 6 2001 issue of the Proceedings of the National Academy of Sciences, showing a picture of plant cells, but with one of the other items, "Explaining congruence in partition functions" highlighted with an added red box and arrow pointing to it.
October 13, 2025 at 2:34 AM
highergeometer.mathstodon.xyz.ap.brid.gy
I almost fell for thinking they were actually by the same person, posting again after it got closed the first time, but apparently not?
Two-nickels two-panel meme. Upper panel: "If I had a nickel every time someone posted a Zenodo-hosted preprint about Navier-Stokes regularity on MathOverflow today..." Lower panel: "....I'd have two nickels. It's not a lot, but it's weird it happened twice in 12 hours"
October 13, 2025 at 2:01 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Oh dear. My current grad student took longer to get up to speed to do any actual work than this proposed trial period, and he at least started knowing what he applied for...
Screenshot of email asking to become a grad student with me: "TL;DR: I am a First-Class Honours Computer Science graduate seeking a Master's-to-PhD or PhD position to apply AI/ML to medical challenges. I propose a unique 1-2 month trial period as a TA/RA to demonstrate my skills in exchange for a full tuition waiver and stipend. Respected Prof. [redacted], I hope this message finds you well. I am writing to you today to express my strong interest in pursuing graduate research under your supervision, ideally through a Master's leading to a PhD program, focused on solving complex problems in medicine and healthcare through the application of artificial intelligence. As I identify research groups that align with my ambitions, the work of your lab stands out as a significant contributor to this field. My goal is to join a team where I can apply my computational skills to make a tangible impact, and the focus of your research is an excellent match for my background and interests. I hold a First-Class Honours Bachelor’s degree in Computer Science, with a specialization in High-Performance Computing, GPU computation, and Data Analytics. Professionally, my experience as a Data Engineer has equipped me with practical skills in building and optimizing data pipelines—a foundation I am confident would be valuable in managing and analyzing the large-scale datasets common in medical research. [truncated]"
October 12, 2025 at 10:28 PM
highergeometer.mathstodon.xyz.ap.brid.gy
Human-performed arbitrary code injection speedrun in the Japanese-only sequel to Super Mario Bros. It's true this was only discovered this year, but that only three people have managed this, all of them with various current top-3 speedrun records in the games […]

[Original post on mathstodon.xyz]
Screenshot of speedrun.com leaderboard for a category with only three entries: 1st scalpel, 2nd Kosmic, 3rd Niftski, with dates ranging from 5 months ago to 1 month ago. All played on the Famicom Disk System, and officially adjusted times ranging from 7 minutes 38 seconds 711 milliseconds, to 7 minutes 39 seconds 560 milliseconds.
October 7, 2025 at 10:12 PM
highergeometer.mathstodon.xyz.ap.brid.gy
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
"In an hour unlooked for by Men this doom befell, on the nine and thirtieth day since the passing of the fleets. Then suddenly fire burst from the Meneltarma, and there came a mighty wind and a tumult of the earth, and the sky reeled, and the hills slid, and Númenor went down into the sea, with all its children and its wives and its maidens and its ladies proud; and all its gardens and its halls and its towers, its tombs and its riches, and its jewels and its webs and its things painted and carven, and its laughter and its mirth and its music, its wisdom and its lore: they vanished for ever."
October 3, 2025 at 5:38 AM
highergeometer.mathstodon.xyz.ap.brid.gy
I guess it's actually appropriate for today's #mathtober, since it turns out that the thing that the integral should be is related to the self-linking number
Mathematical text ending up discussing "The knot-theoretic expression" that is the formula for an expectation value for a quantum observable, giving the "self-linking, or framing, number"
October 2, 2025 at 12:25 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Darkfall, by Isobelle Carmody
I first read this probably within a year of release, in the late 90s when I was in high school. I think it's amazingly written. Heartbreaking with ironic tragedy, tense with political intrigue.

On to read the next book...

#read2025
Photo of the cover of the book Darkfall. The cover shows a fantastical ship with masts by no sails on a unsettled sea at the bottom of a cliff. The sky is orange.
September 30, 2025 at 2:22 PM
highergeometer.mathstodon.xyz.ap.brid.gy
The opening sentence of an abstract on the arXiv today:
"A core goal in modern science is to harness recent advances in AI and computer processing to automate and accelerate the scientific method."
Two-panel meme with Thor asking "Is it really though?" (top pane) and Daenerys Targaryen asking "Are ya sure?" (bottom pane), both with highly skeptical looks on their faces.
September 30, 2025 at 5:39 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Some light reading to cross-reference certain statements/drafts/edits/letters and their dates.

#tolkien
A stack of five Tolkien books on top of a shelf in front of windows. From top to bottom: The Silmarilion, Sauron Defeated, The Peoples of Middle-earth, The Letters of J.R.R. Tolkien, The Nature of Middle-earth.
September 30, 2025 at 4:19 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Oh, and here's a later paper on the general topic of "geometric pooling" (with upco/multiplicative pooling as an edge case) using more or less exactly my example 😄

Richard G Pettigrew, Jonathan Weisberg, "Geometric Pooling: A Users' Guide", British Journal […]

[Original post on mathstodon.xyz]
Screenhot of paper discussion the experiment of two people each secretly rolling a six-sided die and sharing the counts of the results of conditionalising on the rolls, and then geometrically pooling the posteriors.
September 29, 2025 at 6:05 AM
highergeometer.mathstodon.xyz.ap.brid.gy
"So, Dustin, are these Kähler differentials on \\(\mathbb{Q}\\) over \\(\mathbb{F}_1\\) in the room with us now?"

🙃
Blurry screenshot of Dustin Clausen's hand gesturing at a circled mathematical expression, Omega-1 of Q over F-1
September 22, 2025 at 6:10 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Me: "Corporate needs you to find the differences between this picture and this picture."
Outsourced typesetting company: "It's not clear what you mean, please explain using the attached pdf"
Two images of contents panes side by side, the left labelled "In manuscript", the right labelled "In proof". The first is structured cleanly with sections and subsections as you would expect. The other has successive sections nested deeper and deeper the further down, with References a subsection of Appendix C, Appendix C a subsection of Appendix B and so on all the way up.
September 18, 2025 at 1:34 AM
highergeometer.mathstodon.xyz.ap.brid.gy
OK, got it! Very minimal...
Preface to the Special Issue It is our great pleasure to publish a special issue of Publications of the Research Institute for Mathematical Sciences (PRIMS) for Inter-universal Teichmiiller Theory, I-IV by Shinichi Mochizuki. There are two main reasons for publishing this series of papers in a special issue. One is their volume and importance. The other is to avoid the conflict of interest that arises because the author is Editor-in-Chief of PRIMS. As a general rule, when a paper is submitted to PRIMS by a member of the Editorial Board, the member should be entirely excluded from the editorial committee charged with handling it. When Mochizuki became Editor-in-Chief of PRIMS in April 2012, the Editorial Board further decided that, in the case of his submission, they would form a special committee to handle it, excluding him and with an Editor-in-Chief substituting for him. When he submitted the present series of papers on August 30, 2012, Akio Tamagawa took the job of Editor-in-Chief of the special committee. Masaki Kashiwara later joined the committee, and he and Tamagawa served as co-Editors-in-Chief. Several mathematicians kindly accepted an invitation to referee the papers; we are extremely grateful to them for their efforts and patience. Based on their reports, we had numerous editorial meetings. In particular because of the total length of the series of papers, it took a long time for the Editorial Committee to arrive at the final decision of acceptance. Editorial Committee for the Special Issue Editors-in-Chief Masaki Kashiwara, Akio Tamagawa Other Members Tomoyuki Arakawa, Masahito Hasegawa, Takashi Kumagai, Kazuhisa Makino, Takuro Mochizuki, Shigeru Mukai, Hiraku Nakajima, Kenji Nakanishi, Tomotada Ohtsuki, Kaoru Ono, Narutaka Ozawa, Michio Yamada
September 16, 2025 at 7:40 AM
highergeometer.mathstodon.xyz.ap.brid.gy
I cannot.

Just.

No.

Saying "but don't forget to follow your universities rules!" does absolve the authors of this book, published by Springer, of their responsibility
"Using ChatGPT Canvas to Help You Write Long-Form Content Using Canvas to Write a Thesis with ChatGPT Up until now, we’ve been having a back-and-forth conversation with ChatGPT as we're already accustomed to at this point. However, in our next prompts, we’re going to instruct ChatGPT to start using the Canvas feature. In this case, we're using Canvas to help us write an introduction to our thesis. Additionally, we’re going to be asking ChatGPT to look for sources, just like we did in Chapter 4. This is an academic paper, after all. Therefore, we need ChatGPT to provide sources so we can see for ourselves where it got its information from. For our example, we’re going to be writing an introduction to a thesis on how J.R.R. Tolkien’s use of mythology and folklore influenced the development of modern fantasy literature. <!> NOTE It’s important to remember that different universities will have different rules on how much ChatGPT can be used to help with homework. Above all, university rules should be followed. This chapter will provide details that can be used to help write academic papers, but it’s up to a student’s discretion on how much advice to take from this chapter."
September 15, 2025 at 11:49 PM
highergeometer.mathstodon.xyz.ap.brid.gy
The Extraordinary Adventures of Alice Tonks, by Emily Kenny.
Alice is autistic, starting a new (English) boarding school, and finds that she can understand animals talking to her. A fun fantasy YA read that doesn't lean too heavily on its ND heroine, but it […]

[Original post on mathstodon.xyz]
Picture of the cover of the book The Extraordinary Adventures of Alice Tonks: illustration is of a red-haired high-school girl holding a rat that appears to be talking to her, while a cat rubs against her legs. Author is Emily Kenny.
September 7, 2025 at 12:35 PM
highergeometer.mathstodon.xyz.ap.brid.gy
Springer's 'terms of use' for the 'accepted manuscript' version include forbidding sharing the file—say from the arXiv—with others (paragraph 5 is essentially fair use provisions and quoting in an academic context), and even the *authors* are forbidden from […]

[Original post on mathstodon.xyz]
Screenshot of part of Springer's terms of use: "Reformatting and enhancement is prohibited √ 6. Under no circumstances may Springer Nature AM content be reformatted or enhanced, whether by an Author or third parties. Onward sharing is prohibited √ 7 Provision or onward sharing of AM content to third parties without permission is prohibited, except as set forth in paragraph 5 above, and as permitted by applicable law."
September 5, 2025 at 7:14 AM
highergeometer.mathstodon.xyz.ap.brid.gy
De Gruyter Brill charging for access to scans of a mathematics journal from 199 years ago.

This thing is freely available under all copyright laws here: https://gdz.sub.uni-goettingen.de/id/PPN243919689_0001 but the publisher still has a paywall.... why? To […]

[Original post on mathstodon.xyz]
Screenshot of the De Gruyter Brill page for the issue 1 of the journal "Journal für die reine und angewandte Mathematik" from 1826 (usually called "Crelle's Journal"). Access is denied.
September 3, 2025 at 8:06 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Credit where's it's due (digging around old papers):
"This work was undertaken while the author was supported by an Australian Postgraduate Award and by Australian Research Council grant number DP120100106. Further financial support was provided by Mrs R. This article is released under a CC0 license, [Creative Commons url]"
August 29, 2025 at 4:34 AM
highergeometer.mathstodon.xyz.ap.brid.gy
"An Introduction to the Mathematicks"

Who knew, "Bigness" was a technical word...

https://archive.org/details/youngmathematici00john/page/1/mode/1up?view=theater
Screenshot of mathematics book from 1731
August 26, 2025 at 6:13 AM
highergeometer.mathstodon.xyz.ap.brid.gy
However, these records are much nicer to read!

https://leopard.tu-braunschweig.de/receive/dbbs_mods_00065812
Screenshot of the Technische Universität Braunschweig library record page for 'Programm's from the 1880s Scan of a yellowed page titled 'Uebersicht der Vorlesungen und Uebungen', listing subjects and their lecturers, showing Prof. Dr. R. Dedekind teaching Analytic geometry, Differential and integral calculus I and II, and Analytic mechanics. in the summer and winter semesters, together with the number of teaching hours.
August 25, 2025 at 1:16 AM
highergeometer.mathstodon.xyz.ap.brid.gy
Also, I wish someone had paid attention when scanning some of these records, I have practically no idea what this says! (even on top of a) being in German and b) that handwriting)
Badly scanned 19th century German handwriting that as a result is nearly illegible.
August 25, 2025 at 1:06 AM