Omar Antolín

I'm a mathematician at UNAM in Mexico City. I work in algebraic topology, homotopy theory and higher category theory, but am interested in all sorts of math.

I also enjoy computer programming as a hobby and am a big fan of the text editor Emacs.

Website: https://www.matem.unam.mx/~omar
GitHub: https://github.com/oantolin

Public Key

npub1umssnfgeht7fvj26zxkfa6q7xadfqu2y5t4tpww37cqxt4dehafsq57ra6

NIP-05 Address

[email protected]

Profile Code

nprofile1qqswdcgf55vm4lykf9dprty7aq0rwk5sw9z2964sh8glvqr96kum75cprpmhxue69uhhyetvv9ujumt0d4hhxarj9ecxjmntfgpyel

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relay.momostr.pink

Author Public Key

npub1umssnfgeht7fvj26zxkfa6q7xadfqu2y5t4tpww37cqxt4dehafsq57ra6

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Last Notes

2026-04-16 21:58:35 GMT

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I found this paper that seems to take the history seriously and I would believe the author did read Liouville directly: https://doi.org/10.2307/2689612.
It seems that Liouville didn't use the term "elementary function", but rather "explicit finite function". His explicit finite functions do however correspond to the broader notion that is closed under algebraic extensions, not just the "folk elementary functions". Also, the author, believes (like I did) that Liouville's class of functions is what we now call "elementary functions". Funny.
I guess since Liouville's purpose was to prove that certain functions don't have elementary integrals (well, explicit finite integrals), he went with the broader notion to get a stronger theorem!

2026-04-16 21:53:37 GMT

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You're right, I hadn't seen that, thanks!

2026-04-16 02:54:42 GMT

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Really? I thought people very carefully said that the quintic is "not solvable with radicals", and that the original definition of elementary functions given by Liouvile already had them closed under solving polynomial equations, logarithms and exponential (that is, I thought the differential algebra definition @npub1nf4…nqe4 explained elsewhere in this thread is just a modern restatement of Liouville's original definition).
Is this other definition of elementary function you guys are using supposed to be older or more recent than Liouville's?

2026-04-03 23:08:10 GMT

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Turkey is much lower on the list than I expected!

2026-03-27 14:41:18 GMT

Man, LLMs really drive home the lesson that people differ *greatly* in how much they care whether the statements they make are accurate.

2026-03-10 13:39:10 GMT

RE: https://mstdn.social/@rysiek/116204163611415275
It looks like the International Congress of Mathematicians is less serious than the Ig Nobel Prize. 🙁
#note1cxg…d0r7

2026-02-25 19:42:31 GMT

Nice plot summary... Google just keeps getting dumber.
https://media.mathstodon.xyz/media_attachments/files/116/132/973/702/318/690/original/06c5842fe01fb991.png

2026-02-21 21:49:42 GMT

You've probably heard of the Birthday Paradox, that among 23 people the probability that two share a birthday is more than 50%.
This is easy to prove by calculating the complementary that no two of the 23 share a birthday. There are 365 options for the first birthday, then only 364 for the second, 363 for the third, etc. So the probability that all 23 people have different birthdays is (365×364×...×343)/365²³ ≈ 0.4927.
That calculation assumes the uniform probability distribution on birthdays, that is, that every day is equally likely to be a birthday. That's not a very realistic assumption for the actual distribution of people's birthdays, so it's worth thinking about what happens for other distributions. My instinct was that any non-uniform distribution has some higher probability clump, where birthdays would tend to bunch up with even fewer people; so that any non-uniform distribution is even "more paradoxical" than the uniform one.
This turned out to be easy to prove.
1/2
#math #probability

2026-02-02 00:26:06 GMT

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After reading what your wife thought, I took a look at some reviews and it gave me flashbacks of reading my student evaluations: one review sides with your wife on the need for editing, calling it "a tedious, bloated epic"; another review calls it "tightly constructed". When I taught undergrads in the US, I remember getting student evaluations, from the same class, one which said I was "the best math teacher I've ever had" and one which said "I don't know how the university lets him teach".

2026-01-30 21:38:34 GMT

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Hey! @npub19ua…53cv is a coauthor!

2026-01-29 05:10:19 GMT

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Have you also tried Phanpy on your phone (or only on the desktop)? I love it there too. If you did try it, what made you go with Tusky instead?

2026-01-25 17:19:35 GMT

There is much truth to this post about about #math textbooks.
https://media.mathstodon.xyz/media_attachments/files/115/956/870/326/807/020/original/8abb41b70b5f11cc.png

2026-01-22 04:07:21 GMT

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How do you format the links like that? Are you posting from a non-mastodon client? Does that mean Mastodon clients can display links and other html formatting but have no way of producing it? That's funny.

2026-01-16 19:19:42 GMT

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Maybe that's the key! Maybe the methodology is that you compute some global "humanities score" for each university and then "normalize" by dividing by the number of humanities departments. 😛

2026-01-16 16:50:40 GMT

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I agree that the MIT claim is very suspicious, a little funny too.

2026-01-16 16:34:41 GMT

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On my phone it lets me scroll the list to see past the fourth one. I haven't tried on a desktop computer yet.

2026-01-14 14:38:37 GMT

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What was your use case for regexps?

2025-12-23 18:18:04 GMT

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It's probably just a typo for "among us", the popular videogame that features characters that look like that shape. @npub1zz2…9mhx

2025-11-18 15:28:43 GMT

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I wanted to say this, thanks for saving me the effort. (Except I would have said "we" since I only sound like an American.)

2025-09-13 10:58:13 GMT

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Will do.

2025-09-12 23:45:29 GMT

I can't read the nLab anymore! A few days ago it started "verifying" I was human. Each verification took around 30 seconds, which was annoying (a very human emotion!), but at least I passed them! Today I can't get past the verification screen, which makes me sad (another human emotion).
EDIT: I rejoice for the nLab deems me human once again! (Rejoicing also seems pretty human to me.)

2025-09-10 11:27:56 GMT

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Beautiful!

2025-09-04 16:25:21 GMT

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I thought of it slightly differently, instead of mapping the triangle to an equilateral one, I thought of mapping it to itself but permuting the vertices.

2025-08-30 03:16:15 GMT

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Someone printed one! https://mathstodon.xyz/@fractalkitty/115115418786961240

2025-08-11 07:17:59 GMT

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This matches what I was planning pretty closely (and the usual focus on just irreducible varieties also bothers me, as does the similar focus on connected covering spaces, for example). I mentioned you and Dolan because I was thinking of that dimensional analysis/doctrine stuff and wondering if there was a more systematic write up of it now.

2025-08-09 21:15:49 GMT

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I'm particularly interested in what you and James Dolan would suggest, @npub1nf4…nqe4

2025-08-09 21:14:46 GMT

The algebraic geometers at my university were all distracted at the same time and I got assigned the core algebraic geometry graduate course while they weren't looking! What should I endeavor to do to this generation of Master's students?

2025-07-31 14:36:51 GMT

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Arguably this stick insect is both! Also, they've changed illusive to elusive on the website already, I only see illusive in the link preview here on Mastodon.

2025-07-30 17:29:33 GMT

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MEXICO - Pedro Páramo (Juan Rulfo, 1955)

2025-07-21 02:33:44 GMT

You know how people advise you not to use mathematical formulas in section titles in LaTeX? Listen to them!
https://media.mathstodon.xyz/media_attachments/files/114/888/870/407/228/144/original/61e794b3e6e090c9.jpg

2025-07-18 04:16:15 GMT

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Like the Google Buzz trick from Doghouse Diaries (http://thedoghousediaries.com/1267):
https://media.mathstodon.xyz/media_attachments/files/114/872/273/256/613/662/original/066f90a2b68dca17.png

2025-07-07 22:38:49 GMT

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It bothers me a little bit that it has both "National" and "of Athens" in the name.

2025-07-07 19:00:52 GMT

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This is about grouped notifications, that is, seeing notifications for a single toot group together in a single list: instead of a separate notification for each time someone favorites or boosted a given toot, you see a single notification per toot listing all the people that favorited or boosted it.
This could of course be implemented in each Mastodon client separately, but Mastodon decided to do it serverside for efficiency and uniformity. On of the Mastodon clients I use, phanpy, has always shown grouped notifications (at least since I use it); but another client I use, @mousebot's mastodon.el, does not show notifications grouped by default. And today I learned it does have a setting to group them!
Is that what you wanted to know?

2025-07-07 16:34:21 GMT

Oh my god, TIL about mastodon-group-notifications! Now #mastodonEl is perfect! (Or rather: it already was perfect, I just didn't know it was.)

2025-07-02 05:30:24 GMT

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Hahaha, I'm sorry, specially if I just cost you addition to heaven. 😅

2025-07-02 05:21:32 GMT

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This gives new meaning and new higher stakes to the phrase "cinnamon challenge".

2025-06-05 17:21:19 GMT

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Oh, that's right, getting the appropriate link is a little awkward with just Org. I should have mentioned what I use for that: org-ql-find together with embark. Org-ql has several flexible command for searching for heading in an org file, org-ql-find in particular will prompt you in the minibuffer for some search terms in a simply syntax, and then it lists the matching heading as completion candidates. (It's mean to be used with a completion UI that shows the completion and lets you navigate among them, a completion UI such as icomplete, vertico or ivy.) The embark package let's you act on the completion candidates and in particular comes with an action called embark-org-insert-link-to, which inserts a link to the currently selected heading. I bind org-ql-find to M-s q and embark-act to C-., and embark binds embark-org-insert-link-to to j, so altogether I insert a link to a heading in the same org file as follows:
1) M-s q search terms
2) arrow keys to select the correct heading in the minibuffer
3) C-. j
It's very fast and convenient. You could also replace org-ql-find with consult-org-heading, if you prefer, but I like that org-ql-find does full text search in the entire body of the heading by default.

2025-06-05 15:34:50 GMT

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Yes, just use Org on its own!

2025-05-23 13:48:53 GMT

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Damn autocorrect! Thanks for pointing out the typo.
Scotland? I somehow thought you had left the US for Singapore. At any rate, I'm glad you left the US.

2025-05-23 12:34:33 GMT

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I think the article make a pretty convincing case that the brain drastic is already underway, it's funny they called it a "danger" in the title.

2025-05-08 00:20:42 GMT

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The six digit numbers whose first three digits are the same as the last three are the multiples of 1001 (because abc * 1001 = abcabc). Since 999999 is a multiple of 1001, being a multiple of 1001 is well-defined modulo 999999, i.e., if a = b (mod 999999) then a = b (mod 1001). Finally, since 123123 is a multiple of 1001, it doesn't matter what the tower of fives is, the product will be a multiple of 1001.

2025-05-05 12:31:32 GMT

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The author of that article, @npub1hr7…jxyc, was written plenty of sensible stuff on AI including a book, The Intelligence Illusion.

2025-03-17 03:17:56 GMT

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Because of stories like these I cancelled my trips to the US for math conferences for the immediate future. I'm sorry I won't get to see many American friends of mine, but the minute I sent those emails cancelling, I felt relieved.

2025-03-15 15:31:01 GMT

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The partial automorphism you found are inner on the a=1 subgroup, but they might be non inner once you extend them to the whole group.

2025-01-10 12:15:11 GMT

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When I visited Copenhagen I got a public transit card at a machine at the airport. The machine asked me what felt like a very long series of questions in Danish (there was probably an option somewhere to switch to English which I missed). I clicked on buttons somewhat randomly and got a card, so I considered the operation a success. Later I found out that I had obtained a transit card for dogs —which apparently are (1) allowed on public transit, but (2) have to pay!
Now, dog was only the default for the card, mind you, so I could still use it: everytime I got on a bus or train I just had to add one human and remove one dog to my travel order, a little game I called "Copenhagen: Become Human".

2024-11-20 11:37:40 GMT

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I see, thanks. That makes sense.

2024-11-20 04:40:09 GMT

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This thread was pretty interesting and I enjoyed the article of Doctorow's you linked to, but I think I may have missed something: you explained why you aren't moving to bluesky, but did you also say why you are bothering to mirror your posts there?

2024-10-06 00:44:34 GMT

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I guess the answer is yes and a little bit no. There is the Risch algorithm, which does decide whether or not there is an elementary anti-derivative, but it uses as a subroutine a function that tells you whether two constants are equal. Such a subroutine is not know to exist for constants you can write in terms of rational numbers and elementary functions, and I think that if you throw in absolute value it is in fact known to not exist! So, modulo it being very difficult to tell whether a big expression that evaluates to a number is zero or not, you can decide whether or not elementary functions have elementary anti-derivatives. Personally I think "compute the constant to 500 decimal places" is probably correct enough of the time to not consider this a problem. The Risch algorithm is also extremely complicated and I seem to remember either no computar algebra system implements it completely or maybe just one or two do.

2024-10-04 06:49:44 GMT

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Oh, you're right: this is exactly equivalent to asking which does are parallelizable and the classic answer is that only S¹, S³ and S⁷ are! (Though I only know how to prove that using K-theory which was forbidden by OP.)

2024-10-04 06:42:19 GMT

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de Rham cohomology works half the time for this question! For SO(n) with n=2k+1 you have exterior generators in degrees 3, 7, ..., 4k-1; and the slightly different pattern you mentioned for even n is that if n=2k+2 then you have exterior generators in those same degrees 3, 7, ..., 4k-1 and an additional exterior generator in degree 2k+1. This means that when n is odd SO(n+1) has the same de Rham cohomology ring as SO(n)×S^n! (And when n is even the rings are non-isomorphic so the argument does work in those cases.)
When n=1 or 3, then SO(n+1) really is diffeomorphism to SO(n)×S^n, so I'm not sure what to expect for odd n.

2024-08-23 17:48:22 GMT

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Y separando a los burgueses del proletariado.

2024-08-23 12:27:23 GMT

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Or a misunderstanding? Every loop on the sphere is homotopic to one that does not hit every point on the sphere, maybe the lecturer meant something like that.

2024-08-23 11:59:00 GMT

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But there are such loops! They are called space filling curves. The most popular examples are continuous functions [0,1]-->[0,1]^2 which hit ever point in the square but any such example is easily modified too obtain a loop on a sphere.
https://en.wikipedia.org/wiki/Space-filling_curve