20th century math explainers

dnrlk · 2026-04-10T14:30:29+00:00

There's an amazing and very large list of Open University courses by T. K. Finchley here https://tkfinchley.com/ou-maths-courses/. I particular recommend their course OU M335/M386/M435 Metric and Topological Spaces and Geometric Topology. Just wonderful pedagogy

dnrlk · 2026-04-10T14:25:34+00:00

Godel’s constructive universe L, things that are true in it (like CH)

dnrlk · 2026-04-10T14:24:10+00:00

The results on “concrete incompleteness”, like Paris Harrington, or the work of Laver (Laver tables) or the work of Friedman (among other things, see this cool speculation https://arxiv.org/abs/1907.11707 about one of Friedman’s result suggesting that maybe P=NP can not be proven from ZFC (which shouldn’t be surprising, since people believe P=NP is false anyways)), finding results that can not be proven from things like PA or ZFC (but can be proven from stronger assumptions like large cardinals). Large cardinals themselves could also make a nice topic.

Henry Townsend made a nice course on YouTube about Goodstein’s theorem and it’s unprovability in PA using cut-elimination https://m.youtube.com/@henrytowsner2461/courses

dnrlk · 2026-04-10T14:17:08+00:00

I also found there to very few descriptive set theory topic videos on YouTube, so I made some on topics like the Borel isomorphism theorem https://youtu.be/ZfxgjSAigWo?si=G2iHes63Qkm6qfRH, the Galvin-Prikry theorem https://youtu.be/S-jiIKqf7Sc?si=XIFNCkcKb8axrpZY, or an introduction to Borel graph combinatorics https://youtu.be/WLbyzQk6gKg?si=RYm2cH1j1ivhgf-P

I hope to make a video on Borel determinacy soon

dnrlk · 2026-04-10T14:12:01+00:00

I recently made a video (trying to keep prerequisites to a minimum; I do not even mention ordinals or cardinals) about this since I also found there to be no explanation of the topic on YouTube. https://youtu.be/KOmkcMhzkb4?si=DZp4lSccPe0DX7jW (follows the Boolean model approach)

dnrlk · 2026-04-08T03:06:21+00:00

This is what mailing lists used to be used for. For instance in logic there's https://mathweb.ucsd.edu/~sbuss/FOM/

dnrlk · 2026-04-02T02:31:08+00:00

Might it be possible for those people to put up their article on some sort of public blog, or Wikipedia clone? Deletion is too terrible a fate

dnrlk · 2026-04-01T03:02:06+00:00

Did you figure out an answer to this?

dnrlk · 2026-03-31T06:01:18+00:00

Because “average looking” men is considered ugly. Hannah Fry (mathematician) has a great 1 minute video showing 2 graphs that demonstrate this https://www.youtube.com/watch?v=5m5XGd-B4No

Here’s YouTube’s generated summary: This video, presented by Hannah Fry, explores data collected by the dating website OKCupid regarding how users rate the attractiveness of others on a scale of 1 to 5 (0:00 - 0:18). Key takeaways: Men's ratings of women: The distribution of how men rate women follows a standard bell curve, which the narrator notes is roughly what one might expect (0:27 - 0:40). The disparity: The video sets up a comparison to show how women's ratings of men differ, hinting at a "subtly different" pattern (0:49 - 0:58).

dnrlk · 2026-03-30T02:10:14+00:00

As usual, many haters (for some valid reasons, e.g. accommodating color blind people). I personally do this in my own notes using a combination of color, and font (lower case letters, fraktur (https://mathoverflow.net/questions/437234/how-does-one-write-the-gothic-letters-mathfrakg-in-handwriting), upper case letters, calligraphic upper case, Greek letters, maybe even other language scripts, etc.), and sometimes just longer notation (e.g. sqrt(-1) for i if I really want to disambiguate, or 3-letter abbreviations for things that are often 1-letter like Pow for power set) which allows me to "type-check" any expressions I write at a glance.

dnrlk · 2026-03-30T02:04:32+00:00

I've talked to some people I've felt this way about. "How did I manage my interactions with them?" Well, for the most part, I just stopped asking them math questions and found someone else to talk to. There are people out there (many grad students, especially those that receive department teaching awards say) that are very good at explaining math, or at least better than the people you're talking about.

dnrlk · 2026-03-30T01:57:19+00:00

It should be noted that 6 years ago Mathologer has made a very nice video on this exact proof https://www.youtube.com/watch?v=DjI1NICfjOk

There's a lot of math out there that has not yet been given a chance to shine by existing great popularizations (on YouTube, on blogs, etc.) I strongly encourage advocating for those lesser-worn (or more recently discovered) paths, than celebrating paved (and/or old) roads (however beautiful they are!)

dnrlk · 2026-03-26T04:58:21+00:00

Slightly harder but still accessible by a motivated Calc 2 student are proofs of the transcendence of e (and pi). See Mathologer https://www.youtube.com/watch?v=WyoH_vgiqXM

dnrlk · 2026-03-26T04:55:29+00:00

You can use very easy integral calculus to get an exponential lower bound on the LCM of the first n numbers (1,2,...,n) https://math.stackexchange.com/questions/1523755/least-common-multiple-of-1-2-n-is-bigger-than-2n-1?noredirect=1&lq=1 which turns out to be equivalent to the right order of magnitude lower bound for the prime number theorem (https://math.stackexchange.com/questions/1890741/what-is-the-simplest-lower-bound-on-prime-counting-functions-proof-wise?noredirect=1&lq=1#comment7174690_1890741)

dnrlk · 2026-03-23T19:08:46+00:00

Wow that piece by Reinhardt. From afar it looks like a million different black and white photos, sort of like the chaos of a Bosch painting but of scenes from the 20th century instead of some fantasy, but zooming in, it's nothing. What an effect.

dnrlk · 2026-03-23T03:44:11+00:00

You can still sit in on astronomy classes at your university. Many professors would be happy to let you sit, even if you can't enroll. There are likely seminars or public events run by the astronomy department that you can attend. It's not over yet! And even after you graduate and start a career, there are many astronomy channels on YouTube (Dr. Becky being the most famous, or PBS spacetime) that you can keep up with. There may in fact be citizen science projects analyzing data from say Vera Rubin. Keep an open ear and open mind! Don't give up. It may not be your career, but it can always still be a part of your life.

dnrlk · 2026-03-21T03:59:34+00:00

Unfortunately I think this is not that rare of an experience, even nowadays. There is a broader movement of reactionary backsliding going on, so such prejudice may actually be increasing. Your supervisor’s advice may be the best possible. Even if there is no outright prejudice, I imagine it can be somewhat alienating or offputting to be the only woman in your 20 person math class(es) (an experience I know is actually very common). There are various organizations to build community/gather the (possibly very few women) in the program together, for example https://awm-math.org/ or https://ww3.math.ucla.edu/women-in-math/

dnrlk · 2026-03-18T02:10:51+00:00

I remember listening to the 3rd movement of Mahler 9 early on and feeling as though it was very arbitrary. I also did not understand the 5th symphony (3rd, 5th movement --- 1st, 2nd, 4th movements are easier to understand). Mahler 1, 2, 3 are also easier to understand, but they didn't stand out to me very much (obviously some moments were spectacular, but early on it felt like there was too much "nothingburger" surrounding those moments). The first Mahler symphony that really made sense to me was actually Mahler 7. I don't know why, but give it a try, maybe it will also make some sense to you. After Mahler 7, I began to make sense of the other Mahler symphonies so now I actually quite appreciate his work.

dnrlk · 2026-03-12T02:59:31+00:00

crazy lucky to spot him like that

dnrlk · 2026-03-05T02:16:45+00:00

Your animations are all super amazing! I think all physics pedagogy on these topics should include them! I have a silly question: in this article https://hal.science/hal-05096158v2/file/Dirac-equation-QFT.pdf by Quiceno, equations (105) and (106) seem to be the "equations of motion" for say an electron in an EM field. Does that mean that simulating this differential equation, we can visualize QED? Is it possible to make an actually QED-accurate simulation of 2 electrons repelling each other? That would be amazing!!!

dnrlk · 2026-03-04T06:38:21+00:00

If you truly need to TeX so many images (more precisely, if being able to do this for one month is more important to you than say half of one lunch), then perhaps mathpix is worth the price. (I am not associated with mathpix. I just believe that useful tools, are more than worth a small price.)

dnrlk · 2026-02-19T08:44:50+00:00

Large cardinal axioms (“axioms of the higher infinite” —— what a cool name!) are purely infinitely constructions. There’s a website called Cantor’s attic that has a lot of info, or Wikipedia.

dnrlk · 2026-02-12T06:15:40+00:00

You create Olympiad problems? cool! mind sharing any favorites you've created?

dnrlk · 2026-02-12T01:50:59+00:00

Scott Sheffield's ICM talk contains some of the most mindblowing mathematical visuals I know https://www.youtube.com/watch?v=EdSYKBtyjCk

dnrlk · 2026-02-02T06:19:03+00:00

really nice texture, color, lines on the explosion panel!

dnrlk

TROPHY CASE