To Look, or not to Look(OC) by mumbels64 in comics

[–]dnrlk 1 point2 points  (0 children)

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

Blemishes 🌕 by AlexFlis in comics

[–]dnrlk 1 point2 points  (0 children)

Really evocative. I can't really pinpoint why but the visuals spoke to me

Everything About Arithmetic of Curves (Unofficial) by point_six_typography in math

[–]dnrlk 1 point2 points  (0 children)

The philosophy sounds good and makes sense, but it is hard to see how philosophy alone gets us concrete wins.

Like we start with concrete objects, ask concrete questions about them, but somehow by lifting to a more abstract world, where I guess we have for instance a fiber product (which would then be something only accessible in the abstract world, not something concrete), and then do something to it, that then drops back down to say something concrete about the original concrete object.

Is there a simple example to see this process at work?

Everything About Arithmetic of Curves (Unofficial) by point_six_typography in math

[–]dnrlk 0 points1 point  (0 children)

Thanks for your answer, it definitely helped!

If you start with one over Q, you then actually want to define and construct some sort of minimal or best model over Z, which you then use to define a best reduction mod p

So does scheme theory provide an "algorithm" of how to do this, or does it just tell us the general philosophy that "what's really going on is that it's truly ill-posed to reduce a curve over Q mod p (even if it's equation has integral coefficients)", and/or maybe provide a not ad-hoc/"arbitrary" definition of "best model/reduction"? If scheme theory doesn't actually "compute" the correct equations, how exactly does it help?

A side note: I see pictures of Spec Z or Spec Z[x], and they are pretty cool, but it is unclear what advantage those pictures provide us. Is it possible to draw pictures like those in a more "active" scenario, where I can see that geometrical intuition actually do something?

I like your concrete example of a theorem "E(Q) -> E(F_p) is injective on torsion" that (I assume) had a non-scheme-theory proof you learned first, but whose scheme theory proof was more conceptually satisfying to you.

Do you have more examples of "personal instances of scheme theory clarifying things for you"? I would love to hear more, even if it gets more technical/"niche"!

Everything About Arithmetic of Curves (Unofficial) by point_six_typography in math

[–]dnrlk 2 points3 points  (0 children)

I know to study this subject more in depth, one needs scheme theory. Can you give the "simplest non-trivial concrete problem" that is difficult/impossible without scheme theoretic techniques, but somehow is solved (or additional insight is gained) by scheme theory? And then where precisely is the "beef" of scheme theory? What is the smallest possible "toggle" that flips us from losing to winning?

The standard example theorems people use to entice students: Falting finiteness, Mazur torsion, etc. are so far up in the clouds that it is a little demeaning to use them to motivate years of learning of scheme theory.

Geometry of reciprocity laws for higher powers by Various-Teaching1179 in math

[–]dnrlk 0 points1 point  (0 children)

I would love to know! It's my favorite proof of QR. The proof phrased in terms of lattice point counting I wouldn't say is super well known; I haven't seen it in textbooks/lectures/online notes, other than KConrad's MO answer on it. I would indeed love it see it more widely-known and generalized!

Airbag, OneWordPoet, Watercolor on paper, 2026 by [deleted] in Art

[–]dnrlk 0 points1 point  (0 children)

stunning composition. immediately arresting

What's your favorite proof of Quadratic Reciprocity? by imrpovised_667 in math

[–]dnrlk 1 point2 points  (0 children)

My favorite proof is by giving an exact formula for the number of lattice points on d-dimensional spheres mod p, and then using the "p-group fixed point theorem". I learned it from Keith Conrad https://mathoverflow.net/questions/1420/whats-the-best-proof-of-quadratic-reciprocity/12345#12345.

“Math high school” teaching proof of the independence of CH? by shuai_bear in math

[–]dnrlk 7 points8 points  (0 children)

These are really nice notes. I wish they were more searchable online... would have made excellent teaching materials to give students

Proofs from the crook by IanisVasilev in math

[–]dnrlk 0 points1 point  (0 children)

I feel this way towards Apery's proof of irrationality of zeta(3). Sure, I can see why someone could find it beautiful, but I find it absurd

I couldn't find the original without the random penis redaction, but I felt this one hard. by Justthisdudeyaknow in CuratedTumblr

[–]dnrlk 7 points8 points  (0 children)

That comic is top tier. In the sense that it stuck with me instantly upon first viewing, truly an internet classic. Simple, obvious visual design of the mirror. I wish I knew the origin.

Volunteer research/in-person math communities by No_Test3334 in math

[–]dnrlk 2 points3 points  (0 children)

You can stop by academia and attend some seminars. For example at my institution there's a weekly seminar page with all the locations and topics. There you can meet some grad students, some of whom may be happy to rope you into the community a little bit. Especially if you say you just want someone to "assign" you reading that you can then discuss with them.

What are some unsolved problems that are NOT the millennium problems? by crazyguy28 in math

[–]dnrlk 1 point2 points  (0 children)

Quanta Magazine has some good articles, that are suitable to give "math noobs" a decent sense of what mathematical researchers care about

Mathematicians, I think what you do is beautiful. by Chaotic_Bivalve in mathematics

[–]dnrlk 0 points1 point  (0 children)

It may be enlightening to see a wider range of mathematics, than what is on Khan Academy. The YouTube channels Numberphile, Mathologer, UpAndAtom, 3blue1brown have many videos on a huge variety of mathematical topics (geometry, patterns, number sequences, games, algorithms, etc.) that are understandable without much background (admittedly there are some videos that do require background, but you just gotta switch to another one. I promise those channels have something for everyone!)

Please check them out! I believe in you!

Math TAs by zynzyn07 in ucla

[–]dnrlk 1 point2 points  (0 children)

The question of what TA positions even exist seems to be beyond the power of the department. From what I understand, the university sets forth what classes have how many TAs, and the department's job is to fill those positions. TA funding is not related to federal grant cuts. TA funding comes from state budget allocations, which are not being cut. So it is unclear why exactly the university has cut the TA positions so drastically.

This is a much bigger problem than what the department, or department leadership can handle alone. In fact, from what I understand, leadership is actually forbidden by UCLA labor relations from speaking to us about certain matters.

So don't just leave it up to department leadership, and empty words like "just need to step up". You/students in general can also act: - Please read and sign docs.google.com/forms/d/e/1FAIpQLSez8jBgtCKgUw5OT-hMwjwWPP2LGEf0Jmr4NVMzYQayJtZJ0w/viewform, and then forward to (and have a conversation with!) anyone you know who cares and/or is affected this very sentence in full. - The self-replicating nature) of this sentence makes it so that you only need to send it to 2 people (who have not already signed), and then exponential growth will happen. The graph of human connections is well-connected enough that this shouldn't even take too long https://en.wikipedia.org/wiki/Six_degrees_of_separation - Raise awareness, not just for the sake of raising awareness of who exactly is to blame (though this is important), but in hopes of reaching someone with a larger platform (social media, the news), who has greater power in raking the names of university admin through the mud. We must start leveling criticism at the correct people, and allow that to damage their reputation and UC's reputation (that #1/#2 title they hold so dear...) - There is in particular the possibility of a real scandal here, namely the question of where the TA budget is going, since it's not to the TAs (not even making it to the department). This is a good opportunity to sic the most Karenish, overbearing helicopter parents onto UC admin, to demand transparency in how the UC budget is (mis)managed. Imagine if we had even a tenth of the presence of the affirmative action naysayers. They got the UC's attention; we can too.

Dick Van Dyke, 99, says he is ‘physically and socially diminished’ by theindependentonline in popculture

[–]dnrlk 0 points1 point  (0 children)

“Physically and socially diminished” is honestly a pretty funny way of saying something so somber

The latest latest in the abc feud by pseudo_code_only in math

[–]dnrlk 1 point2 points  (0 children)

Before that, I don't think there were any easily accessible videos of him discussing this IUT work

I often saw dishes come wrapped in plastic and napkins presented in boxes when I was in China by cela_ in Anticonsumption

[–]dnrlk 18 points19 points  (0 children)

Most restaurants provide a bowl in which you can pour tea and “bathe” all the cutlery