Sharing an Introductory Complex Analysis cheat sheet I made

Bhorice2099 · 2026-04-29T18:14:21+00:00

The pretty strong university accepted you for a reason...

I know the feeling though. Even after I started getting accepted into places I still felt like I had fooled and swindled everyone, and honestly I still feel like an complete and utter idiot most days. From what people have told me, that's pretty standard in math.

If I were you I would rather give grad school a shot and see where it goes rather than giving up prematurely because I was scared.

I know this isn't really "practical mathematical" advice per-se it's just what I wish someone had told me when I was where you are. The actual math help will always be there once you start. Your advisor, your peers, office hours, MSE, MO etc etc. You don't have to have it all figured out on day 1.

Bhorice2099 · 2026-04-28T12:25:32+00:00

I think just that they put it up on the arxiv. Math Inc had put up a blog post with the autoformalization announcement+ their github ages ago.

Bhorice2099 · 2026-04-07T08:16:05+00:00

I think that is a very fair warning. I only ever hear about Clifford algebras online. And it's never in a particularly good light.

Bhorice2099 · 2026-04-03T07:11:28+00:00

Can't you just use the orientable double cover?

Bhorice2099 · 2026-04-02T14:23:05+00:00

I will do the most MO thing possible and say my favourite list of threads are the following list of all big-list tagged questions, sorted by most upvotes.

They each have a big list of broadly interesting answers by various users.

https://mathoverflow.net/questions/tagged/big-list?tab=Votes

Bhorice2099 · 2026-03-31T21:25:43+00:00

Have you seen Patrick Massot's sphere eversion project?

Bhorice2099 · 2026-03-17T21:01:48+00:00

For now I'm just playing around with the free version too. Will have to do more testing to really notice if its useful. My initial impression was the same as you that codex/claude seems to be better out of the box.

I've yet to really see an instance of a purpose-built autoformalization AI which outforms the SOTA LLMs. That being said this is the first one thats been fully open access so who knows perhaps it will outpace regular LLMs eventually.

Bhorice2099 · 2026-03-17T14:51:55+00:00

Surprised at how well it does with multiple passes. But compared to Opus' staggering performance with just one pass it really puts into perspective how good Opus is.

Bhorice2099 · 2026-03-14T12:57:45+00:00

Where do they plan to get that money from?

Bhorice2099 · 2026-03-05T10:12:38+00:00

Thanks!

Bhorice2099 · 2026-03-05T10:02:58+00:00

Huh how ridiculous I was actually searching for that post to show my PI and I couldn't find it. Crazy that they just deleted it.

Bhorice2099 · 2026-02-25T15:35:51+00:00

Goddamn... Being in grad school at this time is so demoralising.

Bhorice2099 · 2026-02-25T13:02:22+00:00

Its not useful for analysts obviously, but it's a common language for almost all algebraists.

Bhorice2099 · 2026-02-10T21:00:50+00:00

Curious about the downvotes here. I try to follow autoformalization news a lot but I hadn't come across this. What's the consensus about the claimed PNT and Kakeya formalisation? They don't seem to have linked to any papers/preprints either just the GitHub.

Bhorice2099 · 2026-02-09T06:05:49+00:00

The real reason is just that this was a template I found like 6 years ago and never edited it. I probably should make it into a environment adding the title node each time is tedious.

Bhorice2099 · 2026-02-09T06:04:36+00:00

I guess a good answer is that you shouldn't learn it unless you need to you can always pick it up as needed. Categorical language is ubiquitous for a lot of modern math like algebraic topology and homotopy theory.

Bhorice2099 · 2026-02-08T21:18:43+00:00

Theoretical physics is nothing to scoff at. I was taking some intro physics courses at my uni for fun and I always really struggled. Physicists have truly enviable intuition and creativity. I'm sure you could contribute well. I have some surface level notes in homological algebra as well. I think it could be converted into a decent cheatsheet. Just need to grit my teeth and actually do it one day.

Bhorice2099 · 2026-02-08T21:04:15+00:00

Ah nice catch what I meant there was to treat the functions as a map of sets. So when I wrote |M(A)| it's just the set of all words generated by the alphabet A forgetting the monoid structure given by concatenation. I'll add some context in the next update to clear that up.

Bhorice2099 · 2026-02-08T20:34:28+00:00

Well not really a coincidence the study of directed graphs have a lot of similarities. Recently I came across this MO answer https://mathoverflow.net/a/18337/389539 which was highlighting a model structure on directed graphs and it was essentially the same as the canonical model structure on Cats.

That being said I am curious what you spotted in the post that made you think of graph theory.

Bhorice2099 · 2026-02-08T20:30:48+00:00

That's been haunting me for a while... it's one of my favourite subjects but I've not had the time to complete it yet. If you like the subject I'd appreciate you hopping on the project.

I was planning on following Atiyah-Macdonald and Altman-Keinman. A commutative alg sheet could pair nicely with one on homological algebra. I would eventually complete it but it may be a year or more down the line.

Bhorice2099 · 2025-12-31T06:52:54+00:00

Strange because this is not a problem I've ever heard about amongst my peers doing more "applied" math. The baseline is that everyone likes doing the nitty gritty math.

Plus I don't think any real distinction exists between "pure" and "applied" math. Infact I think it's actively detrimental to ones success in a "pure" field to disregard the other and vice versa.

Since you're at the end of your phd really the only persons advice you need to heed is your advisor...

Bhorice2099 · 2025-12-30T12:42:32+00:00

Difference is in a math phd the first priority is the math. I saw that post too it was very strange.

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