People Using A Matrix As Just A Bunch Of Numbers In A Grid Or A Way To Summarize Some Elaborate Calculation

oh and there is the dual thing: sometimes you just know that the professor hates the subject. like when I was taking one of the analysis courses, where the lecture was with one professor and the tutorials were with a different one

at the lectures we were two months into measure theory while at the tutorials haven't even started doing exercises on that topic, but oh it was fine, still plenty of time, he knows what he's doing – we thought, like fools. then the midterm was announced, two weeks left, we still haven't started measure theory. then it was one week left, so the professor tried to solve some lebesgue integrals with us, but he got so bored with each example that he hasn't finished a single one. at this point we just hoped that maybe measure theory just won't be on the midterm, it was too late to do anything. well, unfortunately, the midterm consisted mostly of measure theory problems, it made sense because that was the main content of the course

the professor was clearly very passionate about hating measure theory

One of the really amusing things about college is that if you pay attention you sometimes can discern some of your professor's favorite pet concepts.

For instance, in my Topology course this semester, the Zariski topology has come up at least once in every single homework set so far, and in multiple lectures.

And okay, that's not that weird. The Zariski topology is a really important object in a LOT of fields, especially algebraic geometry. And discussing it at length is a really pedagogically sound move because the Zariski topology is a good example of a topology with a very well motivated structure (the closed sets are the algebraic sets!) that still very naturally gives rise to a lot of strange features, like the way all open sets in the standard topology are Zariski-dense. It was quite effective at startling me out of the complacency of unconsciously basing my intuition of how topologies behave entirely on the standard topology on the reals. So my professor bringing up Zariski so often doesn't necessarily mean he has any special affection for it.

except...

My professor writes many of the homework problems himself. Not all of them - the less interesting ones he lifts from the textbook- but some. Well, every single Zariski topology question I've encountered so far is an original from this guy. I know because the all the questions he writes personally have paragraphs of commentary contextualizing why he thinks the problem is interesting and where the ideas in the problem are going later in the course. And well- let's just say the asides on the Zariski topology have been copious indeed

AND THEN there's the way he talks about the Zariski topology in class! It's with this blend of enthusiasm and fascination only comparable to the way I've seen tumblrites talk about their blorbos. Like hey! Come behold this sgrungy little guy! Isn't he fucked up? Isn't he marvelous? And I look and I can only conclude YEAH that is indeed a spectacular specimen, he's so strange, I want to put him in a terrarium and study him (and then I get to! In my homeworks!)

Anyways. It makes me really happy picking up on how excited my professor is to share this topology with us. I'm kind of baffled that people assume math is a boring field full of boring people when there exist folks like my professor who get this passionate about a topology!

remember if you ever want to read an article for free and the subscription ad prevents you from reading the entire article DO NOT

Reload it and immediately turn off your Internet access (data/WiFi if you are using a phone)

Reload it and click the 'X' next to the return icon on the top left of your window (if you are on desktop)

Reload the page, type 'Ctrl+ A' and 'Ctrl+ C' and paste everything onto an open document

this has worked for me 97ish % everytime hope this works for u too

My favourite fucked up math fact™ is the Sharkovskii theorem:

For any continuous function f: [a,b] -> [a,b], if there exists a periodic point of order 3 (i.e. f(f(f(x))) = x for some x in [a,b] and not f(x) = x or f²(x) = x), then there exists a periodic point of ANY order n.¹

Yes you read that right. If you can find a point of order 3 then you can be sure that there is a point of order 4, 5, or even 142857 in your interval. The assumption is so innocent but I cannot understate how ridiculous the result is.²

For a (relatively) self-contained proof, see this document (this downloads a pdf).

(footnotes under read more)

¹ The interval does not have to be closed, but it should be connected. (a,b), (a,b] and [a,b) all work.

² Technically the result is even stronger! The natural numbers admit a certain ordering called the Sharkovskii ordering which starts with the odd primes 3 > 5 > 7 > ... , then doubles of primes, then quadruples of primes and so forth until you get no more primes left, ending the ordering in 2³ > 2² > 2. Sharkovskii's theorem actually says that if you have a periodic point of order k, then you have periodic points of any order less than k in the Sharkovskii ordering. It is frankly ridiculous how somehow prime numbers make their way into this mess.

well, google, one of them is a giant fuckin red dog

I got 55 and it seems to me that the majority of my answers were heavily influenced by asd

I took a test on like where you are on the ‘nonverbal intimacy scale’ and the average female score is 102 and male is 93.8 and I got 56 lolololol

here it is if ya want (reblog/reply w/ what you get!!)

19 I 2023

this week is kinda crazy

I have a complex analysis test on saturday and the professor said that it will cover the entire semester. thank god I might get away with not knowing anything about analytic number theory lmao

I had troubles sleeping lately, it takes me about 3-4 hours to fall asleep every day. I sleep a lot during the day and it helps a bit but I still feel half-dead all the time. every time I fall asleep my brain can't shut up about some math problem

for the algebraic methods course we were supposed to state and prove the analogue of Baer criterion for sheaves of rings. I was the only person who claimed to have solved this, so I was sentenced to presenting my solution in front of everyone. the assertion holds and I thought I proved it but the professor said that the proof doesn't work, here is what I got:

he said that we cannot do this on stalks and we have to define a sheaf of ideals instead. when I was showing this I had a migraine so no brain power for me, I couldn't argue why I believe this to be fine. whenever two maps of sheaves agree on each stalk they are equal, so if we show that every extension on stalks is actually B → M on stalks, then doesn't that imply the extension is B → M on sheaves?? probably not, but I don't see where it fails and I'm so pissed that I was unable to ask about it when I was presenting, now it's too late and this shit keeps me up at night

I enjoy sheaf theory very much and I can't wait to have some time to read about schemes, I have a feeling that algebraic geometry and I are gonna be besties

during some interview Eisenbud said that when deciding which speciality to choose one should find a professor that they like and just do what that professor is doing lol. I feel this now that I talked some more to the guy who taught us commutative algebra. since my first year I was sure that I will do algebraic topology but maybe I will actually do AG, because that's what he's doing. is having one brain enough to do both?

anyway I'm glad that my interests fall into the category of fashionable stuff to do in math these days. my bachelor's thesis is likely going to be about simply-connected 4-dimensional manifolds, which is a hot research topic I guess. I won't work on any open problem because I'm just a stupid 3-year, not Perelman, but it will be a good opportunity to learn some of the stuff necessary to do research one day

that's an interesting perspective

recently I've been thinking about it in an opposite way. it started during a conversation about brains, in particular how stupid and flawed they are, I realized that I enjoy math because it gives me a break from being human. there is no place for emotion and cognitive bias, only formal reasoning and proofs. it feels so safe and so distant from the day-to-day life filled with problems caused by the human nature, it feels so clean. it's a place for me to enjoy only the best qualities of my existence. it's an acceptable way to separate myself from everyone, and simultaneously stay connected

I love how different this is from what is described above, as if math offered a place for everyone to find something that they will like

Im trying to find a really long Tumblr post that talked about how sad it was that people are so happy to complain about how much they hated math and how math can be a way to connect with your fundamental humanity and...

Yeah, I've been studying a little bit of it on my own, ten years after I dropped out of college, I've been going back to seeing some basics of calculus, and I've been really feeling some of that.

There is this sense that math is this alien thing, separate from the true concerns of humanity. This external topic, strange and inhumane that only those few weirdos with a eccentric and atypical cast of mind, who are themselves separate by a few degrees from human nature, can grasp.

But it's not that, We, messy warm emotional dumb humans came up with it, we silly atavistic creatures dedicated so much time and effort to develop it and explore it, this silly, quirky, wet, ape-like species is the only living creature on this planet that concerns itself with doing math in any serious capacity. It didn't come from aliens or the gods or from dolphins, math came from humans and humans are the only ones that use them. There could be nothing more human, more fundamentally ours, more intrinsic to our nature than math.

And it's not just a tool! Is not just this thing to be celebrated because its useful in a purely base pragmatical, prosaic way. Is not this thing we have to dissapasionatly conceed credit to because I guess it does useful things like bridges and rockets and computers and taxes. Math is not just the civilizational equivalent of going to the dentist or eating your vegetables.

i hesitate to call it a philosophy or an art, it is a way of human thinking, it is a way of thinking like a human, of thinking in a way that only humans can think. its is one of our oldest and proudest traditions, it is a way to feel greater than onself, it is a way of growing. it is a song with a prosody all its own. There is such a profound sense of meaning and beauty and truth and purpose to be found in math, and the best of all is that it works, when it says something it means something, its telling you a thing that is meaningful, that represents something true, that couldnt be any other way, that has consequences and uses and can be relied upon, that it representes something which carries weight and its ours, its truly a part of our nature, of what we are.

i gotta say i don't buy all them planning strategies and tips that require more effort than just sitting and doing the work

i mean that might help some people but i find that when i am doing something important to me i need no plans nor do i need motivation, i also don't procrastinate, everything falls into its right place

and if achieving something takes so much effort in preparation, is this even supposed to be a thing? idk, maybe that's the reason why i have no external proof of my work lol

mathematicians, constantly: god I’m so tired of people telling me how much they hate math whenever i mention what im into

me: yeah it’s fucked up. i do probability theory, what about you

them: oh man I hate probability theory

when a pelican bites you there's no malice in their eyes. they aren't upset at you. they are just hungry and want to see if you fit in their mouths. and if you don't then it's no problem and everything is fine. and if you do then well i guess your fate is sealed but that's ok it's a beautiful animal