17 IX 2022
for the past few days life was treating me quite aggressively. today I had a terrible migraine, I feel weak and tired in general. doing math in a state like that isn't as pleasant so obviously I didn't do much, prioritized my health instead
during the semester I used The introduction to manifolds by Loring Tu to study analysis and I forgot that there were many nice exercises there that I didn't have time for but promised myself I would try them eventually
so tonight was the night and I studied grassmannians
I had some "results" done on my own, which later confirmed to be true, namely that the grassmannian over ℝⁿ for a 1-dim subspace is equivalent to a projective space of dimension n-1. I'm pretty sure that we are getting the projective of the same dimension for n-1 dim subspaces but I didn't calculate anything for n>3 so I might go back to that one day
it's fun to get hunches like that even if they turn out to be completely obvious to the authors of textbooks lmao
I am finally in the place with studying the theory for homology, commutative algebra and apparently differential topology (as it turned out today), where I have a variety of exercises I can try and that's the good part for me, always helps to get deeper insights and allows me to be more active
a friend asked me for a talk about the zariski topology in the context of algebraic sets and spectra of rings, so I'll see her soon for that. she will give me a personalized lecture about her thesis, which is about general topology. I am not a big fun of general topo but I'm always a slut for lectures about math so am excited for that
I hope my body will get its shit together because I still have to prep my lecture on euclidean geometry and when I don't feel good it's super difficult to motivate myself to do things that are not super exciting. I will never see productivity as a value on its own for this very reason lol I can barely do anything I don't find interesting
sn
I know we all have different skills and all and it's supposed to be complementary, but, people who can do math are so morbidly funny to me
I figure it must be like
Imagine being like only one of twelve people in your whole city who can read and write
And it's not just because everyone else is uneducated, most of them cannot even learn the sort of things you can learn. Or they could, in theory, but it frustrates them so much that they never make it past grade school reading tops, and they hate every second of it
And it's not a "luxury" skill, either, like your whole society needs the written word to function, and by extension, they need you. They need you for shit like reading labels and instruction manuals and writting 2 sentences letters, and they pay you handsomely for that, which is nice, but also feels absurd
You read a whole series of novels that rock your life and you can't even talk about it to your best friend because anything more complex than a picture book breaks their brain
hairy ball theorem, stokes theorem, poincaré duality, nullstellensatz, idk too much to choose one
What is your favourite mathematical theorem? I'm personally torn between the compactness theorem for first-order logic, and the fundamental theorem of Galois theory.
I loved the quiz! and the result is quite flattering haha
Well…
Looks like I made a uquiz
Try it here
I love reading stuff on abstract geometry because there'll be some extremely complicated construction of abstract polytopes that takes up like two full pages
and the first example is this
and you're like "wow that's a cube :)"
and then the next example is this
i'm a math student, currently persuing master's degree. this semester I'm taking courses on complex manifolds, category theory, equivariant cohomology and representation theory
my bachelor's thesis was about my partial result in the knot/link theory. right now I'm finishing that proof and hoping to publish it when (if?) I'm done. my interests include algebraic and geometric topology and the goal for this year is to get to know some algebraic geometry
I post updates of how I'm doing, photos of my ugly notes and sometimes share some study methods that proved to be useful to me
oh and math is my special interest, I take it way too seriously lol
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my posts with study tips:
tips for studying math
tips for studying math part 2: you have an exam but the course is boring
my love for topology is a very concave function with a very positive derivative
tietze theorem is fucking beautiful urysohn's lemma is pretty and separation axioms are cute
aand i animated some riemann integration today:
i could've chosen different partitions or a different function in order to achieve more frames but i like this anyway
I think "high value person" can be interpreted as "someone who is liked by everyone and perfectly adheres to social norms" but also as "someone who wants to find their core values and to this end tries many different approaches" and many other things. some of the things listed are pretty good, such as "take care of themselves" or "doesn't equate their worth to sex", some are unnecessary: "perfected first impressions" or "ALWAYS well-dressed". naah, who cares lol
the thing with self-improvement or other forms of conscious existing (I just invented this term, by that I mean something like chosing which parts of oneself to keep and which to change) is that one must start somewhere. it's nice, in general, to have social relationships, sex life or hobbies and I see this list as a guideline for increasing the probability of achieving those and other things in a certain way
in my opinion it's really important to keep in check with oneself, ask if the cost of being likeable and elegant is worth it. some people derive pleasure from wearing nice clothes and make-up, I am not one of them and for me that would be too much of a sacrifice. I guess most people would hate to have my lifestyle: I basically do math all day. it is my decision to so, it's fun, and I hate it when someone assumes that it's bad just because they wouldn't enjoy it
hence I see this controversial list as goals of someone who genuinely wants to be perfect. and yeah I do think that most of those things are completely unnecessary, I don't consider this set of characteristics as a "high value person" but maybe some people do. a part of self-improvement for me was realizing that I don't care about most things and this post reminded me that there might exist people who care about everything. have they not yet realized that they actually don't care? idk, maybe they do care
but yeah if someone came to me and said that this list objectively defines a high value person then I would laugh lol I will respect everyone's values if they respect mine
I want you all to know that an Arab Muslim from Tunis proposed the Theory of Evolution near 600 years before Charles Darwin even took his first breath. Don’t let them erase you.
Thank you, /r/ProgrammerHumor, I love you endlessly.
Redditors competing to make the worst volume sliders possible...
⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
292 posts