Doing (basic) Algebraic Topology In This Context Feels Like Going To That Jungle And Saying You Know

in a way. over the last two years or so. mathematics has become the altar at which I pour out my private grief, and transmute it to something like solace. it does not particularly matter to me if I am ever any good at it. what matters is that the effort I apply to it is rewarded by understanding. I have no natural aptitude for it; I am climbing this hill because it was the steepest and least hospitable to me. there is less agony in the gentler slope, but less valor

21 VII 2023

oh god I haven't posted anything personal in a very long time

I've been super busy with exams, essays and then my thesis, all I did was sleeping and studying

I defended my thesis 40 minutes ago! it's done! in two months I am starting the master's degree program

this was probably the most brutal exam session I ever had lol it started a month ago and I had no day off since. after finishing my normal exams I've been working 12 hours per day to complete my thesis and thanks to my advisor who was working just as hard as me, we did it

I was so close to failing differential geometry. the exam was really bad, probably my worst ever. the questions were mostly about this one topic covered during the last class – we discussed maybe 3 problems and the professor decided that this is good enough lol basically we were supposed to read his mind and guess what else there is to learn. I scored 35% and apparently that's more than enough to pass – the grades go from 3 to 5 and I got 3.5, so that's literally "more than enough to pass". there were only 3 people who scored 50% or more, so yeah, that seems fair

that week of studying differential geometry was the most stressful week in the last 3 years, I fucking hate it when it's unclear what I'm supposed to learn and I have no idea how to do it. thank god I passed, I don't know how I would do it again before taking the september exam

anyway, I passed algebraic topology, number theory and algebra 2 with flying colors and the reviewers really loved my thesis! they strongly suggest publishing it, but I think I will try to finish the second part of the proof before I do that

I already found the advisor for my master's thesis, of course I don't know what it's gonna be about, but since I had some algebraic topology this year, I am thinking it's time to learn algebraic geometry now

sweet jesus it's finally over, I can't believe it. and something new is starting

Me duele la cabeza

ah yes my boy tom cardy. everyone must listen to him, he's the best

I need everyone to see this ABSOLUTE MASTERPIECE

The beautiful modernism of Oliver Byrne’s, The First Six Books of the Elements of Euclid, 1847

ok i get it now, most people need plans and structures so then they can study what they're really into in the future

btw today i'm doing operations on topo spaces, i love that already

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

" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.

september

I decided to start posting monthly, I hope it will help me keep it regular during the semester, it may also bring more structure into my posts

I gave my talk at the conference, I was surprised with the engagement I received, people asked a lot of questions even after the lecture was over. it seemed to be very successful in a sense that so many people found the topic interesting

what I need to do the most in the next 3 weeks is learn the damn geometry. sometimes I take breaks to study algebraic tolology, I did that yesterday

you guys seem to enjoy homology so here is me computing the simplicial homology groups of the projective plane. I tried to take one of these aesthetic photos I sometimes see on other studyblrs but unfortunately this is the best I can do lmao

my idea for mainly reading and taking notes only when it's for something really complicated seems to be working. I focus especially on the problem-solving side of things, because as I learned the hard way, I need to learn the theory and problem-solving separately. what I found is that sitting down and genuinely trying to prove the theorems stated in the textbook is a good way to get a grasp of how the problems related to that topic are generally treated. sometimes making one's own proof is too difficult, well, no wonder, experienced mathematicians spend months trying to get the result, so why would I expect myself to do that in one sitting. then I try to put a lot of effort into reading the proof, so that later I can at least describe how it's done. I find this quite effective when it comes to learning a particular subject. I will never skip the proof again lmao

in a month I'll try to post about the main things I will have managed to do, what I learned, what I solved, and hopefully more art projects

8 V 2022

I am on my way home from a math conference, the first one in which I participated actively – I prepaired the talk about the Borsuk-Ulam theorem

my lecture was centered around the connection between the classic "continuous" BUT and its combinatorial analog: Tucker's lemma

I wanted to talk about this because I was amazed at how cool and "versatile" this theorem is. there is a whole book about its applications and generalizations, which is btw very well-written, I highly encourage everyone to read it:

my presentation went well, although after practicing it for about a week the topic seemed really fucking boring to me, no wonder

other than that I have another recommendation to make. do you also hate how messy multivariable calculus is? I do. calculations and technical definitions everywhere, and at the end everything comes down to calculating the determinant of some jacobian. bluh. I stumbled upon a book that describes everything from a sort of algebraic perspective, smells a little bit like category theory too. very clean, very satisfying to read:

I have been studying covering spaces recently and I can give some dope motivation for learning about the structure induced by the covering mapping:

I will never forget that the homomorphism induced by the covering projection is injective

that would be it for my mathemathical life. my personal life, which is still closely connected to math, brings me some psychological progress. I no longer get stuck in loops of "oh I'm so bad at math. maybe I'm not? I got a good grade from X. ah but I got a shit grade afterwards". it might be because I didn't fall on my face for a while now, only decent grades, good ideas, a good presentation, this is correct. but I also do not negotiate with myself that this is supposed to be proof that I'm good enough, I just stopped paying attention to these and focused on math instead. and paradoxically when I stopped caring about being good at math I was rewarded with getting better at math???

a coincidence,

a pleasant one, nonetheless.

anyway I will have to take a fall at some point, unavoidable. and it will be the final test of my progress, becauase I used to get very elevated in my sense of self-worth after receiving a single good grade among trash ones and now I'm just ok. not the god, just ok. but back then, at some point I would no longer be god, I would get smacked in the face by some "proof that I'm actually trash" and that would be a fall from a significant altitude. so I'm hoping that the fall will also be less painful now

I think the biggest change I made was giving up, I abandoned all hope. nooow here is the moment when people interrupt me with "nooo that's horrible don't give up you're a great person you just have to notice that"

fuck off you don't understand shit

I'm doing better now precisely because I stopped hoping that one day I'll stop feeling worthless, that one day something great will happen that will prove once and for all that I'm meant for something great. I can't stand this anymore, I am disgusted by the fact that deep down I still believe that I'm supposed to be the best and that I can't enjoy anything unless I am winning. I want to puke when I'm reminded that everything I do serves the purpose of winning the negotiations I have with myself about what my actual value is

my self-hatred runs much deeper now than ever before and I have no more patience for self-victimization, no more room for "allowing myself to feel". fuck off, all I feel is rage. I want to be able to do things without the prospect of a reward, my goal is to enjoy things, not the sense of being good at doing things

so that's what I'm doing, I made peace with the fact that I will probably never feel good about myself and that I have no chance at achieving the greatness I crave. and I must say I started respecting myself more, turns out I am actually able to do things without the promise of being the best at them, the vision of bringing value to the world motivates me. and fuck the western culture with its oh you must love yourself you are a great person. no, you don't have to do that and you have no way of knowing what kind of person you are, nobody has ever defined it in a strict formal sense, people just use this phrase to trigger the feel-good in others

I am aware that all of this sounds really bad, but I don't care, it works. and my math will be better like that because now that I stopped crying over being trash I have more time to study

I just hope that the fall won't be as painful