Maybe A Littel Late For Real’s Math Ask Meme 18, 6 And 3, Please?

Square is a rhombus, regular hexagon can be tessellated with three equal rhombuses, and every regular polygon with even number of sides can be rhombi-tessellated.

i've been working on it with my boyfriend for a while now and–

our first video is up!

i hope you enjoy it and subscribe to our channel

https://youtu.be/-X2BBtRI1Xw

10 IX 2022

today I need some extra motivation to study because I didn't sleep well these past few days and it has drastic effects on my productivity, energy, motivation and what have you

also I am struggling to make the choice as to what I should do today

yesterday I started solving some basic exercises from hatcher's textbook

Δ-complex structures are becoming more intuicitve with time. take my solutions with a grain of salt, I am just starting to learn about these things and won't vouch for them lmao

some more complicated objects (the last one is an example of a lense space)

I decided to study commutative algebra today

so far I'm enjoying it. not as much as algebraic topology (which will always be my number 1) but it has its beauty

right now I'm at hom and tensor functors, the structures are fairly complicated, but pretty, and they look like they need to be studied in stages, with repetition and breaks, to fully grasp what's going on

my sensory issues are terrible today and I'm exhausted and hyperactive at the same time uh

I'll try working through a lecture on commutative algebra and give an update on how it went later

update: I studied for a while, but it wasn't going great so I decided to take a nap instead. god knows I tried

30 VIII 2023

aight it's been a while, time for an update

recently I've been doing mostly algebraic geometry, my advisor gave me some stuff to read, so I'm working through that. the goal is to familiarize myself with hilbert schemes – the topic is advanced, so there are many prerequisites coming up when I'm trying to read the book, that's kinda annoying

we are planning for my thesis to be about a certain generalization of the hilbert scheme, so basically the question is "investigate this space" and I've been having second thoughts whether I'm up for the challenge. I'm just getting to know how all that stuff works, so it's quite overwhelming to see how much I need to learn before I can do anything on my own

nevertheless, I'm pushing through as I will have to learn all of that anyway

I am working on finishing the proof from my bsc thesis and honestly I'm kinda losing hope lmao it turns out that what I probably have to do to complete it is a massive amount of extra reading and an even bigger amount of proving lemmas. the thing is that my work is about something like a generalization of results that have been proven by two people (one of which is khovanov, yes, that khovanov) and I feel it in my balls that the case I'm working on should be treated in a similar way. now the problem is that I can barely understand what they wrote for the "easier" case and I just can't see myself doing that for the more complicated one. oh and for my case I should probably use equivariant cohomology. but all I know about it is the definition, I have never even calculated anything for that + I will do a course on it this semester so it feels futile to study it now. idk I need to talk to my former advisor about this and ask him to be honest, does he even believe that this can be done?

other than that I'm applying for a scholarship. I don't think I will get it, but it is worth trying

I moved in with my boyfriend and our cat decided that my desk is way too big for one person, so now it's our desk

uni starts in a month so I should probably spend that time doing something other than math, which I will be doing all the time once uni starts, but I struggle with coming up with things to do that are not math-related. I should complete some tasks for work, but I would also like to have a hobby

there is a number of things that I could try, for instance reading, drawing, singing, grinding metas for geoguessr (apparently I'm a gamer now), but I can't commit to any of those, my interest comes in waves

maybe I could schedule about an hour per day to do one of those things so that my brain gets used to it. it is not like I can focus on math 24/7, I need to take breaks and I have days when my motivation is zero, so I just sit at my desk and watch stupid shit on youtube. but that's the point, days like that could be spent doing something meaningful and refreshing, instead I just procrastinate math lol

you know girls can tell when you look at their boobs

i don’t care how quickly you glance, 1 second is like 5 seconds in boob time

so, for relativistic boobtime, where t is the observer, and t’ is the time measured at the boob. t=t’/sqrt(1-(v/c)^2) solving for t=1, and t’=5, we get that the boobspeed, v, is represented by v=+/- (6*10^8)sqrt(6)i m/s

boobs travel at 1.5 gigametres per second in the complex direction.

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

Me: I should write something

me : … or I could spent 78 hours straight making a miniature library with a working LED chandelier

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

the alphabet is like, there's the "a" region (abc...), for just, things, there's the "f" region (fgh..), for functions, there's the "i" region (ijk...), for indices, there's the "n" region (nm...), for integers, and the "p" region (pq...), for integers that are prime, there's the "t" region (tsr...), for time and progression and other axes that aren't the usual ones, and then there's the "u" region (uv...), for like, i guess open sets and differentiable functions and the such i guess, and then finally there's the "x" region (xyzw...) for just, variables that are more variable-y

there's also o and l but you shouldn't use those