Visualization Of The Rubik's Cube

It's always funny when a math book or a paper starts out with like a foreword/introduction type thing but it calls itself an "Apologia"

Like "Sorry i wrote a new book, this is why i thought i had to do it. Please forgive me."

also a funny thing is happening

my title here on tumblr is "you can't comb a hairy ball" – hairy ball theorem, which says that whenever an n-dimensional sphere admits a continuous field of unit tangent vectors, n must be odd. I love how geometric this is, math is full of memes

anyway when I found out about it I was joking that my thesis will be on it. and now it's actually very likely that my first thesis will be about hairy manifolds, I can't wait till I can start writing

15 V 2022

I have a topology test this friday, not gonna lie I'm kinda stressed. this is my favourite subject and I am dedicating a great deal of time to learn it so if I get a low grade it undermines the efficiency of my work. everyone thinks I'm an "expert", but internally I feel like I lied to them. it's ridiculous, because I can solve all the theoretical problems fairly well but the moment I have to calculate something for a specific example of a space I am clueless. and it's about applying theory to problems, right? so what is it worth

other than that tomorrow is a participation round in the integral competition at my university. I am participating. I don't have any high hopes for this, because it's been a while since I practiced integration and I am not motivated to do so because it's not an important skill – wolfram exists. either way could be fun, that's why I decided to go there

I am dreading the fact that I'll have to sit down and learn all the material from the probability theory until the exams. I've been ignoring it completely so far, because it's boring and complicated. the last homework broke me, it's high time to get my shit together

The chili plant made a deal with their God to only be consumed by things that could spread its seeds and fly. The chili received capsaicin, making itself painful to eat for mammals, but not birds, and all was well for the chili.

Then the human shows up, tastes it, and likes the pain. So now there's this flightless fucking mammal eating the chili. Like not even a fruit bat or anything, a flightless fucking mammal chomping on the chili.

What the fucking shit, God, cried the chili, I specifically requested the opposite of this.

Now hold on, wait a moment, replied the God who talks to plants but has no idea what the fuck these apes are going to do next. It might be something cool.

And in a flash of a second, in barely fraction of the time that chili took to develop capsaicin, the humans went from walking across land bridges and rowing little boats across small waters, into building ships that could cross oceans. More humans tasted the chili, and liked the pain. They took the seeds with them, and planted it elsewhere.

See? They spread the seeds.

They're still not flying, said the chili, still feeling insulted and betrayed.

But before the conversation was over, the humans were still not done fucking around and nowhere close to finding out. The ships became machines, and another machine was invented, capable of flight. Now, not only were the humans farming chili on continents far too far away for any of the birds that originally ate it could dream of flying, but the chili flew with them to lands where it could possibly not grow, so that humans over there could also eat it and enjoy the pain.

You see? They spread your seeds and fly.

It doesn't count as keeping a promise if you only manage it by a fucking accident, said the chili, still somewhat insulted. But nonetheless, the chili thrived.

reverse gaslighting where i pretend to know exactly what you are talking about

Real’s Math Ask Meme

What math classes have you taken?

What math classes did you do best in?

What math classes did you like the most?

What math classes did you do worst in?

Are there areas of math that you enjoy? What are they?

Why do you learn math?

What do you like about math?

Least favorite notation you’ve ever seen?

Do you have any favorite theorems?

Better yet, do you have any least favorite theorems?

Tell me a funny math story.

Who actually invented calculus?

Do you have any stories of Mathematical failure you’d like to share?

Do you think you’re good at math? Do you expect more from yourself?

Do other people think you’re good at math?

Do you know anyone who doesn’t think they’re good at math but you look up to anyway? Do you think they are?

Are there any great female Mathematicians (living or dead) you would give a shout-out to?

Can you share a good math problem you’ve solved recently?

How did you solve it?

Can you share any problem solving tips?

Have you ever taken a competitive exam?

Do you have any friends on Tumblr that also do math?

Will P=NP? Why or why not?

Do you feel the riemann zeta function has any non-trivial zeroes off the ½ line?

Who is your favorite Mathematician?

Who is your least favorite Mathematician?

Do you know any good math jokes?

You’re at the club and Andrew Wiles proves your girl’s last theorem. WYD?

You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?

Who is/was the most attractive Mathematician, living or dead? (And why is it Grigori Perlman?)

Can you share a math pickup line?

Can you share many math pickup lines?

Can you keep delivering math pickup lines until my pants dissapear?

Have you ever dated a Mathematician?

Would you date someone who dislikes math?

Would you date someone who’s better than you at math?

Have you ever used math in a novel or entertaining way?

Have you learned any math on your own recently?

When’s the last time you computed something without a calculator?

What’s the silliest Mathematical mistake you’ve ever made?

Which is better named? The Chicken McNugget theorem? Or the Hairy Ball theorem?

Is it really the answer to life, the universe, and everything? Was it the answer on an exam ever? If not, did you put it down anyway to be a wise-ass?

Did you ever fail a math class?

Is math a challenge for you?

Are you a Formalist, Logicist, or Platonist?

Are you close with a math professor?

Just how big is a big number?

Has math changed you?

What’s your favorite number system? Integers? Reals? Rationals? Hyper-reals? Surreals? Complex? Natural numbers?

How do you feel about Norman Wildberger?

Favorite casual math book?

Do you have favorite math textbooks? If so, what are they?

Do you collect anything that is math-related?

Do you have a shrine Terence Tao in your bedroom? If not, where is it?

Where is your most favorite place to do math?

Do you have a favorite sequence? Is it in the OEIS?

What inspired you to do math?

Do you have any favorite/cool math websites you’d like to share?

Can you reccomend any online resources for math?

What’s you favorite number? (Wise-ass answers allowed)

Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?

Are there any non-interesting numbers?

How many grains of sand are in a heap of sand?

What’s something your followers don’t know that you’d be willing to share?

Have you ever tried to figure out the prime factors of your phone number?

If yes to 65, what are they? If no, will you let me figure them out for you? 😉

Do you have any math tatoos?

Do you want any math tatoos?

Wanna test my theory that symmetry makes everything more fun?

Do you like Mathematical paradoxes?

👀

Are you a fan of algorithms? If so, which are your favorite?

Can you program? What languages do you know?

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

1 X 2022

new month huh

yesterday the commutative algebra teacher sent out the first homework assignment. you know, fuck the holiday, we need that grind

I have a week to solve it but I started yesterday as I was so excited

we need to prove some elementary properties of commutative unitary rings and I am enjoying it, I completed a half of the exercises so far. I can tell that the intuition acquired from studying module theory is paying off. many of the requested properties are the special cases of what I encountered during my module venture, so I feel like I understand them quite well. the problem I come across is how to write it down in a rigorous way, but I guess this is why we're supposed to do those exercises

I just got home from the math camp, it was so exhausting. I am not used to being around people all the time, so I my tolerance for interactions is low. I'm glad I went there tho, because I gained some teaching experience – my lecture, choosing contest problems and then grading the solutions

my university offers jobs as graders, older students can make some extra money checking homeworks of younger ones. the requirement is to have a decent GPA, which I don't have so I'm afraid they won't accept me. I don't know how decent exactly tho, so I'm going to try. in particular I might get bonus points for my extracurricular activities, giving talks at conferences and the grading I did at the camp. I'm so done with being poor, I hope I get in. otherwise I might start looking for some programming jobs, not for this academic year but in general, to find out what I could do at all

a few days ago I found a book that I wish I had found sooner: Vector Analysis, Klaus Janich

these are some of the chapters I needed a few months ago for my analysis course. the book is written like a novel and contains many interesting examples. on the bright side there are chapters about riemannian manifolds and other stuff that I haven't yet had an opportunity to study, so I plan to skim through the topics I already know and stay longer at those new to me

well, the sememster starts on tuesday so I don't have much time for that book, but as a sidequest it seems just right

Iconic Things My Coding Professors Have Said (and it’s only day one)

“that sounds very hacky, but smart”

“i’m not sure where i’m going with this… its quite similiar to my life”

*Entire class and prof spends fifteen minutes trying to solve a problem before eventually giving up* “great work guys, that was some good debugging”

“is this a super big issue?” *longggg dramatic sigh* “… yes”.

Professor 1: “it’s still not working? um… okay, maybe you should… turn off your wifi and turn it back on again?“   Professor 2: "40 years of experience in networking and computing at its finest”

“whenever i’m doing my taxes, i never use the calculator app on my phone, i always just open up a notebook and use python and i think thats very brave of me”

“your life quality with improve when you use python 3 instead of python 2. your skin will improve and you’ll even sleep better”

“so this compiler doesn’t recognise cases, so if you’re really perverse, you could do Apple, aPple, apPle, appLe, applE, but if you do that then i’m going to kick you out”

“so, let’s give an example: "True = False”. Asides from causing the end of the world, much like dividing by 0, this will also cause an error”

“if you want to see my cat, i’ll show her. if you DON’T want to see my cat, too bad, cause I’m going to show you her anyway”

“today we will use three keywords: `if`, `else`, and their weird cousin `elif`.”

“if you want to type something else, like… uh, goodbye world? maybe? is that too dark? i think its too dark, so lets save that for later on in the year… by the way, have you been told about your exams yet?”

Professor : “is everything clear so far? shall i go faster?”   Literally EVERYONE: “no! slower!“   Professor: "Slower?! you can go slow when you’re dead, you won’t need python then!”

“you can’t use functions as your variable names. for example, you can’t call this number "if”. i mean i don’t know why you’d use that as your variable name to begin with, but i’m not here to question your life, i’m here to teach you python”

“it’s probably not the most efficient but its just what came out of me so we’re running with it”

Part 1 | Part 2