Moreover Tiktok Adhd Content Is Not Even Good Lol Most Of It Is Videos Themed "things I Didn't Know Were

ok uh. how do you hypothetically say "i want to study you" in a friendly way

so far the best I've got is "can i join a discord derver that youre in so i can observe you in your natural habitat"

welcome ✨

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

–––

my posts with study tips:

tips for studying math

tips for studying math part 2: you have an exam but the course is boring

Me: *Removes my cat from my lap to do something else.*

My cat: Father is…evil? Father is unyielding? Father is incapable of love? I am running away. I am packing my little rucksack and going out to explore the world as a lone vagabond. I can no longer thrive in this household.

this looks so great! I need to check this out as well

25 VIII 2022

I found the most beautiful math book I have ever seen

it covers the basics of algebraic topology: homotopy, homology, spectral sequences and some other stuff

one of the authors (Fomenko) was a student when this book was being published, he made all the drawings. imagine being an artist and a mathematician aaand making math art

just look at them

other than those drawing masterpieces there are illustrations of mathematical concepts

I'm studying homology right now, so it brings me joy to know that this book exists. I don't know how well it's written yet, but from skimming the first few pages it seems fine

I just finished watching a lecture about exact sequences and I find the concept of homology really pretty: it's like measuring to what extent the sequence of abelian groups fails to be exact

I'm trying to find my way of taking notes. time and again I catch myself zoning out and passively writing down the definitions, so right now I avoid taking notes until it's with a goal of using the writing as a tool for acquiring understanding. I'm trying to create the representations of objects and their basic relations in my mind at first, then maybe use the process of note-taking to further analyze less obvious properties and solving some problems

I will post more about it in the future, we'll see how that goes

*through tears* I don’t ever want to let my fear of failure trump the wonder of mathematics, I don’t ever want to be so scared of it that I forget to treasure it, I don’t ever want to let my feelings of being small deter me from even trying to dig deeper, I don’t ever want to turn my eyes away from the beauty, even though it is blinding. Never, never, never. 

13 X 2022

I dedicated the weekend to meeting with people from the machine learning club, helping my friend through her analysis homework and studying category theory for one of my subjects. then I did mostly the complex analysis homework

here are some wannabe aesthetic notes

my main goal at the time was to truly understand yoneda's lemma and the main intuition I have is that sometimes we shouldn't study the category C, but thw category of all functors from C to Set

after studying for a few hours I can say that the concept became a bit more intuitive

one of the problems in my "putnam homework" was to calculate the product of all differences of distinct n-th roots of unity – or so I thought. for a few days I believed that my solution doesn't work. I ended up with a disgusting fomula interating cosines of obscure angles but the visual intuition is neat, especially for an odd n. aaand that's no surprise since it turns out I'm fucking illiterate. not distinct roots, just differences of distinct roots, so that the whole thing is symmetric and there is no distinction of n odd vs n even

anyway I finally solved it, so that's nice!

I completed 5 out of 10 problems, which was my goal, so I should stop now and do my commutative algebra homework. there is one more exercise I want to solve:

the complex polynomial P with integer coefficients is such that |P(z)| ≤ 2 ∀z∈S¹. how many non-zero coefficients can P have?

I'm almost there with it and it's really cool

ofc the opportunity to include pretty drawings in my homework couldn't be wasted

during my category theory tutorial the professor asked me to show my solution on the blackboard. I was kinda stressed because now is the first time when I have my lectures and tutorials in english and on top of that this is a grad course. that whole morning I was fighting to stay awake, after the blackboard incident I didn't have to anymore

this is what I did

this week is likely to be the hardest out of many proceeding ones, because I won't have the weekend for studying (it's my grandma's birthday) so I need to use the maximum of my time during the week and get as much done as possible. I still need to do two homeworks, and study the theory. I am trying to learn how to prioritize and plan things, this is still a huge problem for me

I found an interesting youtube channel: Justin Sung. he talks about how to study/ how to learn and I like what he says, because it just makes so much sense. it's been a while since I started suspecting that methods such as flash cards or simple note-taking don't work and his content explains very well why they indeed might not work. it's very inspiring to see a professional confirm one's intuition

When banned from using "trivially" in a proof...

“Hello all. In a fellow mathposter's topology class they were not allowed to use the word "trivially" or any synonym thereof his proofs. The person presenting his work then crossed out "trivially" and wrote instead "indubitably." This inspired him to write a program that will insert condescending adverbial phrases before any statement in a math proof. Trivially, this is a repost. Below is the list--please come up with more if you can!

Obviously

Clearly

Anyone can see that

Trivially

Indubitably

It follows that

Evidently

By basic applications of previously proven lemmas,

The proof is left to the reader that

It goes without saying that

Consequently

By immediate consequence,

Of course

But then again

By symmetry

Without loss of generality,

Anyone with a fifth grade education can see that

I would wager 5 dollars that

By the contrapositive

We need not waste ink in proving that

By Euler

By Fermat

By a simple diagonalization argument,

We all agree that

It would be absurd to deny that

Unquestionably,

Indisputably,

It is plain to see that

It would be embarrassing to miss the fact that

It would be an insult to my time and yours to prove that

Any cretin with half a brain could see that

By Fermat’s Last Theorem,

By the Axiom of Choice,

It is equivalent to the Riemann Hypothesis that

By a simple counting argument,

Simply put,

One’s mind immediately leaps to the conclusion that

By contradiction,

I shudder to think of the poor soul who denies that

It is readily apparent to the casual observer that

With p < 5% we conclude that

It follows from the Zermelo-Fraenkel axioms that

Set theory tells us that

Divine inspiration reveals to us that

Patently,

Needless to say,

By logic

By the Laws of Mathematics

By all means,

With probability 1,

Who could deny that

Assuming the Continuum Hypothesis,

Galois died in order to show us that

There is a marvellous proof (which is too long to write here) that

We proved in class that

Our friends over at Harvard recently discovered that

It is straightforward to show that

By definition,

By a simple assumption,

It is easy to see that

Even you would be able to see that

Everybody knows that

I don’t know why anybody would ask, but

Between you and me,

Unless you accept Gödel’s Incompleteness Theorem,

A reliable source has told me

It is a matter of simple arithmetic to show that

Beyond a shadow of a doubt,

When we view this problem as an undecidable residue class whose elements are universal DAGs, we see that

You and I both know that

And there you have it,

And as easy as ABC,

And then as quick as a wink,

If you’ve been paying attention you’d realize that

By the Pigeonhole Principle

By circular reasoning we see that

When we make the necessary and sufficient assumptions,

It is beyond the scope of this course to prove that

Only idealogues and sycophants would debate whether

It is an unfortunately common misconception to doubt that

By petitio principii, we assert that

We may take for granted that

For legal reasons I am required to disclose that

It is elementary to show that

I don’t remember why, but you’ll have to trust me that

Following the logical steps, we might conclude

We are all but forced to see that

By the same logic,

I’m not even going to bother to prove that

By Kant’s Categorical imperative,

Everyone and their mother can see that

A child could tell you that

It baffles me that you haven’t already realized that

Notice then that

Just this once I will admit to you that

Using the proper mindset one sees that

Remember the basic laws of common sense:

There is a lovely little argument that shows that

Figure 2 (not shown here) makes it clear that

Alas, would that it were not true that

If I’m being honest with you,

According to the pointy-headed theorists sitting in their Ivory Towers in academia,

We will take as an axiom that

Accept for the moment that

These are your words, not mine, but

A little birdie told me that

I heard through the grapevine that

In the realm of constructive mathematics,

It is a theorem from classical analysis that

Life is too short to prove that

A consequence of IUT is that

As practitioners are generally aware,

It is commonly understood that

As the reader is no doubt cognizant,

As an exercise for the reader, show that

All the cool kids know that

It is not difficult to see that

Terry Tao told me in a personal email that

Behold,

Verify that

In particular,

Moreover,

Yea verily

By inspection,

A trivial but tedious calculation shows that

Suppose by way of contradiction that

By a known theorem,

Henceforth

Recall that

Wherefore said He unto them,

It is the will of the Gods that

It transpires that

We find

As must be obvious to the meanest intellect,

It pleases the symmetry of the world that

Accordingly,

If there be any justice in the world,

It is a matter of fact that

It can be shown that

Implicitly, then

Ipso facto

Which leads us to the conclusion that

Which is to say

That is,

The force of deductive logic then drives one to the conclusion that

Whereafter we find

Assuming the reader’s intellect approaches that of the writer, it should be obvious that

Ergo

With God as my witness,

As a great man once told me,

One would be hard-pressed to disprove that

Even an applied mathematician would concede that

One sees in a trice that

You can convince yourself that

Mama always told me

I know it, you know it, everybody knows that

Even the most incompetent T.A. could see,

This won't be on the test, but

Take it from me,

Axiomatically,

Naturally,

A cursory glance reveals that

As luck would have it,

Through the careful use of common sense,

By the standard argument,

I hope I don’t need to explain that

According to prophecy,

Only a fool would deny that

It is almost obvious that

By method of thinking,

Through sheer force of will,

Intuitively,

I’m sure I don’t need to tell you that

You of all people should realize that

The Math Gods demand that

The clever student will notice

An astute reader will have noticed that

It was once revealed to me in a dream that

Even my grandma knows that

Unless something is horribly wrong,

And now we have all we need to show that

If you use math, you can see that

It holds vacuously that

Now check this out:

Barring causality breakdown, clearly

We don't want to deprive the reader of the joy of discovering for themselves why

One of the Bernoullis probably showed that

Somebody once told me

By extrapolation,

Categorically,

If the reader is sufficiently alert, they will notice that

It’s hard not to prove that

The sophisticated reader will realize that

In this context,

It was Lebesque who first asked whether

As is tradition,

According to local folklore,

We hold these truths to be self-evident that

By simple induction,

In case you weren’t paying attention,

A poor student or a particularly clever dog will realize immediately that

Every student brought up in the American education system is told that

Most experts agree that

Sober readers see that

And would you look at that:

And lo!

By abstract nonsense,

I leave the proof to the suspicious reader that

When one stares at the equations they immediately rearrange themselves to show that

This behooves you to state that

Therefore

The heralds shall sing for generations hence that

If I’ve said it once I’ve said it a thousand times,

Our forefathers built this country on the proposition that

My father told me, and his father before that, and his before that, that

As sure as the sun will rise again tomorrow morning,

The burden of proof is on my opponents to disprove that

If you ask me,

I didn’t think I would have to spell this out, but

For all we know,

Promise me you won’t tell mom, but

It would be a disservice to human intelligence to deny that

Proof of the following has been intentially omitted:

here isn’t enough space in the footnote section to prove that

Someone of your status would understand that

It would stand to reason that

Ostensibly,

The hatred of 10,000 years ensures that

There isn’t enough space in the footnote section to prove that

Simple deduction from peano’s axioms shows

By a careful change of basis we see that

Using Conway’s notation we see that

The TL;DR is that

Certainly,

Surely

An early theorem of Gauss shows that

An English major could deduce that

And Jesus said to his Apostles,

This fact may follow obviously from a theorem, but it's not obvious which theorem you're using:

Word on the streets is that

Assuming an arbitrary alignment of planets, astrology tells us

The voices insist that

Someone whispered to me on the subway yesterday that

For surely all cases,

Indeed,

(To be continued)

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

mathermatical notation explained

symbol        meaning

=                   equals

=/=                not equals

<                   left

>                   right

!                    LOUD NUMBER

~                   worm

π                  stonehenge

√                   right answer

x                   wrong answer

⋯                  soon…

∮                   what Exacrly the fuck

∝                   fish

∞                   fish with 2 heads

↯                    lightning

:⇔                 he Scream