Hairy Ball Theorem, Stokes Theorem, Poincaré Duality, Nullstellensatz, Idk Too Much To Choose One

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

I need everyone to see this ABSOLUTE MASTERPIECE

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"

i'm conducting an experiment on how to study the theory effectively

there are i guess two main ways:

(1) read and take notes simultaneously

(2) read first, then take notes

so for the first one, there is the risk of going passive with the note-taking, writing down the symbols without focusing on their meaning. for the second one there is the risk of zoning out and just reading the symbols, again, losing their meaning

the problem seems to be that the processing of sheer symbols and processing their meanings might be disjoint and their natural tendency seems to be so

from my recent actions i noticed that (1) doesn't work for me as effectively as (2)

it might be that when i don't plan to write something down right away, i am more inclined to remember these things short-term as "i won't be able to check it later so remember it now in order to understand what comes next", and when i'm taking notes simultaneously it's "i have it written down anyway so i can take a peek anytime"

so now i'm testing the strategy of

read → try to understand the idea and memorize the elements → why all the elements are important → understand the construction in more detail and write it down

this is how i imagine my mind working:

it means that at first i start to remember the elements as points of its own but simultaneously my brain builds its idea on how they interact and then i notice the inner structure of how the elements are connected with each other in less obvious ways

this idea is cool to visualize how i imagine my thinking, because it shows how learning the topic reduces possible permutations and paths. i have this problem that when i start learning something new i see so many possibilities of what can happen to the elements that i can't discern between crucial and additional stuff. in order to use the knowledge i need to provide some structure

thus the main goal of optimized learning is to take the leap from "i memorized the elements" to "i understand their structure" as fast as possible

and so the strategy (2) might be more effective as it forces the memorization of the elements first and then it is easier to provide structure for them, where i would be defining order on something that's already in my mind. whereas (1) strikes at memorization and structuring simultaneously, it is too difficult for me to see at first in which direction the topic is going, i must know the next point

in a few days i will focus on how "the point" can be defined in this and how to characterize the connections

honestly tho this is some sorta pseudo graph theory and pseudo topology and i don't believe this could be as straightforward. otherwise nobody would ever post any study tips and we would have a field of study called "learning optimazation", this would be too big to go unnoticed. i wish it was so easy to just know how brain works and be able to build such an algorithm that would optimize the desired processes lmao

i wish i was a σ-field or something

side not is, i love this kind of thinking and i love to analyze how the thinking works, especially when it can me algorithmized or structured in some ways. the moment i see something is structured or algorithmic it becomes interesting to me

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.

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

omg this + bonus points if this is yet another "autistic genius" representation. don't even get me started on how harmful both of those things are for various reasons

Fuck the way media talks about “child prodigies” and “geniuses” especially in fields like music and mathematics.

Like they are gods whose level of understanding we could never reach.

How come we rarely hear about all the people who started young and then fizzled out? How come we never hear the stories of people who started late in life and made a huge difference.

Why do we only hear about their natural aptitude and not the hard work and misteps they took to get there.

For gods sake…

Terry is just a guy!

Artificial intelligence makes accurate sheep counting.

Me: I should write something

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

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

that's an interesting perspective

recently I've been thinking about it in an opposite way. it started during a conversation about brains, in particular how stupid and flawed they are, I realized that I enjoy math because it gives me a break from being human. there is no place for emotion and cognitive bias, only formal reasoning and proofs. it feels so safe and so distant from the day-to-day life filled with problems caused by the human nature, it feels so clean. it's a place for me to enjoy only the best qualities of my existence. it's an acceptable way to separate myself from everyone, and simultaneously stay connected

I love how different this is from what is described above, as if math offered a place for everyone to find something that they will like

Im trying to find a really long Tumblr post that talked about how sad it was that people are so happy to complain about how much they hated math and how math can be a way to connect with your fundamental humanity and...

Yeah, I've been studying a little bit of it on my own, ten years after I dropped out of college, I've been going back to seeing some basics of calculus, and I've been really feeling some of that.

There is this sense that math is this alien thing, separate from the true concerns of humanity. This external topic, strange and inhumane that only those few weirdos with a eccentric and atypical cast of mind, who are themselves separate by a few degrees from human nature, can grasp.

But it's not that, We, messy warm emotional dumb humans came up with it, we silly atavistic creatures dedicated so much time and effort to develop it and explore it, this silly, quirky, wet, ape-like species is the only living creature on this planet that concerns itself with doing math in any serious capacity. It didn't come from aliens or the gods or from dolphins, math came from humans and humans are the only ones that use them. There could be nothing more human, more fundamentally ours, more intrinsic to our nature than math.

And it's not just a tool! Is not just this thing to be celebrated because its useful in a purely base pragmatical, prosaic way. Is not this thing we have to dissapasionatly conceed credit to because I guess it does useful things like bridges and rockets and computers and taxes. Math is not just the civilizational equivalent of going to the dentist or eating your vegetables.

i hesitate to call it a philosophy or an art, it is a way of human thinking, it is a way of thinking like a human, of thinking in a way that only humans can think. its is one of our oldest and proudest traditions, it is a way to feel greater than onself, it is a way of growing. it is a song with a prosody all its own. There is such a profound sense of meaning and beauty and truth and purpose to be found in math, and the best of all is that it works, when it says something it means something, its telling you a thing that is meaningful, that represents something true, that couldnt be any other way, that has consequences and uses and can be relied upon, that it representes something which carries weight and its ours, its truly a part of our nature, of what we are.