Quatrefoil Knot

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

me when Čech cohomology

i love math. i hate math. i can do it all day, everyday. i cannot solve a single question. it's my favorite subject. I would rather kms than open the book. it's beautiful and everything makes sense and it's the best. it's fucking useless and nothing is logical and it's the worst. it's the loml. it's my arch nemesis.

25 XII 2022

this chunk of the semester is finally over, sweet jesus I'm so exhausted. I'm getting the well-deserved rest and later catching up with all the things I put on my to-do list that I kinda learned but not really

the test I had last week went fine. frankly I expected more from it after solving more than 50 problems during my prep, but I scored 74%, which is objectively great and more than I predicted after submitting my solutions

here is my math plan for the break:

in algebraic methods I started falling behind a few weeks ago when I missed two lectures while being sick. they were about resolutions, derived functors and group homology and afterwards I wasn't really able to stay on top of my game like before. high time to get back on track. in commutative algebra I was doing ok, but there are some topics I neglected: finite and integral maps and Noether's normalization. for complex analysis everything is great until we introduced the order of growth and recently we've been doing some algebraic number theory, which btw is a huge disappointment. don't get me wrong, I understand the significance of Riemann's ζ, but the problems we did all consisted of subtle inequalities and a lot of technical details. I am doing mainly algebraic stuff to avoid these kind of things lol

when we were doing simplicial sets I stumbled upon some formulas for the simplicial set functor and its geometric realization and I thought it to be a nice exercise to probe them, so here it is:

I won't know if this proof actually works until I attend office hours to find out, but I am satisfied with the work I put into it

I already started making some notes on the derived functors

other than that I have this nice book that will help me prepare for writing my thesis, so I'd like to take a look at that too

as for the non-math plans, I am rewatching good doctor. my brain has this nice property that after a year has passed since finishing a show I no longer remember anything, the exponential distribution is relatable like that. this allows endless recycling of my favourite series, I just need to wait

I wish you all a pleasant break and I hope everyone is getting some rest like I am

(Points at the function I'm doing my thesis on) this is my son who has every disease

yes, this, but also among other stem courses in a typical school, math is taken the most seriously. idk about other countries, but in poland in highschool people study chemistry, biology, physics and geography only if they decide to take the advanced final exams in these subjects. with math, everyone has take the standard level exam, so it can't be ignored like other subjects

up to highschool everyone has to complete their share of stem courses, but with the subjects other than math, the teachers often allow students to pass by memorizing the theory or by making some extra projects to earn points. with math you can't do that. when someone struggles with physics, the teacher sometimes says "alright, next year you won't have to study physics, so just learn those formulas and definitions and write them down on a test and I will let you pass". in math this is not an option, the student will have to take n more years of math courses

also, math mainly requires learning new skills, not just new information. many people never memorize the "dry theory" in highschool, because you have access to a reference table of formulas during exams and your job is only to know where to use those formulas – no need to memorize anything. but this does not come naturally to everyone and I think a huge part of the problem is teaching people how to work on their problem solving skills. I tutored a few students who believed they were bad at math and their mindset was "I can solve this type of problem because I know how to substitute into this formula, but when the problem is slightly different I panic, because the teacher never showed us how to solve it", which can be fixed by practicing a wider variety of problems and practicing the awareness of one's thinking process

people do not understand that problem solving is a skill on its own and I blame schools for that, because what we are offered is the image of math being about re-using the same kind of thinking processes but with different numbers. heck, when I was in elementary school I thought this is what math is about and I hated it because it's so boring and repetitive. I can imagine, when someone believes that this is what math is supposed to be and then they see the "more real math", which is about creativity, they panic (and rightfully so, they've been lied to)

my unpopular opinion is that not everyone can be good at this, just like I will never be good at understanding literature – my brain just sucks at processing this kind of stuff and I have aphantasia which doesn't help at all. but what makes it even worse for those people is the belief that it should be about repeating the same patterns over and over, so when they see that it's something completely different, it must be very frustrating – the reality is inconsistent with their beliefs

I am sure it doesn't cover the entirety of the "oof I always hated math" phenomenon, but it certainly does explain some of it, especially in the context of the education system in my country

As I said in a previous post, I have deep sympathy for the frustration of people who are good at math when they see math so almost universally hated by children and adults

And again and again, they try to explain that math is very much within everyone's reach and can be fun and, at least in western countries, education was to blame, messing up this very doable and fun thing by teaching it wrong

But I still gotta wonder - why math? If it is really just education messing this up, why does it mess up so much with math, specifically? I'm sorry but I still cannot shake the sense that even if it's just bad teaching, math is especially vulnerable to bad teaching.

Or is it maybe just that math is the only truly exact science, so there is no margin of error, so unlike every other field where you can sortof weasel around and get away with teaching and retaining half-truths and oversimplifications and purely personal opinions, math is unforgiving with the vague and the incorrect?

I want to follow all of you!

moreover tiktok adhd content is not even good lol most of it is videos themed "things I didn't know were adhd" and they actually are personality traits and it's not helpful at all with anything

just saw a post complaining about how hard it is to find adhd resources for adults and one of the comments said “tiktok has a lot of adhd tips” as if telling someone with adhd to enter the algorithmic quicksand of perpetual dopamine hits isn’t the most insane thing you could suggest for someone with adhd