high school to university grind montage, will need help during that tho.

[tame lynx]

your process is ill defined

[timid flume]

what would I need to well define it

[tame lynx]

i gotta prep for work, I'll just leave 2 thoughts

1. You are in way over your head right now. Curiosity is good, but you should really start from basics.
2. You must learn to let go of ideas that don't work.

[buoyant trail]

2 in particular is something I do like 5 times a day.

Whenever I try a problem, I'm almost always either completely stuck or completely wrong the first time I try it. Just being willing to move past that and not dig in your heels is a big step towards learning math.

[timid flume]

I see

[buoyant trail]

(for what it's worth I'm a phd student actively working on a research project with a renowned professor in my field, as my full time job - and again, I get stuck on things constantly, and I'm wrong about things constantly)

And @timid flume I seriously cannot recommend these books more highly.

[timid flume]

Alright

I'll check them out

but I'll be a bit sad for now

I spent 20 hours a day tryna prove this right for the past few days

without sleep almost

and no food except some

[buoyant trail]

You should sleep properly and eat food.

I don't do those things, but you should.

[tame lynx]

very capable mathematicians can spend months and years stuck on a problem

[timid flume]

hmmmmmm so people were worse than me? in a false illusion of some sort of?

but if so how do people actually make breakthroughs

[buoyant trail]

And look. I get it. Being wrong sucks, especially if you're new to it. Honestly, if you want to succeed in mathematics, you need to forget the distinction between being so frustrated that you want to bash your fucking skull in on a metal pipe, and having the best time of your goddamn life. But I want you to know, these feelings are perfectly normal.

[timid flume]

I see

well thanks

I still like how much I thought on this tho

it was fun

[buoyant trail]

Oh, yeah, thinking is always good.

I remember when I was around what I assume your age is, I independently derived the quadratic formula, and I got pretty close to the parametrization of solutions to pythagorean triples. I also did a lot of weird fucking non-rigourous crankery.

[timid flume]

do u know how I can complete the 4 years of high school's science and maths in just a month or few tho?

compared to this, I feel those are relatively easy

[buoyant trail]

Start by reading this book, cover-to-cover, and doing all the exercises contained within: https://ia600307.us.archive.org/24/items/basic-mathematics-serge-lang_20240418/Basic Mathematics - Serge Lang.pdf

[tame lynx]

don't ask for shortcuts please

there are none

[buoyant trail]

It will cover everything you need to learn before you can take on calculus.

[timid flume]

No not short cuts

like what do I do

till where

[timid flume]

I see

alright thanks

[buoyant trail]

It's not a shortcut, and it'll be a fuck ton of work. Especially near the end, when things will be more new for you. But, it will bring you about halfway through a highschool curriculum.

[timid flume]

alright thanks. I wasn't asking for a short cut of effort tho, I was asking for a short cut of time (which increases effort instead)

so that I be able to complete all of high school in a few months

[buoyant trail]

Afterwards, you can dive into Stewart's Calculus, https://archive.org/details/calculus-early-transcendentals-8th-edition-james-stewart/page/n3/mode/1up. Chapters 1-8, and 11, are standard for highschool, and are typically covered over the course of a year.

[timid flume]

okay thanks

a 1400 page book

I'm cooked

[buoyant trail]

Throw in Hammack's Book of Proof too (https://richardhammack.github.io/BookOfProof/), and you'll be ready to take on university level mathematics.

Don't set a deadline of 2 months. If you're nowhere close after a month, it'll demotivate you completely.

Instead, just work through everything I sent at your own pace.

[timid flume]

so I have to study and practice these 3,i can do maths till all of high school level?

[timid flume]

hmm alr

[timid flume]

alr

[buoyant trail]

So, what counts as "high school" varies significantly country to country. In almost every country, these would be sufficient. In many countries, even just the first book I sent (Lang's book) would be sufficient to be done with highschool. There are a very small handful of countries where you need to learn more things, but if you're in one of those we can deal with that when you get to it.

[timid flume]

I see

they cover all topics in math and not only calculus right?

but what if I wanna learn science

is there anything for that

[tame lynx]

start with basic math, that's enough to keep you occupied for a few years

[buoyant trail]

Lang covers all the prerequisites for calculus. Stewart is a calculus book. Hammack will take you further into the realm of mathematics, introducing you to set theory and rigourous proofwriting. They do not cover all topics in math.

[tame lynx]

later you can see to learning about applications

[timid flume]

oh..

[buoyant trail]

As for science - this will be controversial, but I would recommend putting it off until you've at least finished Lang. Something like Young and Freedman (https://www.andrew.cmu.edu/user/bbji/Desktop/University Physics with Modern Physics 15th Edition By Hugh D. Young_compressed.pdf) could then be read alongside Stewart, at least for physics.

[timid flume]

so I'm even more cooked even after studying 2500 pages worth of books

[timid flume]

I see

[buoyant trail]

If you want to become mathematically proficient, there are no shortcuts, or at least very few. I never promised that my suggestions would be easy, just that they would be sufficient to bring you up to the same level as an early uni student in mathematics.

[timid flume]

that link shows like a black blank page tho

[timid flume]

hmm

[buoyant trail]

It's a 1500 page book, give it time to load.

[timid flume]

it covers all topics in high school?

for science at least

I feel like I'm being tooo pecky right now

[buoyant trail]

Young & Freedman covers that (for physics, but not other sciences), plus some.

[buoyant trail]

(Again, depending on the specifics of what your country's curriculum is like. I don't know where you live, and you're young enough that you shouldn't tell random strangers on the internet where you live.)

[buoyant trail]

I don't know any standard intro chem or intro bio books, etc., depending on what other sciences you want. You'll need to ask people more knowledgable in those fields than I am.

[timid flume]

so not for chemistry and biology (in my country, u need chemistry in 11th and 12th and biology in 9th and 10th)

[timid flume]

hmm alright

I don't know if I'll go that far

this is gonna be soo hard

I might even have a higher possibility of getting into an accident and dying than finishing it within the time I want

[buoyant trail]

You asked what you need to get past the highschool level, and I told you. Now, I want you to download those pdfs, put them in a folder on your computer, and forget about everything except for Lang. Open up Lang, and start reading through it. The first chapter or two might be review for you, so it'll ease you into it - but even then, still try to do some exercises. And just focus on Lang.

I used to swim laps, and I would do a lot of laps back in the day, in a local olympic-size pool. One year, I tried to build up to 200 laps. I never focused on, "I've done 47 laps, only 153 to go!". I always just focused on the lap ahead of me, on what was directly in front of me. Same as when I walk or hike long distances - focus on putting one foot in front of the other, step by step, rather than how daunting the overall goal is.

[timid flume]

alright so this is lang (the second link)

[buoyant trail]

No. Those are intro proofs books.

[timid flume]

oh

which is lang

[buoyant trail]

Lang (book 1, read this first): https://ia600307.us.archive.org/24/items/basic-mathematics-serge-lang_20240418/Basic Mathematics - Serge Lang.pdf
Stewart: https://archive.org/details/calculus-early-transcendentals-8th-edition-james-stewart/page/n3/mode/1up
Young & Freedman: https://www.andrew.cmu.edu/user/bbji/Desktop/University Physics with Modern Physics 15th Edition By Hugh D. Young_compressed.pdf
Hammack: https://richardhammack.github.io/BookOfProof/

[timid flume]

Hmm I see

[buoyant trail]

Lang should absolutely be first. Stewart and Hammack you can do in any order. Young/Freedman can be done either after, or alongside, Stewart. But don't worry about any of that now - just focus on Lang.

[timid flume]

okay I read that, that, that and that and then the physics thing and I'm set for going to university

[buoyant trail]

Read those 4 books, and you are in a super fucking solid position to go into uni, at least for mathematics and physics.

[timid flume]

but u said they only focus on calculus tho?

[buoyant trail]

Stewart focuses on calculus.

Lang is all the pre-calculus highschool mathematics.

Young & Freedman is intro physics, much of which includes calculus, but that's not the focus per se.

[timid flume]

others will give me the full high school math experience, I see

what about stuff like trigonometry

Do I learn it in these

[buoyant trail]

Covered in Lang.

[timid flume]

alright

thanks for the guidance

I'm defo gonna over estimate myself and under estimate how hard these are

[buoyant trail]

Hubris is part of being young.

Don't worry about that.

Just - if your wax wings melt off, instead of falling to your death, take a rest and ask Daedalus to rebuild them even stronger.

[timid flume]

hmm

what part of maths u do for your phd tho?

[buoyant trail]

I focus on an area called topological dynamics.

[timid flume]

I see

[buoyant trail]

But my work is very similar to work in C* algebras, descriptive set theory, ergodic theory, and it uses a lot of combinatorics and graph theory right now.

You won't know what any of these are from the books I sent. The books I sent are prerequisites to all of them.

Don't worry about that for now, and instead just focus on Lang's book.

[timid flume]

if I manage to read those within 1 or 2 months and understand them completely

can u teach me one of your higher graph thingies so I can do something with those?

[buoyant trail]

I will make no promises, because you will overexert yourself and burn out if I do.

[timid flume]

hmmmm but by some miracle if I do do that

[buoyant trail]

Whenever you finish those books, we'll talk more, and I'll give you more books to read if you'd like. They won't be on my research, but they'll be books that hopefully will slowly build you up to understanding it.

[timid flume]

alright

I'm gonna start grinding

[buoyant trail]

But, I will make absolutely no promises, and in particular no time-dependent promises like that 1-2 months thing.

[timid flume]

thanks for all your help

yea alr I'll just see how efficiently I can do it

[buoyant trail]

I pinned the list of books for your convenience.

[timid flume]

thanks

high school to university grind montage, will need help during that tho.

[buoyant trail]

I honestly can't tell if I've been incredibly helpful, or if I'm just an evil bastard for putting you through this. Time will tell, I suppose.

[timid flume]

well, you gave it for what I asked in a good intention so you're helpful no matter the outcome.

[sweet smelt]

So how's the revolutionary math coming along

[timid flume]

utter flop (not yet but yes I'm near to it)

I can't really expect to make a groundbreaking thing which people have been studying for hundreds of years

without even knowing what calculus is

[timid flume]

which is why I've got new goals in life now instead of tryna prove this right

[sweet smelt]

Btw if you wanna learn how to write formal proofs you should read a discrete mathematics textbook

I'm pretty sure proof methods are covered in those

[thorny folio]

Hey @timid flume , I'm not sure you want it, but I'm gonna give you my opinion. If you really want to study math this young (do you?), I suggest you first get the basics. And I mean the very basics. If I were you, I'd probably look into the stuff that your school teaches to students older than you, and study that. After that is done (if it ever is), maybe start looking into university stuff (linear algebra, ...). Basically what I'm saying is, do things in the right order. You don't currently understand maths, and you have to accept it. But if you 're motivated, and study the topic correctly in the right order, it'll come for sure!

[buoyant trail]

Already covered that with my Lang suggestion.

[sweet smelt]

Aww man it's a lil late for me now...

Oh wow is that Lang book literally a pile of axioms

[buoyant trail]

I realize, I did not explain this. The convention when people talk about mathematics books is that the actual name of the book is rarely relevant; you refer to books typically by the surname of the author; then maybe the subject matter if the author has written multiple books. Lang is a weird one because he's written a lot, but broadly speaking that's the rule. Context often carries a lot of weight, too.

[sweet smelt]

You weren't kidding when you said learn math from the beginning

Mr Pear do you think a small child can read this book

[buoyant trail]

I would describe Lang's book as covering completely highschool level mathematics, but written in the manner of a university textbook.

[sweet smelt]

Ahhhh yea good good

I never liked the way high school math is taught

They drop a the formulae on you with no proof or explanation

Oh wow Euclidean algorithm

[buoyant trail]

Not without struggle or dedication. But ultimately, yes. I think it's easier with guidance, I think it's easier with help and support from an adult - but ultimately I think the book is gentle enough, and covers material simple enough, to be readable by a child.

[sweet smelt]

Is that taught in high school

Niceee

What's the smallest child you've seen in university

I reckon this book can get a 10 year old in with enough dedication

[buoyant trail]

When I was in undergrad, one of my professors would occasionally bring her toddler into class.

[sweet smelt]

That doesn't count

I want a child who's in uni for the lectures

Not because the professor had to do babysitting

[buoyant trail]

Then I suppose the newborns at the university hospital's maternity ward don't count either?

[sweet smelt]

Let's only count these children

[buoyant trail]

Probably 15 or 16, from those I've interacted with directly. But I'm also not in the habit of ID-ing random people.

[sweet smelt]

I see I see

[buoyant trail]

I know people as adults who have attended university classes when they were much younger, though.

[sweet smelt]

What's the average age of people who go into university where you live?

[buoyant trail]

I want to say that 18 is the typical age?

Somewhere vaguely between 17 and 19, let's say, seems to be standard for first-years here.

[sweet smelt]

Mmmm okok

Variance comes from the difference in educational backgrounds then

[buoyant trail]

Difference in educational backgrounds, students getting held back a year or taking a gap year before starting uni, plus the country I'm in is quite a popular one for international students to go to for university so there's a lot of people with very different backgrounds.

[sweet smelt]

Mmm alright alright

Cool

[buoyant trail]

Alongside the occasional kid who manages to graduate highschool a year early, but they're not super commonplace.

I've heard that "dual-enrollment" is common, where highschool students take uni classes. So far I've only really taught the remedial courses, though, where a highschool student would just take that in their school instead of here; and for some reason or another I never really ran into those sorts when I was in undergrad.

[timid flume]

they're nerds

actual nerds

I'm not

Because I don't even get top 5 in my class

I feel like memorizing is very different than being able to do something

because I might know a question which the topper might not

I might know how to solve a problem and think deeply

which is why I wanna learn the subject rather than giving some imo tests

[timid flume]

hey I got an offer if you would take it

if I manage to read it all within a month (till may 31st)

can u tell me about any topic within your field of expertise?

if I fail, I give you anything when I can

[sweet smelt]

I'm not an expert in any field

I'm a child like you

My level's a little higher yes but I'm no expert in anything

[timid flume]

o

my only hope for a benefit of learning all of this is pear then. (If universities don't take me in after learning because of age)

[tame lynx]

you don't have to

you do you

[sweet smelt]

Odds are you're not gonna get into uni simply by reading 4 books

They look at more than your math grade and also the Lang book doesn't seem to be sufficiently high level to get into uni

[timid flume]

but pear told me if I read those books I'll have enough knowledge of all of high school in maths n physics

[sweet smelt]

Ah yea all the books

Then probably yes

I was talking about just 1 book mbmb

[timid flume]

around 3000 pages

so like a 100 pages each day

I could try doing 10 pages an hour without efficiency breaking

[sweet smelt]

Why would you read that fast

[timid flume]

anything more than that, the efficiency and quality break

[sweet smelt]

The point is to absorb the knowledge

[timid flume]

yea

[sweet smelt]

Not to speed run the book

[timid flume]

10 pages an hour and 30 minutes for expressing that knowledge and understanding

should be enough to get the 3000 pages with efficiency

Most probably

15 hours a day tho

very hard

[sweet smelt]

Don't you have school

And also, 10 pages an hour is nuts so good luck

[timid flume]

yes I do which is why I have to finish it within end of may

[sweet smelt]

I barely get through 10 pages per day

Ah school holidays

[timid flume]

but a 30 minutes for reflecting that information and trying to comprehend it

[sweet smelt]

Just read it while you have classes

[timid flume]

should increase the Efficiency a bit

[sweet smelt]

Ok yea that's most likely not happening

[timid flume]

nah I don't like school

it's a burden

[sweet smelt]

That means 30 minutes for 10 pages

[thorny folio]

Take your time, it's necessary to absorb the knowledge properly

[timid flume]

no no

[sweet smelt]

Oh 1.5 hours for 10 pages

[timid flume]

30 minutes to absorb and reflect the knowledge

and 1 hour for 10 pages

[sweet smelt]

Good luck maintaining focus for more than 20 pages

After 3 hours straight of studying maths most people get tired

I strongly recommend that you do not push yourself on this

[timid flume]

well I have worked on for like 13 hours on developing this theory each day although it's near to an utter failure

so that would be theoretically possible

I just need to plan and stay focused well enough

[sweet smelt]

Well you can give it a shot

[timid flume]

if I suceed

[tame lynx]

the books are a starting point

[timid flume]

I don't have to go to school

[sweet smelt]

Most likely it won't work because it's too much

[thorny folio]

Have you ever read a math textbook @timid flume ?

[sweet smelt]

Oh you absolutely do

[timid flume]

uh maybe not really

[sweet smelt]

Wait do you think that reading these books will get you out of school and into university?

[tame lynx]

@timid flume please get some sleep, it's been almost 24h now, did you even take a break in between?

[timid flume]

why? I could just try to apply somewhere

[timid flume]

yeah

[timid flume]

for 3-4 hours yea

[sweet smelt]

Yeah no that's not happening

[tame lynx]

not gonna happen

[timid flume]

but but I'll have enough knowledge as a high school completed person

[sweet smelt]

No you will not

[timid flume]

so why won't they hire me in?

[timid flume]

why not

[sweet smelt]

This is only for maths

You are lacking science and language

And also that's not how it works

[timid flume]

alr but

if I do this

[tame lynx]

you have no formal training

[thorny folio]

You're pretty delusional

[timid flume]

I can convince my parents to let me have 2 months of break for science and languages too

[sweet smelt]

Depending on where you're from, the way we judge if you're ready for uni is exam

[tame lynx]

dude, focus on finishing school right now

[sweet smelt]

For me that's how it works

[timid flume]

I know but I don't really wanna live in school anymore

[tame lynx]

that's your one and only job

[timid flume]

but 8 hours a day of doing absolutely nothing

literature nothing

They're teaching me about rational numbers and irrational numbers right now

[tame lynx]

yes and we've all been through it at one point or another

[timid flume]

that's the only thing other than that a load of bullshit things

[sweet smelt]

Well the difficulty spikes around year 10

You said you're in year 9?

[tame lynx]

it is unfortunate, but that's what you'll do

[timid flume]

yea

[sweet smelt]

Also why would you say this

[thorny folio]

You have to go to school, it's not your choice. If you want to study more maths on the side, good for you. But school is priority, whether you like it or not

[sweet smelt]

As you said you're not top 5 in the class

There is much for you to learn

[timid flume]

but I don't think that matters really

I just have to understand the concept well enough

[sweet smelt]

But as pear said, you'll get the occasional oddball who goes to uni early

[timid flume]

to be able to explain it and work on it

[sweet smelt]

But you'd need to be smart

[timid flume]

I'm smart enough to think

[sweet smelt]

Well most people are

[tame lynx]

maybe it does, maybe it doesn't, if you can't focus on this, then you won't develop the discipline required to get a phd

[timid flume]

most people don't try to pursue what they like

[sweet smelt]

But being smart enough to think rationally and critically is a different thing

[timid flume]

hmm

what would happen most if I fail

I'd just go to school

[tame lynx]

assuming that you still are interested in getting a phd

[sweet smelt]

I wanna be nice but you are definitely delusional

[timid flume]

always.

[timid flume]

well

maybe

[sweet smelt]

What are you studying

Where*

[timid flume]

uh india

somewhere in that

[sweet smelt]

Oh snap what

India???

[timid flume]

yes

[sweet smelt]

Indian exams are some of the hardest in the world

[tame lynx]

I have little idea how education is organised in india

[timid flume]

nah they're just memory tests

[sweet smelt]

I'm pretty sure it's really competitive

[timid flume]

I don't think anybody remembers anything after the exam

[tame lynx]

makes sense, there are a lot of people there

[sweet smelt]

Tell that to the Indians complaining about the exam

[timid flume]

it is hard yes

but because of that

nobody understands the concept

[sweet smelt]

Are you doing GCE A levels or Indian national exam

[timid flume]

Cbse

[sweet smelt]

Well if you go out of your way to understand the concept you have an edge

[timid flume]

I don't want an edge, I want to leave high school

[tame lynx]

complaining that it is pointless or hard or whatever in discord is a waste of energy

you know what you have to do

get it done

[sweet smelt]

You're not gonna without that edge

[timid flume]

alright

no more talking without actions from now

cya guys

[sweet smelt]

I'm gonna be honest with you, your dream of leaving high school this early is unrealistic and impractical

[timid flume]

thanks for your concerns

[sweet smelt]

It's possible but not in the way you are going about it

[timid flume]

maybe but nobody hasn't really tried doing that tho

[sweet smelt]

Say what now

Is that a triple negative

[timid flume]

??

[sweet smelt]

Ok nvm

But let me tell you this, if you wanted to leave high school early, you are already too late to try that

[tame lynx]

if it's mandatory for citizens, then get it done

there's nothing more to it

[timid flume]

what if I try for something like princeton

or brown

[sweet smelt]

Like if you want to be on the level to skip high school and go straight to uni, you needed to read these books 5 years ago

[timid flume]

Or any foreign university

[tame lynx]

you can try

[timid flume]

where it doesn't require Indian degrees

[sweet smelt]

Yea absolutely not

[timid flume]

surely they'll consider it

hopefully

[sweet smelt]

They require other degrees which you don't have

[timid flume]

ah hmmmm

[sweet smelt]

.

Also they are expensive

I assume you are going to a public school?

[timid flume]

no private

but

[sweet smelt]

Oh wow ok

[timid flume]

what about scholarship

[tame lynx]

@timid flume there are many many people in the world, you are not special, follow the rules like everyone else, I'm sorry but that's how it is

[timid flume]

based on merit

[sweet smelt]

What merit

As you said you are not even top 5 in your class

And you are in a year 9 class

[timid flume]

hmmmm yea but even many people follow things which are wrong or just useless

[timid flume]

hmmm

I think it can't be done

but I don't wanna think like that

agh

[sweet smelt]

I see a lot of kids which hate school, but from my experience these are the kids who lack the skill to skip school

[tame lynx]

you just have a lot on your plate, your immediate focus should be getting through school

[sweet smelt]

If you are really really smart you will see the point of school and you will be able to skip into uni

[tame lynx]

learn what you can on the side if you want

[sweet smelt]

I am willing to help you learn math on the side

But I won't be helping you skip school

[tame lynx]

I get that you're young and impatient etc etc, that's fine

[sweet smelt]

Ngl when I first came here I thought you wanted to learn more about math and develop some theorem

[timid flume]

yea

but I can't develop enough with mathematical rigor

[sweet smelt]

But it seems like you just wanted to skip school lol

[sweet smelt]

Skipping school will not help with that

[timid flume]

hm but

my idea is

I could try to learn high school myself

[sweet smelt]

Going to school also won't help with that btw

[sweet smelt]

You could

But why would you

I did that to skip a couple years

[timid flume]

so I get a time advantage

[sweet smelt]

Why would you do that

[timid flume]

and complete 2 phds

with being young enough

[sweet smelt]

yea buddy as someone who did in fact skip a few grades, lemme just say that you are too late for that

[tame lynx]

there has been almost no progress in this discussion

[sweet smelt]

lol

[sweet smelt]

Why rush lol

[timid flume]

alr how about this

We don't talk anymore

[sweet smelt]

Just do 2 PhDs at 40 or smth

[timid flume]

until I do something

[timid flume]

too late id be doing jobs and stuff

[timid flume]

because it just seems like a way to satisfy my ego as of now

so I wanna DO something

Then I'll talk

Alr bye

[sweet smelt]

Just work as a professor

[tame lynx]

finish school, you still have time to grow up and change your opinions about things

[sweet smelt]

we could let him try his 15 hour/day strat

for 1 day

he'll give up in like a week or less

I know cuz I've tried similar things and given up wayyy sooner

We were all young and delusional once

[tame lynx]

15h a day on what? studying?

[sweet smelt]

Yes

[tame lynx]

yeah nah..skip

[sweet smelt]

What's the max time you've spent studying

[tame lynx]

4ish hours

[sweet smelt]

Hmm

Consistently?

For like a long period of time

Or just 1-off

[tame lynx]

back in undergrad when I tried to memorise things

[sweet smelt]

So consistently 4h/day?

[tame lynx]

are you crazy hell no

[sweet smelt]

Oh what

Fr?

[tame lynx]

like 1 week before exam

late at night

[sweet smelt]

Hmmm ok

[tame lynx]

you know how it goes

[sweet smelt]

I've done 6h/day for a month before

[tame lynx]

I switched it up in my master's studies, I did consistently like 90-120 min a day after lectures

[sweet smelt]

mmmm ok

[clever swallow]

Congratulations @timid flume, you have been awarded the <@&1257594408103317575> for being the most active user today.

[sweet smelt]

LMAOOOOOOOOOOOOOOOOOOOOOOOOO

[timid flume]

Huh

[sweet smelt]

AHAHAHHAAHAHAHHA

now das funny

[timid flume]

it's trolling me

😭

[tame lynx]

I set time limits for myself, I wanted to learn a given concept within a given time limit

[sweet smelt]

Interesting

[tame lynx]

so instead of memorising I focused on definitions and examples

and it worked

[sweet smelt]

Does that stick?

I try to learn given concepts period

No time limit

[tame lynx]

at the time I needed to focus on several subjects

[sweet smelt]

I feel like time limits get me through the exam, but in the long term I don't retain anything

Ah fair enough

uni do be like dat

[tame lynx]

most of my focus was on definitions and (counter)examples

reproducing some proof came..naturally somehow

[sweet smelt]

Interesting

Well that sounds like a lot of fun

[thorny folio]

Did you not have to learn the properties that come from the definitions?

[tame lynx]

as an example, I wasn't even reading a given proof I was working with the formulation of the theorem itself

draw pictures, see what the claim was, which assumptions could (if any) be weakened and some such things

[thorny folio]

They're not always obvious (to me)

[sweet smelt]

Interesting

You must be really smart if you can do that

[sweet smelt]

I need to look at this

[sweet smelt]

same

[tame lynx]

im a natural blonde..

[sweet smelt]

how does that relate to anything

[tame lynx]

i was moreso looking for ways to improve my learning, cuz I tried memorising for about 2 years.. it didn't work

[sweet smelt]

mmmmm ok

[tame lynx]

blondes are st00pid

[sweet smelt]

Ngl I'm a memoriser myself

But I memorise the technique from which the final solution was spawned

And not the final solution itself

[visual edge]

ghostpings

[buoyant trail]

This is nearly impossible. A page an hour is a more reasonable pace for mathematics.

[wary kindle]

i mean it kind of depends on the book, 10 pages an hour could actually be reasonable for a high school level book

even if it seems a little on the fast side

1 page per hour seems more like what you would expect in some graduate level maths book. which is obviously not whats happening here

[dark grail]

kid has motivation, damn

i need me some of that

[sweet smelt]

oh ok in that case I'm not total garbage at math

the book is just hard

whew

[timid flume]

an update guys

it's going well (if u don't consider my health, body, mental stability)

I'll most likely be able to read all 4 of the books before may 31st

[timid flume]

motivation is like a temporarily boost most of the time. I've had many 3am motivations where I wanted to change my life, so it isn't trustable and stable. but this time it's different, I'm feeling the same motivation since January. even after I sleep and wake up or watch a comedy show, it's not going at all

[urban dust]

@timid flume what math have you studied

forgive the ping

[urban valley]

beginning of this thread was hilarious

[buoyant trail]

I do consider those things. They are important. Do not ignore them.

Jesus fucking christ

Math is fun, but not at the expense of your health!

[wary kindle]

best part was usap saying he wants to become a dictator and invade other countries

i was so caught off guard?? like where did that even come from??

[urban valley]

personally i thought the best was when techie was just stating facts at the beginning it was funny asf

it was like a comedy sketch

[buoyant trail]

Wait, what?

[wary kindle]

@buoyant trail

[buoyant trail]

Huh.

[wary kindle]

hehe

[visual edge]

this thread is so weird lmao

[timid flume]

yo

I'm well on my way to completing the first book

probably will complete it by today or tomorrow afternoon

once I do that

there's like 3300 pages left for the others

since April hasn't ended yet

I might complete them all by doing 100 pages a day (10 pages an hour)

[urban dust]

I meant what type of math have you studied already disregarding the resources the others provided.

[urban dust]

also this sounds really ineffective

especially if you're exposing yourself to unfamiliar concepts continually

[thorny folio]

What book are you reading @timid flume ?

[timid flume]

the first book in this

then I go to the next

and next and next.

I hope I can complete those within the end of may

otherwise I'm cooked

[timid flume]

without the stuff in the books provided by pear, I've honestly studied nothing

just learned some things while I was tryna develop my theory

but uh really nothing else

[thorny folio]

I'm inclined to believe that you have not understood what youve read, because you're reading too fast

I'd love for you to prove me wrong though

Can you show me that the product of two odd numbers is odd? Please do not cheat it'd be obviously pointless

[urban valley]

yeah im going to have to agree with itsf, Math books arent meant to be read at 10 pages per hour espiecllay higher level books where it can takes hours to even fully comprehend what a page is trying to get you to think intuitevly

[buoyant trail]

This is definitely true. I would like to point out that Lang's Basic Math is not exactly a higher-level book, so I'd expect most pages to not take more than 15 minutes per page. But even then, and accounting for the fact that the first half of the book is review material, this still seems fast.

@timid flume How many exercises are you doing?

[buoyant trail]

If you're really just about done with the book, then you should have no difficulty sending here the solutions to the following randomly-selected problems from throughout. Yes, this is 14 problems (which can be a lot), but if you've been working as fast as you say you have it should be relatively quick for you to do.

(Which sections are these exercises from? I can't remember. But, the book has a table of contents, and chapters and sections have descriptive names, in case you need to look up definitions and theorems from the book. At worst, you can use the index.)

[buoyant trail]

Yeah, I just ran the numbers. The book is 500 pages; assume you skip the first half-ish, so let's say you're reading 250 pages at the claimed 10 pages per hour. That is still 25 hours. So we're looking at essentially three days of eight hours per day intensively studying. This is very fast, but it's technically possible to be where they say they are, if they're treating it the way they say they're treating it, and assuming an absolute best-case scenario. But, this still stretches credibility.

[thorny folio]

Plus, being 14 yo, I don't think he skipped the first half, nor do I think he should.

The book while being quite simple, seems pretty rigorous at first glance

And school isn't usually

At his age at least

[buoyant trail]

Compared to highschool texts, yes. But I still stand by the recommendation, honestly on that ground. If the kid's going to do math they need to get used to this kind of writing style, and need to learn how to learn from a book like this.

[timid flume]

yo

I woke up

[thorny folio]

Yes, I do think it's a good thing too

[buoyant trail]

Good morning. Please do as many of these problems as you can, to verify that you're actually learning from the book instead of just lightning-fast flipping pages and looking at words: #1364337781102612702 message

[timid flume]

hmm it is taking me longer for some pages but I'm only going to the next page when I understand something

[thorny folio]

Also I think trying to solve one exercise without checking the book at all may be a good idea

Might give you some kind of reality check, see if you have read the book properly

[timid flume]

okay

I don't think I've come far enough for the first page

and the second page

didn't learn graphs

I got a doubt

in the third page, 2nd question

[buoyant trail]

How far through the book are you?

[timid flume]

till like page 70

[buoyant trail]

This is far more reasonable than what I thought you meant when you said this (#1364337781102612702 message).

So you're almost done with chapter 3, right?

[timid flume]

well, when I said that, I read 50 pages in some hours

but problem came when they asked me to show proofs

how do I show proof of something if they won't accept examples

[timid flume]

chapter 3?

[thorny folio]

Can you try to show, without cheating, that if a is even and b is a any positive integer, then ab is even?

[timid flume]

yeah

because

[buoyant trail]

There's an interlude after chapter 4 that introduces it briefly.

[timid flume]

if b is multiplied to a

then the product is divisible by a

because the number of times it's multiplied is b

the odd factor doesn't come in the product

because it's being multiplied to a

and if it's divisible by a

and a assuming positive number

then it's even

[buoyant trail]

I feel like you're talking a bit in circles.

Write out the full proof; send it as one message.

[timid flume]

ya I don't know the correct way of making proofs yet

[buoyant trail]

Alright.

Then let's break it down.

[timid flume]

okay thanks

[buoyant trail]

What does even mean?

[timid flume]

hmm

hmm

[buoyant trail]

If I say, "a is even", what does that mean about a?

[timid flume]

that

a is divisible by 2?

[buoyant trail]

What does this mean?

[timid flume]

hmmmmmmmmm

wait what's even

uh

any numbers that end with

2,4,6,8,0

shit... I'm wrong

can u explain me?

[buoyant trail]

This is on the right track. Thinking about the last digit, I think, will just complicate and confuse matters.

[timid flume]

hmm i see

so if a is divisible by 2 (2 specifically because it's the smallest even number)

Than any number becomes even

because 2 reaches every number when multiplied

[thorny folio]

suppose a number a is even. What happens if you divide it by two? What can you say of a/2

[timid flume]

then

a/2 is exactly half of the number

which is also even

and

[buoyant trail]

Nope. Consider 6/2=3 is not even.

[timid flume]

oh

I see

[thorny folio]

try something else

[timid flume]

if the end is a positive integer

than it's an even number?

[buoyant trail]

Right!

So, what does "a is even" mean?

[timid flume]

if a is even, then a/2 should be a positive integer

?

[thorny folio]

perfect

[timid flume]

OMG REALLY

wait uh

yea

I think it's right

[buoyant trail]

Almost exactly correct. I would throw out the positive requirement; I see no reason why -2 and -4 can't be even as well.

[timid flume]

hmm

but

is something like 3.4

also even?

[thorny folio]

From that, can you make up a defintion of an even number?

[buoyant trail]

It's not even an integer.

[thorny folio]

no

[timid flume]

but why do integers only have to be even?

[buoyant trail]

"Even" and "odd" are properties of integers.

[timid flume]

oh

I see

[timid flume]

hmm

[buoyant trail]

(Well, I suppose they're well-defined in the context of other number rings, but let's not overcomplicate things needlessly for now.)

[thorny folio]

I'll summarize what you have said: If a number is even, then it's half is an integer

[timid flume]

any even number, if results in an integer when divided by 2, is considered even

can this be the definition?

[thorny folio]

not exactly

[buoyant trail]

This is a workable definition, and I believe equivalent to the classical definition. Let's try and make a definition that works with multiplication, though.

[timid flume]

hmm any number that can be reached when multiplied with 2

maybe is considered even?

[buoyant trail]

Right on!

[timid flume]

I see

[buoyant trail]

Do you think you can write this more formally? `a number a is even if...'

[thorny folio]

I'll give you the beginnng of a defintion: An integer a is even if there exist an integer k such that ...

[buoyant trail]

Our brains are on the same wavelength.

[timid flume]

an integer x is even if there exists an integer y such that x can be reached when multiplied by 2, y number of times.

how about this?

[buoyant trail]

Seems a bit wordy, but this is absolutely the right idea.

[timid flume]

is there a formal way to give proofs tho? like the concept of it

[thorny folio]

use this

[timid flume]

for example when questions like " Prove that.... "

[buoyant trail]

There absolutely is. But formal proofs require formal definitions.

[timid flume]

I see

[buoyant trail]

So, let's rephrase this slightly simpler. `an integer x is even if there exists an integer y such that x=2y', I think, might be slightly less wordy, and gives you an immediate algebraic tool that you can use as you will.

[timid flume]

so I have to find out the definition related to the question's thingy

and then apply it to the question's thingy

[timid flume]

I see

[buoyant trail]

Or, more formally, $$x\in2\mathbb{Z}\iff\exists y\in\mathbb{Z}\text{ such that }x=2y.$$

[ionic mortar]

Pear Category Theorem

[thorny folio]

It's almost always that way, to prove something, you go back to the definitions

[buoyant trail]

(Though, this one might perhaps be slightly too formal)

[timid flume]

hmm i see

[thorny folio]

Can you maybe define an odd number now?

that'd be a good exercise i think

[timid flume]

yeah uh lemme try thinking what they are

[thorny folio]

take your time

[timid flume]

an integer x is odd if there doesn't exist an integer y such that x=2y

is it correct?

[thorny folio]

That is not wrong, but i don't like "there doesn't exist".

[timid flume]

how do I say it then

uhhh

[buoyant trail]

It's easier to do things in math if you can say "I have this tool that I can use" than if you say "I can't do this".

[timid flume]

hmmmm

[timid flume]

I see

not equals to sign?

[thorny folio]

The advantage of the defintion of even, as pear said, is that you have a tool right away: a is even: a = 2k for some k

[timid flume]

I see

[thorny folio]

You have the same with the definition of odd

try to follow the same phrasing as the even definition, changing the maths slighlty

[timid flume]

alr

an integer x is odd if there exists an integer y such that x = 2y does not result in an integer?

[buoyant trail]

Not quite.

The definition of even is: x is even if there exists y such that x=2y.
The definition of odd is: x is odd if there exists y such that...

[timid flume]

an integer x is odd if there exists y such that x = 2y ≠ to an integer

how do I do the

E Greek letter striked out

[thorny folio]

$\neq$

[ionic mortar]

ltsf

[thorny folio]

but that doesnt matter

[timid flume]

okay is it wrong?

[buoyant trail]

This is not correct. By assumption, x is an integer.

[timid flume]

I see

but 2y is not an integer tho

[buoyant trail]

From here, I'll give you a tiny bit more.

[timid flume]

I mean y*

[buoyant trail]

The definition of even is: x is even if there exists y such that x=2y.
The definition of odd is: x is odd if there exists y such that x=

[thorny folio]

Try with examples, just to get the intuition

[timid flume]

hmm

3

[thorny folio]

5 = ...

[timid flume]

okay 5

= 2.5*2

[thorny folio]

only use integers

[timid flume]

2*2+1

[buoyant trail]

Right, but let's forget about anything that's not an integer. For now, we don't know about decimals or fractions, just the counting numbers.

[buoyant trail]

Exactly!

[thorny folio]

right

perfect

[buoyant trail]

And 7?

[timid flume]

so

3*3+1

[buoyant trail]

That's 10

[thorny folio]

either try with another, or generalize and see what happens

[timid flume]

2*3+1

[thorny folio]

what pattern do you see?

[buoyant trail]

Right on!

[timid flume]

wait I think I have this

alr one sec

X is odd if there exists y such that x= y*z+1 where y is any even number.

is it correct?

[thorny folio]

it's not

[timid flume]

hmmmmmmmmmmmmmm

[thorny folio]

try a couple more examples on a sheet i suggest

and you will be able to see a better pattern

which looks very much like the even def

[buoyant trail]

So far, you have:
5=2*2+1
7=2*3+1

What about the following?
9=
11=
13=
15=

[timid flume]

24+1
25+1
2*6+1
...

uh

so 2 is the same

and the right side changes

[thorny folio]

yup

[timid flume]

one by one

[buoyant trail]

Yeah

[thorny folio]

so,...

[buoyant trail]

So returning here once again, how can we define odd?

[timid flume]

x is odd if there exists y such that x = 2*y+1

[buoyant trail]

Brilliant!

[thorny folio]

perfect! (note that x and y are integers)

[timid flume]

ohhhhh

[buoyant trail]

Do you think now you want to try and tackle ltsf's problem?

[timid flume]

what is the problem

[buoyant trail]

Let $a$ be an even number, and $b$ any integer. Prove that $ab$ is an even number.

[ionic mortar]

Pear Category Theorem

[timid flume]

ab is an even number if there exists an integer x where ab = 2x

but ab is an even number

because

[buoyant trail]

Well, what do we know?

[timid flume]

a is even

[thorny folio]

what does it mean?

[timid flume]

so b of a must be even

[thorny folio]

what does it mean that a is even?

[timid flume]

then ab is even

[thorny folio]

yes, that is what you are trying to show

but we have defined "even"

[timid flume]

yea x = 2y

so

if a is even

then there exists an integer y where a= 2y

[thorny folio]

yes good

[timid flume]

how do I relate it with ab

[thorny folio]

well, you have something about a

i'll let you try to figure out the rest for a bit

[timid flume]

if a is even, a × x is even where x = any integer

because there exists an integer y

Where a × x = 2y

[thorny folio]

that is what you are trying to show

[timid flume]

and we have a as even

so a times x = 2z times x

[thorny folio]

i'll give you a hint: you know that a = 2y. And you want to say something of a*b.

go from there: a*b = ....

[timid flume]

definition of an odd is y*x+1 where y is even

so

2y aka a is even

[buoyant trail]

Not the definition of odd.

[timid flume]

but it's not a*b+1

so if it's not odd

it's even

[buoyant trail]

This was the definition of odd.

[buoyant trail]

And we don't know this.

[timid flume]

but they said it's a*b

[buoyant trail]

You're assuming two facts that we don't know yet:

• Every integer is either even or odd.
• There are no integers that are both even and odd.

We don't need to use either of these facts.

[timid flume]

hmm

2y times b

[thorny folio]

right path!

[timid flume]

2y times b can be represented as 2by

Or can it

[buoyant trail]

Yeah.

[thorny folio]

it's the same thing

[timid flume]

okay it can

so

[thorny folio]

wait wait

[buoyant trail]

There's parenthesis things to worry about, but multiplication is associative, so we don't need to worry about any of that.

[thorny folio]

you know what "ab" means right?

for random number ab

[timid flume]

yea

a*b

[thorny folio]

alright

[timid flume]

if a is 4 and b is 3

then y is 2

then 2y*3

is 32y

32y

[thorny folio]

go back there, idk where you are going

[timid flume]

ok 2y times b

hmmmmmm

the definition of an even

is y exists where x is 2 y

so

2Y times b

by 2

exists

because 2y is 2y where y exists and is even

and so 2 y times b is

I'm cooked

so 2y times b

=

2x

where x is an integer

BUT... how do I prove

that it's confirmed

hmmmmmmmmmm

Uh

if 2y is even

then 2y times b is even

[buoyant trail]

I think you're once again going in circles.

[timid flume]

BUT how

[buoyant trail]

Let's remember where we're starting and where we want to end.

[timid flume]

okay

[buoyant trail]

We are starting with $a=2x$ for some integer $x$. We want to end with $ab=2y$ for some integer $y$.

[ionic mortar]

Pear Category Theorem

[buoyant trail]

(This is just the definition of even, applied to both a and to ab)

[timid flume]

alright

we started there

and

uh

uhh

so

[buoyant trail]

So, if a=2x, what does ab=?

[timid flume]

2xb

[buoyant trail]

Right

And what can we say about xb?

[timid flume]

an even number x multiplied by any integer b

is an even number

[buoyant trail]

We don't need x to be even.

Remember, a=2x means that a is even, not that x is even.

[timid flume]

oh

[buoyant trail]

But two integers multiplied together, is always another integer, right?

[timid flume]

yea

it is

[buoyant trail]

So, what about xb?

[timid flume]

xb is Z

OMG

XB IS Z

SO 2Z

[buoyant trail]

Right on!

[timid flume]

Ab= 2Z

[buoyant trail]

So do you think you can write up the proof formally?

[timid flume]

yeah

[thorny folio]

lmao, well done

[timid flume]

When a is an even integer, and b is any integer. ab = an even integer because,
a=2y
2yb = 2(yb)
yb= z where z is an integer (because y and b are integers)
= 2z
following the definition of even numbers, if x = 2y then it is even,
We get ab = 2z and hence, it is even

something like this?

[buoyant trail]

Yeah.

[timid flume]

ah that took a lot of pain in my life and it's just a small thing, I'm cooked if I don't learn things fast

[thorny folio]

Here is a slightly clearer version:

If $a,b \in \mathbb{Z}$, and $a$ is even, then $ab$ is even. Proof: Since $a$ is even, there exists $k \in \mathbb{Z}$ such that $a = 2k$. Therefore, $ab = 2kb$. Since $kb$ is an integer, we deduce that $2kb$ is even.

[ionic mortar]

ltsf

[buoyant trail]

Yeah. This is more in the standard math-writing style; but I think that will just come naturally with practice reading and writing mathematics.

[thorny folio]

It's a good thing you understand that there is a lot work to be done. However, you have time

[timid flume]

hm

[thorny folio]

I thought it couldn't do any harm to read a proper proof

[timid flume]

welll

can u give me any other question

I'll try to do that, similar to this where I have to prove something

[thorny folio]

Sure

[timid flume]

alr thanks

[thorny folio]

A little harder, but very similar: show that the product of two odd numbers is odd

[timid flume]

definition of odd is 2*x+1

so

[thorny folio]

no

[timid flume]

huh

[thorny folio]

Be more precise

[buoyant trail]

In addition to the next one that ltsf gave, there are two ideas that you wanted to use but can't. Also try proving that:

• Every integer is either even or odd.
• No integer is both even and odd.
  And the three addition identities:
• Even + even is even
• Odd + odd is odd
• Even + odd is odd.

[timid flume]

odd + odd is even though

[timid flume]

an integer k is odd when k = 2*x+1

[buoyant trail]

Really? Prove it, then.

[thorny folio]

Where there exists an integer X such that

[buoyant trail]

Anyway; I've got other stuff to do today. Good luck!

[timid flume]

because k+x where k = 2y+1 and x = 2z+1 where y and z are even integers
gives 4*z+y+2 where everything is even and end is even

[timid flume]

okay thanks

[timid flume]

alr So the product of two odd numbers x and y where x = 2k+1 And y = 2m+1
so xy = (22)(km)+(1+1)

so

4*km+2

where k and m are even

results in evenness

[clever violet]

so usap

what are you working on now?

[timid flume]

uh I'm working on these

[timid flume]

^

[buoyant trail]

We helped him define even and odd numbers; now he's proving basic things about them.

[clever violet]

okay

so he is reviewing or is he looking for patterns

[clever violet]

did you take algebra in 8th yet?

[timid flume]

yea

[timid flume]

both

veritasium just uploaded a new video

ima go check it out, brb

[clever violet]

i'll just have the skyscraper vid on the small screen thing

but aren't these applied maths books?

[timid flume]

I think so

but they teach me everything in high school

[clever violet]

not really

[timid flume]

of maths

[clever violet]

I think I've read all but the 3rd one

[timid flume]

uh

[thorny folio]

Your multiplication is wrong

[timid flume]

yea

noticed it

(2k+1) (2m+1)

[clever violet]

4km+2k+2m+1

[thorny folio]

Have you learnt the distributive property

[clever violet]

4km+2(k+m)+1

[thorny folio]

Giving away the answer doesn't help

[clever violet]

sorry

[timid flume]

well yes

[thorny folio]

I'll say this last thing then I'll go: you just need to apply it properly, then the answer should appear nicely

[clever violet]

from this, what does this tell you about the product of two odds?

[timid flume]

alr

[timid flume]

it tells me that, uh

[clever violet]

remember any integer multiplied by 2 is even, and any even number + an odd is odd.

4km is even

2(k+m) is even

[timid flume]

Yea but then

the result is odd

[clever violet]

sum of two evens is even

even +1 (odd) is odd

[timid flume]

yeah

but it's odd

shouldn't it be even

[clever violet]

no

[timid flume]

odd times odd

wait

3*3

[clever violet]

=9

[timid flume]

5*5

[clever violet]

9 is odd

[timid flume]

ahhhhhh

[clever violet]

25

25 is odd

[timid flume]

I had the answer all along

I was thinking it's wrong

sheesh

thanks

[clever violet]

sorry for giving you the answer

[timid flume]

no no it's fine

[clever violet]

is there any part of those books you need help with?

[timid flume]

hmm I needed help with giving proofs

but I think I'm familiar with it now

[clever violet]

what kind

[timid flume]

any kind, just giving proofs

[clever violet]

any specific one!

?

[timid flume]

uhhh

like not anything in general lol

[clever violet]

like induction?

[timid flume]

the format of giving proofs

[clever violet]

contradiction?

ohh

proofs are mostly grammar tbh

[timid flume]

hm

I'll go over more pages

and see if I don't understand something

alr then cya for now

ty all

[clever violet]

okay

[thorny folio]

You're not. It's not big deal, but there is a long way to go

[inner pulsar]

Ik you didn’t ask me, but let the 2 odd numbers be 2n+1 and 2m+1, where n,m∈W. 2n+1+2m+1=2(n+m)+2. Let n+m=k, where k∈W (Since 2 whole numbers always add up to a whole number). So, 2n+1+2m+1=2k+2, where k∈W, which is divisible by 2.

[drifting wasp]

What even is this thread

I thought this was some old thread popping back but no this is recent

[buoyant trail]

Right now; it's me yelling at usap to learn math.

[drifting wasp]

Cinema

Bro he's a child, be a bit nicer

Actually way more than a bit

[visual edge]

The best way to learn something is to explain it to urself like you're a 5 yr old @timid flume

[timid flume]

hmm

[visual edge]

It's basically the feynman technique

[timid flume]

well no one who I see explained those higher topics like that

so I assume it's not really valid for higher topics

starting from senior high school

[visual edge]

It is a valid option

[timid flume]

hm

I'll try it

ty

[buoyant trail]

See, I always thought the feynman technique was to sexually harass your female students, then take the teenage kid of one of your friends who looks up to you to the strip club so that he thinks you're cool.

[timid flume]

wha- Lol

[visual edge]

Don't worry about his autobiography

Pretty sure he's dead so who cares

[buoyant trail]

It's not even really his autobiography. It was written by ralph leighton (robert leighton's son)

[visual edge]

You know you can separate the work from the creator right, just because something is bad about it doesn't mean you need to ignore everything related to a person

I didn't know anything about him except that learning technique until you bought it up for example

[buoyant trail]

Alright. If you want a legitimate critique of the method rather than just potshots at Feynman; here it goes - most concepts worth learning are, in fact, too difficult to explain to a five year old. I cannot explain my research to a five year old, yet I understand that quite well. Five year olds typically lack the context to learn the context for my work. Particularly within mathematics, your average five year old probably doesn't even know the y=mx+c formulation of a line, in plane geometry.

"Explain it so that a five year old would understand it" may be legitimate for some things. It is nonsensical in mathematics.

[visual edge]

Nah I knew that as a kid

From this yugioh card

Slightly older and worder version

[buoyant trail]

Then you were quite a bit smarter than the average five year old. A cursory google search suggests that five year olds are generally just starting out kindergarten; this is what might be appropriate to expect from them. My comment about lines was still a grotesque overestimation.

[visual edge]

Weird

I did the taylor series and theory of relativity when I was around 8

[buoyant trail]

Bullshit.

There is no way that you learned relativity simultaneously with calculus.

[visual edge]

its pretty easy

all my mistakes just occur because its just mental maths

[buoyant trail]

I'm pretty sure you need to know manifolds to do relativity.

[visual edge]

yeah

[buoyant trail]

So you learned about manifolds before you learned about taylor series?

[visual edge]

earlier than manifolds

[buoyant trail]

Still, by the time you were 8?

[visual edge]

No, I was 9