serious-discussion

[eager minnow]

my condolences, jesus

[cinder zephyr]

I've never used Magma

[glass peak]

It’s nice when it works and I know what I’m doing, any time I need to turn to the docs a little part of me dies

[cinder zephyr]

any fellow GAP haters in chat ⁉️

atrocious language

[vivid halo]

GAP is okay

kinda sucks but is good for some things

[static loom]

Yeah sage is alright don't get me wrong but the docs do leave something to be desired sometimes lol

[glass peak]

I’ve never used GAP but it means not doing group theory so I’m sure it’s worth the pain

[vivid halo]

some of the stuff that is implemented in sage is magic lmao

[cinder zephyr]

I should get off my ass and try to improve Sage docs

just don't have the time to sit down and do it

I could be lazy, file a GH issue, and let someone else figure it out

[vivid halo]

hello sage here is a modular form, please tell me all the data about the infinite dimensional representation of GL_2(Q_p) that is attached to this

insanely useful

not even the lmfdb has all this stuff in its data

[glass peak]

I should also learn to use Macauley2 properly at some point

[vivid halo]

oh yeah macaulay2 is very good

[cinder zephyr]

macaulay2 is cool

[static loom]

yeah same

[vivid halo]

I find it kind of annoying to use but that is skill issue

[static loom]

I feel like I might have something to gain by playing with maxima a bit too but maybe not lol

[glass peak]

Yeah ive done some very basic stuff in it but from what my advisors said it seems to be basically magic when you know what you’re doing

[cinder zephyr]

never heard of Maxima

[glass peak]

At least for the things it can do

[cinder zephyr]

my (potential) advisor is of the mind that Sage is overrated and people should be using Julia (at least for algebraic combinatorics)

and he says he's had great success with this thought process

because he says Sage is way too slow

IMO Sage being slow to execute is worth the trade off for Sage being easy to write

[static loom]

agreed

[sharp mulch]

Cringe!

[vivid halo]

find a better advisor

[cinder zephyr]

no he's cool

the only other two people I'd work with have other issues

[static loom]

My advisor washes his hands in the toilet and is very cool

[vivid halo]

yeah but can sage or mathematica do this

[static loom]

why would I want to write infinity! and have it do anything lol

[cinder zephyr]

winning the biggest number competition

[eager minnow]

∞! + 1

boom you lose

[static loom]

uninstalling julia for being a googolology crank

[unborn meteor]

i used to be a googologist

i still am to some level

[cinder zephyr]

What is googolology?

[unborn meteor]

study of extremely large finite numbers

a lot of cranks lol

[cinder zephyr]

I see

[glass peak]

I don’t really get that stuff, there’s some numberphile videos on it, and I just don’t see the appeal

Tree(3) is big?! Ok, try Tree(4)

[unborn meteor]

imo the largest finite well defined well known number is loader's number

[glass peak]

I’m guessing there’s more to it that I don’t understand but like, just add one bro

[unborn meteor]

that's against the rules

[unborn meteor]

it's defined as the output of a c program

[cinder zephyr]

ok then take the c program and add a + 1 to the return statement

[glass peak]

Express the number as a string, append 0, qed

[vivid halo]

you mean for Simpletons

[cinder zephyr]

unironically may go give that a read

[narrow carbon]

wow (btw sorry for random ping)
Can i get these quiz online? (like if your prof has uploaded on online web page)

[cinder zephyr]

no

she has not uploaded them sorry

and I don't have access to this course anymore I just have this one saved from complaining about it before

[narrow carbon]

oh, its okay
Thank you for informing me this

[terse fiber]

That is just wrong lol

[sharp mulch]

https://math.stackexchange.com/a/506832

You can tell what field of math you're in by what 2pi equals

0, 1, (infinity!)^2

etc...

[vivid halo]

nope! this is correct actually

[brave flare]

because of this, i would rather call googology as the study of fast growing functions. of course Tree(4) is greater than Tree(3), but its still the same function, so its nothing crazy. thats why in googology, things are measured by where they fall into certain "hierarchies" of fast-growingness. think of O-notation but complexer

[glass peak]

I guess that’s somewhat interesting

[somber sandal]

https://www.youtube.com/watch?v=shFUDPqVmTg
what do y'all think

[neat lintel]

Hello

[floral grotto]

@somber cliff the people is wild hahahah

0 knowledge

[somber cliff]

yeah lowk i don't wanna talk to them

i don't want a stupid argument about elon

[floral grotto]

literaly

[somber cliff]

i wanted to talk ab my theories

[floral grotto]

lets talk about your theories

[somber cliff]

alr so

[floral grotto]

i have a good one too

[somber cliff]

lemme hear it

[floral grotto]

like

what happens after death, was all of this a simulation? or really how they told us

[somber cliff]

well

that would branch outside of science

[floral grotto]

i think this is a simulation, becuase we will probably create a universe like ours

[somber cliff]

into the world of spirituality and faith

[floral grotto]

nooo

[somber cliff]

actually

i have a lot to say about that

science is the study of the physical world

for all we know, our entire physical realm could be simulated

we don't know

as soon as you step outside that physical realm, it's not scientific

[floral grotto]

lets say in 10.000 years we have very very good technology. We will try to create a world like the one we live, and we will add live creatures to live in that world and see how they act

[somber cliff]

and that's where religion could come into play

oh

[floral grotto]

we dont know thtas the thing

[somber cliff]

it could be a cycle

[floral grotto]

exactly

[somber cliff]

we could be in the simulation of someone from 10,000 years in the future

[floral grotto]

exactly!!!

[somber cliff]

ASSUMING humanity is around by then

[floral grotto]

i think that is the most accurate theory of our existance

[somber cliff]

this ties into my 2nd theory actually

if AGI takes over, then they try to simulate what life was like before robots

[floral grotto]

and what we call "god" are the superiors controllling us

[floral grotto]

hmmm

[somber cliff]

wow that's really interesting

[floral grotto]

live has a lot of mysteries!!!!!!

i want to find them all!!!!!

[somber cliff]

Artificial godly intelligence

AGI

[floral grotto]

HOLY

nahh

hahahah

[somber cliff]

WAIT

[floral grotto]

we are going to 5th dimension!!!!!!

[somber cliff]

well

do you believe in god?

[floral grotto]

not the god we know as god

like something else

not a perosn

like idk

something

but it exist

yes

[somber cliff]

ok how about this

is god dead or alive?

[floral grotto]

alive

[somber cliff]

really?

[floral grotto]

but not the god like a person

[somber cliff]

asigning a life value to god is like trying to divide by 0

or have a mutable string in python

it just won't work

[somber cliff]

yeah ik

[floral grotto]

hmmm

[somber cliff]

you believe God isn't a supernatural being

[floral grotto]

bro every time i talk with someone about this things i get super super pensative

[somber cliff]

yeah

well

that's how i feel right now

[floral grotto]

for expamle

another thing

the pyramids

[somber cliff]

religion can be disproved very easily, god's existence can't

[floral grotto]

how are the coordinates of the pyramides the same numbers as the speeed of light

[somber cliff]

ok that's a coincidence

[floral grotto]

coincidence 9 numbers?

hmm

[somber cliff]

yeah

[floral grotto]

it has a PC chip form if you look with a drone

[somber cliff]

huh

[floral grotto]

like,

yes

i cant send pics here sh8t

[somber cliff]

not everyone believes in m/s (AMERICANS)

[floral grotto]

hahaha

where you form

[somber cliff]

and it's just one coordinate point

[somber cliff]

america lmfao

[floral grotto]

damn

im spanish

spain

[regal dome]

Interesting conversation btw

[floral grotto]

what do you tihnk about it

[woven rapids]

the egyptians didnt know what meters were

btw

[neat lintel]

so funny story

apparently that is a longitude line

[somber cliff]

ohh cool

[neat lintel]

not co ordinates

[somber cliff]

yeah i found out

[neat lintel]

they were ahead of their time

[somber cliff]

29.9° N right

[somber cliff]

but they were also VERY backwards too

incest

[floral grotto]

the speed of light is 299,792,458 m/s

and teh coordinates are

[neat lintel]

I do not know

[neat lintel]

standard

[floral grotto]

29,9792458ºN

[somber cliff]

yeah

[neat lintel]

didnt most early civilization indulge in incest? pretty normal stuff back then

[somber cliff]

that's just a latitute line

[neat lintel]

that isnt co ordinates, thats a longitude line

[somber cliff]

latitute*

[neat lintel]

latitude, not longitude

[somber cliff]

right?

ye

[neat lintel]

yh

i think

[somber cliff]

lmao

[neat lintel]

cause north

[somber cliff]

ye

[somber cliff]

bro what

[floral grotto]

29.9792° N, 31.1342° E

[digital laurel]

you guys realize coordinates are a recent invention and arbitrarily defined

[neat lintel]

what would they gain by doin that anwyay?

[digital laurel]

sorry to interrupt

[neat lintel]

and now the specialness is gone

[floral grotto]

no is not

[somber cliff]

ye

[hot ledge]

There's also an infinite amount of points that could be on that latitude line

[neat lintel]

HOW

[hot ledge]

Cherry picking at its finest

[neat lintel]

sorry, accidental caps

[somber cliff]

ANYHOW

[neat lintel]

well, technically not infinite

[neat lintel]

incest was pretty normal in early civilization

[somber cliff]

can we go back to the theory

[neat lintel]

oh wait

im wrong

[neat lintel]

hm>

[somber cliff]

this is just a random latitute line anyway

i wanted to talk about the theory of simulations

[floral grotto]

do you think you can like go to another dimension or state in your dreams

[somber cliff]

no

if you've never experienced something irl, you can't experience it in dreams IMO

[floral grotto]

how no?

thats the thing!!

[somber cliff]

but this is false

[floral grotto]

you cant experience it because you are in real life

[somber cliff]

my mom died in my dreams many times

but never irl

[floral grotto]

exactly

[floral grotto]

sorry to hear it anyways

[somber cliff]

it's nothing lmfao

[floral grotto]

btw

why there are no clocks on the dreams?

[somber cliff]

i've never seen a tiger irl or a flying robotic guardian but they've appeared in my dreams

[floral grotto]

and why when you realize you are dreaming everythingg is super rare =?

[floral grotto]

exactly!!!

[neat lintel]

speak

[somber cliff]

well

we are speaking lmao

[somber cliff]

wellll

[floral grotto]

how is possible that

[somber cliff]

there's no proof of that

[flat cloud]

there are if you start thinking daily about clocks

[somber cliff]

UNLESS we record those dreams

that's correct

[flat cloud]

you dont tho so you wont see many in your dreams

[floral grotto]

if i dreamt about something, a week later i continiou the same dream, and one week later or even a year later i continiu the same dream

[somber cliff]

whatever you think about a lot will show up in dreams

[pure obsidian]

not rlly

i dont think about the dark alot

[somber cliff]

well that's from my experience

[pure obsidian]

and it shows up in my dreams

[somber cliff]

subconciously you are then

thinking a lot about the dark

subconcious thinking means you're thinking, but you're not aware of your own thinking

[pure obsidian]

oki

cool

[floral grotto]

guys you can call me crazy about what i have thought:
we are like robots and
food = to reset our mind
water = like oil idk
sleep = energy or reset mind

[pure obsidian]

ur crazy

[floral grotto]

and i also thought like im the only "human" and all of you npcs

i mean

it can be true or not

[pure obsidian]

lifes a simluation ah

[floral grotto]

it can not be demonstrated

[somber cliff]

ur crazy

we can reproduce and have chemical processes going on yk

robots HAVE NO CHEMISTRY

[flat cloud]

what does resetting mind have to do with food or robots

[floral grotto]

yes but i dont mean that

[pure obsidian]

wowzers

[somber cliff]

except fucking metal

[floral grotto]

nooooo!!!!!

[somber cliff]

they don't have blood

[floral grotto]

bro

[pure obsidian]

yeap

[somber cliff]

they don't have lymph

[pure obsidian]

wat

[somber cliff]

they don't need oxygen

[floral grotto]

peopple with 100.000 years technology will able to create robots without metal bro

our brain is like the AI

[pure obsidian]

wow

uh huh

[somber cliff]

how would they power it then

[neat lintel]

technology

trust

[floral grotto]

with us sleeping!

that why if we dont sleep we die

or food or water

[somber cliff]

the whole definition of a robot revolves around being artificial

[pure obsidian]

it b like that

[flat cloud]

implying the asteroid isnt getting us all in 7 years

[somber cliff]

there is nothing natural about a robot

[neat lintel]

what asteroid?

[pure obsidian]

i dont wanna die

[flat cloud]

YR2024

[somber cliff]

robots might be able to dream with AGI though

[flat cloud]

ok you wont then

[floral grotto]

i think we are robots but our brain which is the AI was desinged with some rules for us to think that we are not robots

[pure obsidian]

yas

https://tenor.com/view/flashbang-flash-cat-betterttv-gif-10690574645280585754

[somber cliff]

again

by definition we are not robots

[neat lintel]

Asteroid 2024 YR4 has a roughly 2 percent chance of hitting Earth in 2032, and “is large enough to cause localized damage,”.

[floral grotto]

why not?

[somber cliff]

we have metabolic processes going on in our bodies

and can reproduce

[floral grotto]

we are creating live in labs with only 2000 years old techonoly, just add another 100.000 years

[flat cloud]

i know, it was a joke

[neat lintel]

'localized damaged'. I am going to be so mad if it hits somewhere near me. Then again, 2% chance. I think I am still chilling

[neat lintel]

More like a half-joke, there is still a chance it could hit.

[flat cloud]

it isnt "getting us all" if it does though

[dull linden]

It's going to hit me, it's targetting me I'm pretty sure

[flat cloud]

send this guy to space NOW!

[dull linden]

[somber cliff]

huh

[floral grotto]

i cant explain sorry i cant find the words to express myself, my english is not htat goood hahah

[neat lintel]

That's why I am upset if it hits somewhere near me. It's localized damage, and of all places it can hit, had to land somewhere near me?

Well, if it does hit, it would be awfully convenient if it hits in the middle of the ocean, away from everywhere

[floral grotto]

btw do you thnk there is really somehting in area 51 ?

[flat cloud]

hmm at worst you will know it will hit you several months before

[somber cliff]

¿hablas español tambíen?

[flat cloud]

so you can get most of your stuff out of there

[floral grotto]

i told you im from spain!! yo hablo español de toda la vida

[neat lintel]

That's true. I think that might be what will happen. Most will evacuate or something, which will actually cause massive refugee crsis. lol one asteroid can really cause huge issues huh?

[somber cliff]

ahhh sí sí

(my spanish is bad)

[floral grotto]

tu hablas español?

ahhh

okk

hahahah

[somber cliff]

no no

uhhh

no sé la "future tense"

[floral grotto]

hahahahh

dw

[somber cliff]

o "preterito"

[floral grotto]

bro i want to find the secrets in the world

[floral grotto]

thats the pas

t

[somber cliff]

idk any of the tenses outside of present tbh

it's too confusing

uhh

[floral grotto]

there are a lot yes

[somber cliff]

estoy hablaba

[floral grotto]

like 20 different forms

[somber cliff]

20???

[somber cliff]

no sé

[flat cloud]

imagine doing all that and then it hits the sea or hits nowhere at all

[somber cliff]

jueges deportes?

[neat lintel]

omg that would be so fricking annoying XD

[somber cliff]

cualquier

[floral grotto]

yo: juego, jugué, haya jugado, habré jugado, habría jugado, jugar, jugando, jugado, jugaré, hubiera o hubiese jugado, jugara o jugase, jugare, había jugado, jugaba

etc etc

thats the verb play

[somber cliff]

what the heck

[floral grotto]

like i play football

and thats only with I

[somber cliff]

estoy jugando means i am playing right

[floral grotto]

yep yep

y estaba jugando

i was

[somber cliff]

that's the only one i know

idek any of those other tenses

[floral grotto]

y estaré jugando

i will

[somber cliff]

will you teach me?

[floral grotto]

if you want

hahahah

[somber cliff]

hell yeah!

[floral grotto]

its too complex

[somber cliff]

da me spanish lessons

[floral grotto]

btw how old are you

[somber cliff]

i'm 17

[floral grotto]

same as me

lol

[somber cliff]

OHH nice

[floral grotto]

when is your birthday

[somber cliff]

october

[floral grotto]

ahhhh

then you are a year older

[somber cliff]

y tu?

[floral grotto]

february

[somber cliff]

2008?

HA

[floral grotto]

yepp

[somber cliff]

wait happy late birthday

[floral grotto]

thanks!! hhaha

[somber cliff]

uh

Como es España

?

[floral grotto]

im gonig to usa in september

[floral grotto]

muy chula

[somber cliff]

i'll be in college by then

bien

[floral grotto]

college is university?

[somber cliff]

yes

La universidad

[floral grotto]

those american words ahhhhhhhhhh

[somber cliff]

lol

[floral grotto]

chips fried

s

[flat cloud]

wdym kids born in 2008 are 17

[somber cliff]

idk when to use El vs La if it doesn't end in "o" or "a"

[floral grotto]

yes 😭

[somber cliff]

but

when in doubt, use "la"

that's my rule

[floral grotto]

doesnt matter if it ends in o or a

[somber cliff]

la mano

ur right

[floral grotto]

el agua

[somber cliff]

whyyyy is it like that

[somber cliff]

what year were u born bro

[floral grotto]

some words have both, for example water

[flat cloud]

la agua is also valid btw

[floral grotto]

the correct one is EL, but people use both

[flat cloud]

2005

[somber cliff]

ohh cool

ur turning 20 then

have fun!

[floral grotto]

people use it but its not correct

[somber cliff]

no one's saying "el mano" lmao

[floral grotto]

hahahah

[flat cloud]

:0 its true

[floral grotto]

there are some funny things

for example

trousers

el pantalon

o

los pantalones

its the sme thing

[somber cliff]

ahh

[flat cloud]

actually yes but in other contexts

[floral grotto]

dame el pantalon / ponte los pantalones

[flat cloud]

el hermano gets abbreviated to

el mano

[floral grotto]

doyou speak spanish nano??

[flat cloud]

yup

from chile

[floral grotto]

where you from

ohhhh

nice

some words change

el celuularr

el carro

hahah

[somber cliff]

is car carro or coche

[floral grotto]

in south america
car = carro
in europe (spain)
car = coche

[somber cliff]

oh i see

[floral grotto]

same with phone

its too complex

[somber cliff]

i always thought spanish was an easy language

[floral grotto]

nooooo hahhaahh

[somber cliff]

and tbh it can be easier than english sometimes

[floral grotto]

im lucky to be born here

[somber cliff]

ah

how did you learn english

[floral grotto]

i think enlglish is easiser, but it english has much more words

[floral grotto]

in school and academy

[somber cliff]

english doesn't have as many patterns

[somber cliff]

oh nice

like not all the verbs end in "r"

[floral grotto]

here in europe we use english words because we dont have a created word for that

[somber cliff]

if a spanish word ends in "io", that means it's past tense right

[floral grotto]

all verbs on infinitive end in "ar" "er" or "ir"

[floral grotto]

hmmm i think NO verbs end in io

[somber cliff]

Yo jugío, ellos jugíeron

like that

[floral grotto]

that doesnt existtt

[somber cliff]

oh what

[floral grotto]

yo jugué

ellos jugaron

[somber cliff]

OHH

cause it's an ar verb

not an ir verb

uhh

[floral grotto]

ir

yo salí

ellos salieron

[somber cliff]

yeah

so "io" doesn't exist?

[floral grotto]

él salió

[somber cliff]

SEE

it does exist

[floral grotto]

yes but with tilde in the o

[somber cliff]

well yeah

i have an american keyboard

tildes are hard

for me to type

[floral grotto]

Aaª

á

é

í

ño

ó

ú

[somber cliff]

ª

what is aª

[floral grotto]

nothing

its used for girl names

[somber cliff]

how is aª related to a!

[floral grotto]

instead of maria

Mª

but it is not used at all

only in very formal places

[somber cliff]

man oh man

i'll learn one day

[floral grotto]

hahahah

you will

btw

[somber cliff]

i hope

yeah?

[floral grotto]

do you tihnk

stars are real

[somber cliff]

yeah

[floral grotto]

hmmmmm

idont know bro

[somber cliff]

if stars weren't real, we'd all be dead

[floral grotto]

everything is strange

for example why gravity exists

[somber cliff]

refer to the theory of general relativity for that one

[flat cloud]

if stars arent real what is the sun

or all you see during night

[floral grotto]

i think this theories were created to be talked in real life

[digital laurel]

stars are flashlights in the sky

[floral grotto]

too many texts

[digital laurel]

someone's holding them up

[floral grotto]

my keabord gonna explode if i kepp texting

[flat cloud]

actually the night sky here is so polluted if you told me all night stars disappeared

id have no way to tell

[floral grotto]

we are trapped!!!

i want to go to the moon

[flat cloud]

again the sun is a star and im pretty sure it exists

[floral grotto]

i will be millionaire and goo to the moon

[flat cloud]

thatd be cool

[floral grotto]

it obviously exist but is it really a star as we know

[floral grotto]

i just need where to start

i already tried 3 diferent thing

but i think i got the one

[flat cloud]

what do u wanna go to the moon for anyways

[floral grotto]

i think it would be fucking amazing

it wont feel real

[flat cloud]

true

[somber cliff]

chile??

[flat cloud]

yup

[somber cliff]

aw man

[flat cloud]

the north and south remain nice

centre is fucked

[somber cliff]

just the central?

ye

[flat cloud]

id love to work in the north

when I grow up aka get my degree

as a kid I really loved space

and all that had to do with it

like black holes white holes quantum particles

watched all quantumfracture videos

I still chose math and cs over physics

[floral grotto]

the worm holes

[flat cloud]

but id love to work in something related to space one day

[floral grotto]

i would love to

have a good job

and my hobby to explore space and misteryes of earth

[flat cloud]

you could be a marine biologist

not many people are one but the sea is just as mysterious and vast as space

[sharp mulch]

I met with a planetary scientist yesterday

We have ideas about jupiter's great red spot

[flat cloud]

well not vast as space LOL but still very big

[sharp mulch]

And saturn's hexagon

And jupiter's pentagon

[floral grotto]

eing

in normal people terms?

hahahah

[vivid halo]

that's where they keep the demons

[floral grotto]

how can you send pictures

[bright hill]

skill

[neat lintel]

ok

[visual thorn]

Is anyone else bothered by the hand-wavy definition of the real numbers? I don't think the real number axioms lead to any contradictions, but they seem to be just the rational numbers jerry-rigged with an axiom that says "if an output of an operation on rational numbers is undefined, just define it and treat it like a rational number."

[sharp mulch]

How do you feel about the constructions of the real numbers

[visual thorn]

Integers make sense. Everyone understands negative heights. Everyone understands the idea of a half or a third.

[visual thorn]

As I said, it feels like they were built in a jerry-rigged way.

There are the rational numbers which make sense as a field. The addition, subtraction, multiplication, and multiplicative inverses all came about naturally.

The idea of half a pie minus a third of a pie makes sense.

The way the real numbers are built, almost all of them are uncomputable.

I would like to see a more careful construction. For example, we know about sqrt(2), and that it is not rational. We can find other similar numbers like the square root of any prime integer.

We have all those and we have rational multiples of them.

[sharp mulch]

Do you find algebraic numbers to be more satisfying

Or computable numbers

[visual thorn]

I don't know what you mean by "satisfying".

[sharp mulch]

Well you're dissatisfied with the reals aren't you

[visual thorn]

It's not just a matter of taste. They are just jerry-rigged rational numbers.

We have the field axioms which really are only based on the rational numbers.

[cinder zephyr]

can u elaborate more on this?

[visual thorn]

Then, we make up this set called the "real numbers", we say every rational number is a real number, and we then say any subset of R has a least upper bound. Now you have a mess of numbers that you know nothing about. That's my elaboration.

[cinder zephyr]

I think in some sense you are saying that the rationals are a "smallest" field in that any field of characteristic zero contains the rationals?

Is that what you mean by "based on the rational numbers" ?

[visual thorn]

That's another way to say it more accurately, sure.

[cinder zephyr]

well in that case, many fields don't contain the rationals

and we also have other characterizations of the real numbers

it is the only complete, totally ordered field

so it's the only field that
1: is complete, meaning that every Cauchy sequence converges with respect to the metric of the field
2: has a total ordering on the elements of the field (so you can say which numbers are bigger than others)

[visual thorn]

Looking for all totally ordered, complete fields is a top down approach, though.

[cinder zephyr]

and really these are the things we care about most with the reals, not the specific construction

[visual thorn]

The irrational numbers are defined by what they are not.

The idea of a complete field came from the idea of numbers such as sqrt(2).

What fields are you talking about that don't have the rationals as a subfield?

[cinder zephyr]

finite fields

or even infinite ones such as rational polynomials with coefficients in your favorite finite field

they don't contain the rationals

the rationals are characteristic zero, finite fields are characteristic p for some prime p > 0

the field of rational polynomials with coefficients in a field of characteristic p also have characteristic p

[visual thorn]

I'm not as familiar with fields of rational polynomials.

What are the domain and codomain?

[cinder zephyr]

do you know what rational polynomials are?

And do you know what finite fields are? Like F_p for some prime p for example

[visual thorn]

you take some set S, some set T, and take all functions f from S to T such that f(x) = sum from i = 0 to i = n of x^i, where n can be any nonnegative integer.... (continued)

[cinder zephyr]

no

there's no S and T

rational functions are quotients of polynomials

[visual thorn]

yes, examples would be integers mod some prime with modular arithmetic.

[cinder zephyr]

f(x) / g(x) where f and g are polynomials with coefficients (real, complex, rational, finite field, whatever)

those are rational polynomials

[visual thorn]

For the rational polynomials, yes, you need to then treat each function f as an element of a set.

That's the step I had not yet typed. But a function only makes sense as a mapping from a set to another (possibly equal) set.

[cinder zephyr]

they're polynomials

just formal objects

[unborn trellis]

Positive characteristic isn't real, you can't trick me

[cinder zephyr]

we don't necessarily care about evaluating them as functions

we can evaluate polynomials yes, but for defining the field of rational polynomials we don't care about evaluating them as functions

[visual thorn]

you need to be able to say something about a polynomial, and what it is or is not though, right?

[cinder zephyr]

I can write $q(x) = \frac{3x^2}{2x + 1}$, this is a rational polynomial with real coefficients and it is very clear what it is

[fathom swallow]

Spamakin🎷

[cinder zephyr]

so idk what you mean by "what it is or is not"

[visual thorn]

Well, f(x) = sin(x) is a function but not a polynomial.

[cinder zephyr]

yes which is why everywhere I have specified polynomials

not arbitrary functions...

[unborn trellis]

two polynomials that have the same values can be different in finite fields

[visual thorn]

so if you have all your polynomials f, g, h, ..., then you have to be able to say what each one of them is.

you have to be able to say it's a sum of weighted powers of a variable.

you don't need to specify that S is the integers, the reals, matrices, whatever, when I mentioned S above.

But there needs to be a placeholder as far as I can understand.

[unborn trellis]

Yes, the definition is exactly what you say

Polynomials over a ring R are just formal sequences of powers of x with coefficients in R

They are equal iff their coefficients are equal

[visual thorn]

Back to my original point though, rational polynomials are clearly based on the rational numbers.

We took the idea of adding them, multiplying them, and finding additive and multiplicative inverses.

[unborn trellis]

In that they're fractions?

Yeah definitely

[visual thorn]

yes

[unborn trellis]

This formalized in the notion of a fraction field of an integral domain

We define operations exactly as you would a fraction in Q

[visual thorn]

it's quite abstract. Say if grade 1 is counting numbers, grade 2 is integers, and grade 3 is rational numbers, then we just say "now add the least upper bound property" and we are suddenly in some unknowingly high grade just working with some things called "real numbers" as if they were rational numbers.

I'd like to see some more careful, tedious construction where we do something like taking the set {sqrt(2), sqrt(3), sqrt(5), sqrt(7), ...}, taking the set union of that with the rationals, and seeing what properties might be added.

[unborn trellis]

You would love galois theory

[visual thorn]

Then, perhaps you could add other numbers and look at the structure. You could add things like pi or e, or outputs of trig functions. I don't know. Going from the rationals to the reals feels like a leap of faith. It's too big a jump.

I've heard of galois theory but not studied it. I might look into it if I can

I know that it can be proven that there's no formula to find the zeroes of an arbitrary quintic using galois theory, but I don't know the proof itself.

[icy heron]

Are you familiar with the difference between axiomatic and constructive definitions of the reals? When you say "just add the least upper bound property" it sounds like you're just adding that as an axiom

[visual thorn]

Here's a better analogy: teaching a kid the rational numbers and then giving the kid the real numbers is like teaching a kid how to use like the earliest version of Windows OS, then giving him a later version loaded up with all sorts of IDEs for all sorts of programming languages, as well as a bunch of advanced software. Sure, this fancy new OS runs solitaire too, and you can play solitaire on it, but the kid has no hope of using all these IDEs or advanced softwares.

[visual thorn]

I know you can construct them with dedekind cuts.

there's a whole process of set theory.

[icy heron]

Yep 👍 there's also the Cauchy completion, which I find a bit more intuitive

[visual thorn]

I'm not just being bitter about infinite math. I think some nice and elegant things get missed by a lot of people when we just teach people to jump straight from the rationals to the reals.

[unborn trellis]

they explain it in high school just as "it has all all the numbers" basically

[visual thorn]

Yes, that's a very lazy way to teach it.

[unborn trellis]

too hard formalizing the existence of such a thing

maybe they'll throw in an adjective like dense or complete

[visual thorn]

A kid will learn some basic arithmetic, and a bit of basic algebra, and then will basically be told in one sentence "the reals are all the decimal numbers and the complex numbers are a complete field and that's it and now you know everything you'll need for math in physics"

I'm poking fun, sometimes they learn other useful things.

Why hide math from people, though?

A random person likely just thinks of math as "something done with a calculator from the stationary and office supplies store"

[fresh oriole]

I think the proper way to introduce real numbers is as all possible decimal expansions. And point out that infinite trailing 9s can be replaced with adding 1 to the digit right before the 9s and following with 0s. As in .999… = 1 and similar.

Point out that various rational numbers already have nonterminating decimal forms, and then say we’re going to call ANYTHING with a decimal form a real number.

The only tricky part then is giving a rigorous account of how to do arithmetic with arbitrary decimals. This can be done, but is better to handwave a bit with for beginners

And at the same time, it’s a good idea to emphasize right then that not all numbers have a decimal form, e.g. sqrt{-1} can’t possibly have one (demonstrate why)

[visual thorn]

What are you going to do with the idea of "all possible decimal expansions" though? All you can really do is start writing out strings of random numbers, and get bored after finitely many digits.

Then, after you have finitely many, you have a rational number, and now you are just working with rational numbers.

[fresh oriole]

you can observe that it includes various interesting numbers that aren’t rational, like sqrt(2), e, and pi

[unborn trellis]

it's not even true that finite decimals = rationals

[visual thorn]

yeah, but I could write out 3.141592653589793238462643383279502884197169399375105... and so what?

[unborn trellis]

1/9 = 0.111111...

[fresh oriole]

that’s not how we go about showing pi is a worthwhile number to think about

[visual thorn]

yes, that is my point

[unborn trellis]

i think students get the gist that arbitrary decimal precision specifies "any number"

[visual thorn]

in the case of pi, the digits aren't the interesting part

[unborn trellis]

so that when you establish a number as existing in a natural way (like pi in terms of a circle) then it must have a decimal expansion. you got all the numbers

of course then you ask about x^2 + 1 = 0

[fresh oriole]

I don’t get your point. One can say to students that there is a proof the decimal form of pi never terminates or eventually repeats, so it’s not rational. The proof is too advanced for the course. But the point is gotten across that pi is an irrational real number

it’s just not that weird of a leap conceptually to go from certain decimal forms to all possible decimal forms

well, it turns out it kind of is, in sophisticated ways, but a beginner can get the idea as familiar

[visual thorn]

I don't think they'd get the point though. It's a popular misconception that 0.999... isn't 1.

So, people have failed to understand by just being told "repeating or terminating means rational, otherwise it's irrational."

[fresh oriole]

yeah because nobody bothers to tell them that growing up, and almost nobody has the kind of curiosity needed to discover it for themselves

[visual thorn]

I was tutoring a student who thought 0.142857142857... was irrational because it didn't look like 0.333333... or 0.444444444444444....

[fresh oriole]

but once somebody spends 10 minutes explaining this, most students understand

[visual thorn]

Can you blame them for being incurious if they aren't shown what's worth looking at?

[fresh oriole]

somewhat, yeah. A lot of students just suck. And the extent to which math teachers never say what anything means and just make people memorize things, is greatly exaggerated by many students

the relationship between fractions and decimals and long division is standard material and the kids who pay attention and do their homework tend to be alright with it

but that’s a minority of kids

[visual thorn]

I remember very many times having one or two class clowns disrupting the whole class, and it's really because the class clown was more interesting than the teacher.

I remember many times where everyone was just talking, again, I assume because whatever the conversations were were more interesting than the teacher.

[fresh oriole]

yeah, that’s an unfortunate situation. Most teachers would love to just remove such clowns from their classes, but they don’t have the power to do so

the system is broken

[visual thorn]

Well, here's my idea for a solution: allow teachers to be a little eccentric.

People remember eccentric teachers who made things interesting.

[eager minnow]

the classical "first day maths undergraduate proof" is that √2 can't be written as a fraction n/m
I think this a really good motivator to wait, so what the hell even is √2?

[fresh oriole]

yeah, it’s great

[eager minnow]

I found this satisfactory reason to build the reals

[fresh oriole]

it should be shown in high school algebra, but I don’t know how standard it is

[eager minnow]

probably did it in both

[visual thorn]

I don't worry about what numbers are, I worry more about what they do. sqrt(2) is something that shows up as the hypotenuse of an isosceles triangle with both legs unit length.

you can ask "what's sqrt(7)" and I don't quite know what that is right away.

[fresh oriole]

it’s the length needed for a square to have area 7

[visual thorn]

that's sort of starting at the answer though.

[eager minnow]

not sure how you can do maths past the Greeks like this though

[visual thorn]

I'm asking "how would sqrt(7) come up naturally?"

[eager minnow]

why

[visual thorn]

I'm just showing that stuff that has a practical use is better than this abstract stuff.

[eager minnow]

that's what high school is for

[visual thorn]

general relativity is very practical

[eager minnow]

specifically the practical use of √7

not practicality in general

asking "why do we care about √7" by the time you build the reals seems unrealistic to me?

unless I'm misunderstanding you

[wild lantern]

@wraith roost the purpose of the help channels is to help people actually learn stuff. If you just give people answers they aren't really learning anything

[fresh oriole]

how about as the long leg of a right triangle with hypotenuse 3 and short leg 2? is this satisfactory?

[visual thorn]

I'm sorry, I can't understand your shorthand grammar.

[fresh oriole]

wait, I think I got that wrong

yeah I meant hypotenuse 11

[eager minnow]

what shorthand? /gen

[visual thorn]

Yeah, that's the idea, so that's somewhere this number would actually come up.

[fresh oriole]

or better yet, the right triangle with short leg 1, and hypotenuse 8

wait no

yeesh what’s wrong with me rn

ok here we go

leg of 3, hypotenuse of 4

[visual thorn]

point being, now you are actually thinking about how the number gets used, and it appears you are a little unfamiliar with the use of it. This way you don't just skip past and say "consider all limits of all sequences who are cauchy convergent"

much like there are gaps in the rational number line, there are gaps in peoples' mathematical abilities.

saying "lets fill all the gaps with an axiom" doesn't fill peoples' gaps in abilities for free.

[eager minnow]

I've lost you

[visual thorn]

then get learnt

[fresh oriole]

I mean this is kinda silly. Sure I’m not as familiar with a place sqrt(7) naturally comes up compared to sqrt(2). But it’s good to understand that for any natural number n, sqrt(n) is either a natural number (when n is a perfect square), or an irrational number like sqrt(2) and sqrt(7)

then you know something about infinitely many numbers at once

and I know how to use all these numbers algebraically and arithmetically equally well

[eager minnow]

you're saying the fact that mani' struggled a bit to come up with a geometric situation where √7 shows up shows we can't skip to Cauchy sequences?

[visual thorn]

you fumbled when trying to make a triangle with one side having sqrt(7) if the other two had integer lengths, though. It's not necessarily important to be able to do construct such a triangle, but you fumbled, so perhaps you really don't "know something about infinitely many numbers at once"

you might superficially know and eventually construct the triangle

but if all of your knowledge is superficial, you will always be fumbling like that.

[eager minnow]

or perhaps at the postgraduate level your 7th grade geometry skills are rusty?

[fresh oriole]

I literally did the Pythagorean theorem wrong in my head, probably because I’m tired

that doesn’t mean I understand sqrt(7) less than sqrt(2)

[visual thorn]

I'm saying applied math is better than pure math

[eager minnow]

that's not what applied Vs pure means tho

[fresh oriole]

you’re certainly welcome to think so, but you haven’t made a very good argument for it

[visual thorn]

I may not have articulated it well, but I don't talk about this a lot.

Perhaps to my point, I've not practiced my reasoning very well and I'm fumbling with it.

So, it would be better to practice applying my reasoning.

Hence, application is better than abstraction.

Applied math is better than pure math, in other words.

[sick parrot]

bro fell off

[visual thorn]

you aren't on any level high enough to fall off.

[sick parrot]

bro refers to you bruh

bro fell off english class

[fresh oriole]

there’s no need for insults

[visual thorn]

I'd be fine with insults if they were a bit better than that.

I don't have too much to respond to.

[eager minnow]

you say as if applied maths doesn't use abstraction to progress itself

nor would I call finding a geometry problem where √7 shows up "applied"

[visual thorn]

Anyway, it was a productive discussion because I see galois theory might be worth looking at in the future.

[neon garnet]

#discussion message
https://apps.apple.com/us/app/5-calls-contact-your-congress/id1202558609
https://play.google.com/store/apps/details?id=org.a5calls.android.a5calls&hl=en_US
5 calls feels super empowering towards holding elected officials accountable and making your voice heard. 5 calls 5 minutes!! ☺️ 📱

[lost forum]

Time to flex my friends

[lapis summit]

yoo guys anyone do gcse math

[heady salmon]

shii is that some high lvl math beyond algebra

[upbeat heart]

[fresh comet]

[sharp mulch]

<@&268886789983436800>

[warm umbra]

welcome to the server @heady salmon

[storm sage]

it's british

[north topaz]

it's like algebra 1 level don't worry

[covert nymph]

im still in yr 10 and learnign like basic trig functions like tan theta = sin theta over cos theta is ther any other stuff i should be aware of or??

[north topaz]

sin^2 theta + cos^2 theta = 1

in general you should try to learn the unit circle definition of sin and cos, in all 4 quadrants

the alternative is memorising separate graphs for sin, cos, and tan
and I think that's the hard way

there's a lot of practice on Khan Academy and so on

converting say sin(280) = sin(-80) = -sin(80)
converting any angle back to a first quadrant angle

[wind cairn]

Quick Question guys how would this parallelogram look like as a diagram? Let O be a fixed origin in 3-space, let P and Q be any points in this space,
with position vectors p and q respectively, and let R be the point such that
the figure OPQR is a parallelogram.

[north topaz]

it'd look like a parallelogram, just in 3D

[wind cairn]

i mean just a 2D drawing

[north topaz]

yeah the 2D drawing would be the best representation you could make

then try to imagine it possibly being in 3D

[wind cairn]

yeah how would it look like?

in 2D

because aren't the letter arrangment supposed to be cyclic ?

[north topaz]

yeah it's not cyclic

which is the question's fault

[wind cairn]

ah so its the question fault then

[north topaz]

they should say OPRQ

yeah

[wind cairn]

yes yes that's what i was thinking

thank you

[north topaz]

ah I see now, no worries!

[north topaz]

practice with common angles like cos(135) for example and write the exact form, and practice with other angles like the sin(280) from before

that's all you need to know for now then

there are more trig identities (angle addition/subtraction and double/triple angle come to mind)
there are trigonometric proofs
there are trigonometric equations also and those really need you to recognise multiple solutions per period, except for tan or cot

the unit circle is at the foundation of all this

[wind cairn]

oh but 1 question

full question was Let O be a fixed origin in 3-space, let P and Q be any points in this space,
with position vectors p and q respectively, and let R be the point such that
the figure OPQR is a parallelogram. For each of the following bound vectors,
determine an expression in terms of p and q for the free vector represented
by that bound vector:

but finding OR vector would result in a different answer

so it might not of been a mistake

@north topaz

[tranquil spruce]

Hey

[lyric hornet]

Y'all, exam stress has turned me into a star-making ball of anxiety

How do people

Stress management

[gusty socket]

you should realize that any particular exam is going to have very little impact on your future development as a mathematician first

one idea is to treat exam day like just another tuesday and make studying the norm, not because you have to do it to score well on this test, or even to score well on tests in general, but actually just to grow as a math student and that it’s fun. this worked for me but ymmv of course

or monday i guess since today is monday

[lyric hornet]

You see I had this fight with my mom because she thinks I'm not studying and then I told her that I am and she said she'll see it when I get my results. And I, the oblivious confident fool that I am said, "YEAH! YOU'LL SEE-"

So uh

Yeah

I kinda have to live up to it now

Timer, you been typing for a while bro 😭

[untold sun]

Your mother will realize at some point that she is not living your life, she does probably care about how you're doing at school but after all she will care about social image like some parents do depending on where you live, now the most important part, if she yells at you or whatever, I don't think it really matters when you truly try your best, even the argument becomes meaningless when that happens cause you will just know it happened and you will look out for yourself in a way or another, it's another story if you're lazy and playing around tho it means probably that you are not using the best of your skills but there you go, you will have to show for yourself not for her, I don't have to prove to anyone that I care about my own life

[lyric hornet]

I'll be honest, I've been insanely stressed all year and my grades have been dropping (I'm failing) cause of that and I can't bring myself to admit that I'm stressed. I have a very bad history with stress management and my mom knows that and she has legit mocked me for it (like who makes fun of sh???)
And because of the stigma surrounding the fact that smart kids are always cool under pressure, I can't tell anyone that I'm stressed because I have the "smart kid", "bright student", "sharp" and "intelligent" on my head

[neon garnet]

i say, "okay" a lot

[untold sun]

Good now you admit that, you will have just to see what are your worst possibilities around, I will try my best to make the picture clear for you, since I have dealth with stress before, a shit or catastrophe situation doesn't mean by any chance that you have to cope with that and evade it with another substance, your mind will try to evade the stress somehow by doing something that will already puts stress more on you (here you look for your habits) any kind of addiction like eating patterns, sleeping, etc... are meant to tell you something, what can you do here is to look for a professional if possible and within your budget limit, if it's not possible then you have to be surrounded by healthy kind of people (relationships, mainly friends) that you won't take all the load on yourself, internalizing all the expectations of your parents without looking outside isn't the best strategy in my own opinion, that's living in a bubble, look for healthy habits like meditation, as the guy above mentioned, sport, etc... and practice journaling if that's what you love doing, you will get a better idea about yourself, and you will understand other people better this way "like not all people are raised in healthy families" I won't dig deeper here it's already personal

So anyways take care

[lyric hornet]

Yeah I actually got into boxing last year (on and off)

[neon garnet]

https://restore-mentalhealth.com/gifted-kid-syndrome/
i'm curious. i like to state what i dont know and ask a question. those are intelligent actions to me. i feel like i am what i practice. that works for me.

i hope you feel better!! 💗

[lyric hornet]

Also I would totally do that if I wasn't so anxious all the time. My brain is almost never quiet 😭

I've actually just resorted to making paper stars

If I can sit still for that long I will totally try that

I think my main problem is that I constantly require stimulation

So I kinda just have to get over that

[neon garnet]

@lyric hornet

#serious-discussion message

[neat lintel]

Wish you good luck! I will believe in you ^-^

[lyric hornet]

Like a 3 days now? I was making paper flowers for a week before that

[lyric hornet]

oh fuck, I just realised my exams start in 4 days

and I need like 1 day for my first paper

so I have 3 days

ya'll is it possible to inject info into my head

I'M SO SCARED WHAT IF I FAIL

I mean I've finished most of the easy stuff

but my school

loves torturing us

and they probably set the finals paper

to be very

very difficult

okay ykw

I'll manage

I've done this before

I just need really angry music, a few cups of coffee and a bottle of water

[neon garnet]

https://www.project2025.observer/

[upper bone]

Love how unbiased this is

Really useful website ty!!

[neon garnet]

https://5calls.org/ 5 calls has a website too!

[neon garnet]

https://www.nytimes.com/2025/02/17/world/canada/delta-toronto-plane-crash.html from minneanapolis. four incidents since washington now.

how many incidents were there in 2024?

[leaden torrent]

there were much fewer in 2024 than 2025 (assuming the trend holds) but actually much more in 2024 than 2023

it seems like theres been a gradual trend towards increased airline fatalities beyond just who's in charge politically

its still safer than driving but i know a lot of airline safety experts are concerned

might just be a bad couple years, might be climate change causing worse flying conditions, who knows

[heady salmon]

hello

[jagged forge]

<@&268886789983436800>

they even bolded it so i would notice it right away

[north topaz]

HI CRAMERUS

hey Matt

long time no see

[jagged forge]

hey south

long time no see indeed

[peak tide]

Copy and paste this so others can know the truth!

[jagged forge]

@ mods

[peak tide]

go up, thou bald head

[jagged forge]

oh i get it now. you copied and pasted it

[peak tide]

i was told not to ignore it

[north topaz]

Jesus Chwist is the Way, the Twuth, and the Wife. No one comes to the Father except thwough Him (John 14:6). He died for your sins, He wose again, and He offers you etewnal wife. No matter what you've done, no matter how far you've stwayed, His awms are open. Wepent, beliewe, and be sawwed. This wowld will pass away, but Jesus wemains fowwewer. If you see this, don’t ignore it—this message was meant for you. Jesus wuvs you. Accept Him today. Copy and paste this so owwews can know the TWUTH!

[peak tide]

you missed a few: "Chwist", "etewnal", maybe even "awms"

"wowld"

[north topaz]

jesus christ this is harder than I expected

[surreal sapphire]

@deft plume this is a math server, please take your soapbox elsewhere

[candid kestrel]

@onyx holly I agree with you wrt the stuff you said in nt

[round cobalt]

hi

[upbeat heart]

Legit?

[fresh comet]

<@&268886789983436800>

[fresh comet]

no

[upbeat heart]

[neat lintel]

bro

@fresh comet stop lurking

go bed

sleep

night

late

close eye

put phone down

sleep

no

w

?? 😭

have you never had a friend or what

he was typing

😭😭

dude

thats someone wlse

SEE

[upper hatch]

LMAO

WHYD YOU PING ME

[neat lintel]

@fresh comet what did i tell you

u have 1 minute to go

[upper hatch]

[lavish iris]

Yo guys do you think you need a teacher that works with you constantly to take a good result in math olympiad or you can do it alone?

[upbeat kraken]

I’ve never been a very good Olympiad student but I had friends that were in India and the teachers were needed and were very loyal to us and other students

I think you need a teacher from what I’ve seen in other students they would do coaching at some tutoring company come home do schoolwork go to school get help from other teacher

[reef forum]

Hello

[storm sage]

Mentors definitely help

[neat lintel]

noice

[long matrix]

@supple flame

[dull sail]

hey, my fellow mathematicians, i'm looking forward to improving my understanding of maths, i have practiced basic maths for school but never been really good at it, currently i have seen this github : https://github.com/ossu/math , it seems like a decent course to get into it but if you guys know anything else more appropriate i'd be glad to hear about it, thanks

[hollow ingot]

any thoughts on taking either diff eq or linear algebra in the summer ?

im thinking either taking one in the summer or both in a full semester

[crystal stone]

differential equations will be better in the summer

since it's mainly computational and the concepts are lighter

You want more time with linear algebra

[icy heron]

wtf, math courses are seasonal? what subject is in season right now?

[crystal stone]

It's the spring semester or winter quarter depending on what system you're on

[icy heron]

I thought you meant take diff eq in the summer because that's when it's at its ripest

[long matrix]

cat season

[lunar python]

Depends on the Linalg course imo

A computational linalg class should be fine

[hollow ingot]

https://i.imgur.com/S6Yt524.png
https://i.imgur.com/NqZ8lBO.png

our linear algebra vs diff eq

[dreamy bronze]

Anyone want to help me out with me life project its 200 pages? its about finding a way to stage 5 civilization. needs to be organized, updated and finished.
Write a private message to me.

[sharp mulch]

[warm umbra]

welcome to the server @hollow ingot

[warm umbra]

you have disturbed my rest

what is it you need

ight i gotchu

❤️

[lost forum]

@proven raft why u beef with intergrals

[proven raft]

u sub

trig sub

what else

partial farction decomposition

∫1/(1+x²)dx

arctan

needs trig sub

derivatives have rules and stuff and derivative definition

so easy to understand

[lost forum]

Fr

[foggy path]

Tf?

[vivid chasm]

des francais

[foggy path]

Tbh the way integration is taught in general is pathetic

[burnt ledge]

How much silver

[burnt ledge]

It shoild have been 100 grams to complete the geometric sequence

Wait that wouldnt

178 would

10^3 gram copper, 10^2.25 gram silver, 10^1.5 gram gold

you alr had the first and last it eas just silver you hadnt specified

but then you randomly chose 10^11.27 gram silver

which tbf

is almost exactly one billion times larger than what i suggested

[delicate tendon]

@versed drum howve you been

[versed drum]

been good, a bit busy with schoolwork and preparing vector calculus notes for a dude ive been teaching, how about you?

[delicate tendon]

I got into a research lab and also doing math research on the side outside of my classes

Its nice that I have a light term

[versed drum]

whoa that sounds cool af

[delicate tendon]

Yeah, my project is in Topological Data Analysis

So basically computational algebraic topology

This is for my research lab ^

[versed drum]

that sounds hella cool, ive heard about topology + statistics before but never looked into it

[versed drum]

i wonder if computational topology involves classes like for example, class TopologicalSpace

or child classes like class MetricSpace : TopologicalSpace

[delicate tendon]

Ohhh you mean code?

[versed drum]

ye

[delicate tendon]

I mean there is implementation but im more on the research side of it

Its closer to topology than computing

From what I understand its a lot more about optimization similar to numerical analysis but from a topological approach, meaning im more so dealing with homologies and manifolds

If you can reduce a data set or a problem down to a homology, you can find an efficient way to do a certain thing or also being able to have a specific result/how to get that result in theory

[versed drum]

where are you "will i ever need this in real life?" dudes 😂

[versed drum]

i wonder if it has applications in ML

[delicate tendon]

Dude this is honestly so applicable, its crazy as hell

[delicate tendon]

lmfaoooo thats literally the project im working on

[versed drum]

ohhh

damn bro, where is the CS enthusiast dudes now who be like they wanna be data scientist but at the same time they dont wanna learn math

[versed drum]

at this point is there any pure math subjects left that are completely useless?

[delicate tendon]

Yeah no I dont even know how I got in because im no where related or that knowledgable on the DS sector but I got in through math and really suprised and happy because I know there are so many people who are definitely more qualified/ept at doing ds studies

[delicate tendon]

what? no pure math is still really useful

it still comes down to a niche to niche area, but the general idea of pure math, atleast imo, is that you keep advancing a field until you get to a point where you can solve a "bigger problem" that can be more applicable in other fields/even irl

you wouldnt have applied math without pure ||here comes the onslaught of applied mathematicians to dig my grave||

corrected the spoiler

[eager minnow]

you wouldn't have pure without applied too

[delicate tendon]

Yeah I can see they definitely drive each other if that is what you are saying

[versed drum]

me when string theroy proves some random theorem in pure math

[delicate tendon]

this is def the imposter syndrome in me though

During my interview with the grad student, he said that I could explain TDA better than he could but I just feel inept in the data sciency part

[versed drum]

@delicate tendon topological cyber security when

[delicate tendon]

i meannnn AG exists

cryptography was the reason i became math major

Crypto is currently a mix of NT and AG, or the purists would say Arithmetical Geometry

[surreal sapphire]

thats a pretty wild mischaracterization of the field lol

cryptography is a pretty big and very interdisciplinary field; there is some use of algebraic geometry but most of it is pretty niche und kind of memey

[long matrix]

cryptography: anything goes, use all weapons to hack

[river yew]

unless you make cryptography your life the most math you'll see is some combinatorics and group theory

[long matrix]