serious-discussion

[latent edge]

No you did. Z is a dedekind domain

[deep mango]

Moth to a lame

[timid bronze]

Stfu

You don't like Starboy either

[vast wraith]

more generally…

[timid bronze]

You have the taste of a 13 year old 💔

[vast wraith]

ive just glanced over their definition in lang

[deep mango]

No, i have the taste of a 27 year old...

[timid bronze]

I still remember what you told me, btw

[vast wraith]

good number

[timid bronze]

Bro was about to get moderated

[deep mango]

it was a fucking lyric

"i" didnt tell "you" anything

[timid bronze]

Ok, but you knew what you were doing

[latent edge]

https://www.youtube.com/watch?v=fHI8X4OXluQ

peak

[timid bronze]

My Spotify told me that I have the taste of a 29 year old

[deep mango]

mine said 23...

[timid bronze]

Then shut your bitch ass up

[deep mango]

anyway yours is cause you listen to shitty millenial pop

i listen to good new music its just underground

[sonic field]

didn i let you listen to my recording by radio head?

[latent edge]

If you told me to list the first song that comes to mind by this guy I would say this song

[timid bronze]

I don't listen to shitty music.

WAIT RYC

[hidden isle]

both of u listen to carpenter yall on the same team bruh

[vast wraith]

i was 40 something

[slender echo]

Friendly fire

[vast wraith]

channeling that aunt energy

[deep mango]

Ew the idol is so cringe

[timid bronze]

You have no fucking taste

This is pure ragebait

[solid shale]

😭 😭 😭 might have to watch just to experience how bad

[timid bronze]

WAIT WHAT

[jagged forge]

i was….. drumroll 26

[timid bronze]

LMAO

[vast wraith]

i have never (intentionally) listened to the weeknd so i will make no judgement

[deep mango]

little known fact, jay was in the band Radio Head

[sonic field]

i'ma take that as a no LOL

[timid bronze]

@deep mango Favorite Carpenter song, drop right now

I know your taste will be bad

[deep mango]

im basic, Feather

[hexed tangle]

Juno pose

[timid bronze]

But O'm asking anyways

[latent edge]

https://www.youtube.com/watch?v=u6lihZAcy4s

peak

[timid bronze]

OK WAIT, I RESPECT YOU FOR THIS

[hexed tangle]

Oh wait that is not a song

[cold needle]

Maybe i can try streaming around 12:15 est or something

[hidden isle]

wow a live moogle stream

[cold needle]

im unsure because im on my laptop over the break and like

[deep mango]

Is the :3 in the song title or did you just add it

[cold needle]

the performance could dip too much for me to play well

we will see

[timid bronze]

I added it

[cold needle]

Also no hand cam

[timid bronze]

Juno

[hidden isle]

do we have hip cam yet

[cold needle]

Not yet

[timid bronze]

Nah but @deep mango you actually piss me off with your take on The Idol

It's such a good album

[cold needle]

I need more funds if we want hip cam

[deep mango]

Oh i meant the show

[hidden isle]

you can buy gopro off facebook market

[timid bronze]

OK, BUT THE SONGS ARE FUCKING GOOD??

[deep mango]

i didnt listen to it

[timid bronze]

Listen to them when you can

[deep mango]

i skipped between dawn fm and the new one

i mean ive heard most of them im sure

ofc

i just like havent actually went to listen

so idk whats what

[timid bronze]

Respect

[fringe summit]

Shocker

[fringe summit]

W

[fringe summit]

Why hip cam

Are you becoming an egirl streamer

[deep mango]

Save Your Tears is actually not that good

I used to love it

then one day i did it at karaoke

[timid bronze]

Don't piss me off

[deep mango]

and like

once you do it in front of a crowd

[timid bronze]

Do you have Spotify premium ryc

[deep mango]

you begin to realize it's a little slow and basic

[deep mango]

yeah

[hidden isle]

ryc seems like an apple music kind of guy

[deep mango]

no

[timid bronze]

I meant premium

Oops

[deep mango]

i mean

i have a cracked client

so yes kind of

[timid bronze]

Can you join my Spotify

[deep mango]

sure

[sonic field]

you cracked fr

[timid bronze]

Ok

[sonic field]

..

[jagged forge]

yup..

[timid bronze]

You're listening to this album

One sec

[deep mango]

wait

no im not doing it RN

i dont have my headphones nearby

[timid bronze]

THEN GET THEM

[deep mango]

im not getting out of bed

im sleepy

[sonic field]

dang were you actually gonna get ryc to finally sing

smh

[deep mango]

i dont even want to stay up for this dumb new year

[timid bronze]

Lazy ahh

[timid bronze]

Emo

[deep mango]

not that emo

[hidden isle]

do you feel your age mark

[deep mango]

just sleepy

[turbid sedge]

Hi fiscussy 2

Happy new year

[timid bronze]

I'm staying up to watch the date change

[deep mango]

and no im not "eepy" whatever that means

[turbid sedge]

It's not 2026 yet?

[timid bronze]

Idk what that means either

[turbid sedge]

Sleepy

[jagged forge]

yea

[timid bronze]

Not for me

[turbid sedge]

Holy backward time zone

[timid bronze]

Happy New Year

[turbid sedge]

Regressed time

[hidden isle]

really do you get back pains

[timid bronze]

Do I act like my age

[ocean harbor]

only one hour left

[turbid sedge]

Ay peak

Good luck staying up

[jagged forge]

no i just feel boredom

[ocean harbor]

thanks

[turbid sedge]

If we are to be honest you're better than the dumbasses out there

See this is unnecessary glaze

[hexed tangle]

Are you single

[timid bronze]

What

[hidden isle]

tm wants mark so bad

[turbid sedge]

I mean

[timid bronze]

How is this glazing lil bro

This is just a simple yes/no

[hexed tangle]

HELL NO

[turbid sedge]

When it comes to acting according to your age

[hexed tangle]

I'm straight

[turbid sedge]

y/n? Zamn

[ocean harbor]

what is tm

[turbid sedge]

Hi straight

[hexed tangle]

This man

[ocean harbor]

thank you

[timid bronze]

I was told it means "this motherfucker"

[deep mango]

this motherfucker / this man

[ocean harbor]

😭

[turbid sedge]

Is there a tw

[hidden isle]

tsm (this shit man)

[turbid sedge]

Csm

[hexed tangle]

You silly child

[sonic field]

THIS IS WHAT BOTHERS ME ABOUT THESE ACRONYMS

[timid bronze]

I'm not a child lil bro

[sonic field]

CUZ THEY BE MEANING DIFFERENT THINGS

and ppl be like
'read the context"

mofo

it can mean both USE YOUR WHOLE WORDS

[turbid sedge]

Just use it

[sonic field]

no.

[timid bronze]

I still don't understand "ts"

Is it "this" or "this shit"

[sonic field]

my brain is always literally like, which did they mean

https://tenor.com/view/flow-gif-5631704562545346741

[deep mango]

having multiple meanings is part of the appeal. using tm enables you to mke your sentence mean 2 things

[timid bronze]

Do any of your students use "pmo" via email

[sonic field]

you eat apple skins for breakfast

[sonic field]

thankfully not

[timid bronze]

"Your grading pmo"

[turbid sedge]

Ts teach lwk untuff

[sonic field]

if i got anything like that in email i honestly would probably laugh

[turbid sedge]

Probably.....

[sonic field]

continues grading

[timid bronze]

I can’t take people seriously when they say “pmo” but are actually pissed

[sonic field]

"ts tm pmo sybau"

[timid bronze]

LMAO

[ocean harbor]

🥀

[velvet dagger]

Ono

[pure hollow]

Non hilbert spaces doesn't exist.

[jagged forge]

breh

[pure hollow]

I would like to imagine a sane world

[jagged forge]

this would be defensible if u said banach spaces

[velvet dagger]

Yeahhh

[jagged forge]

even then frechet spaces exist

[velvet dagger]

L^p does not want to know your location

[pure hollow]

Ok this is fair

[hexed tangle]

https://tenor.com/view/hilbert-quantum-qft-physics-memes-goofy-ahh-pictures-gif-26860624

[fringe summit]

L^1 sucks but spectra of operators L^p -> L^p for p in (1,\infty) are chill

[hexed tangle]

L^1 is pathological

[fringe summit]

\infty \to \infty isn’t unsalvageable either

Sometimes

[severe turtle]

This just feels cursed without the actual latex formatting 😭

[fringe summit]

A lot will die because of reflexivity issues, but you can work by hand

[latent edge]

why is he doing the 67 thing

[jagged forge]

probability proofs be like. we prove this in L^p for p = 12, 2, and 1, where pain is inversely proportional to p

[timid bronze]

I accidentally scared my dad so bad

[fringe summit]

Well, by some heavier duty harmonic and functional analysis b.s., we have salvation in p \in (1,\infty) realm

[timid bronze]

I was trying to find him but stood still as soon as I saw him come out of the bathroom

[latent edge]

WEIIIIIIIIIIIIIIIIIIIIII

[timid bronze]

😭

[fringe summit]

Unfortunately you need to read specialized treatises but

[velvet dagger]

Something something interpolation?

[fringe summit]

Miraculously it works

[velvet dagger]

Oh hmm I guess not that easy

[timid bronze]

Ew harmonic

[fringe summit]

Not quite, we don’t have two values to interpolate

[timid bronze]

Get that word out of here

[fringe summit]

And interpolating linear operators tends to kinda cross over

Like 2 -> 2 but 1 -> \infty

For the fourier transform output moving contravariantly for p in [1,2]

Anyway, the issue is you’re starting with just 2 -> 2

And we magically want to pull p -> p out of thin air

[latent edge]

society if non abelian extensions were not a thing

[fringe summit]

Since we don’t have two endpoints to interpolate, contravariantly or covariantly, and uhhh extrapolation is VERY scary

[jagged forge]

what about music

[fringe summit]

We will uhhh magically extrapolate by praying and just using integral kernels

[latent edge]

proof tech: praying

[fringe summit]

Well, if you have magical conditions, they work

[hexed tangle]

Magical conditions

[sonic field]

smh

[fringe summit]

Namely, $\int_\gamma f(\lambda)(\lambda - A)^{-1} \dd\lambda$

[fathom swallow]

Sharp, Archon of Severing

[fringe summit]

Observe

This is $2\pi i f(A)$ as we know from complex analysis

[fathom swallow]

Sharp, Archon of Severing

[fringe summit]

And this always works with no issues

[latent edge]

mfs be like "observe" and they say the wildest shit ever

[fringe summit]

[timid bronze]

Music is fine

[fringe summit]

(You need a lot of work to make this work, and what f work, and what A work, etc)

[timid bronze]

I just mean in a math or physics context

😁

[fringe summit]

And, then, what is the norm of A

So, I will claim without proof that if A is an elliptic differential operator

[latent edge]

oh so you study ECs? proof:
The proof:

[hexed tangle]

https://tenor.com/view/panda-spinning-spinning-panda-giant-panda-cute-panda-gif-4148261905191282079

[latent edge]

THAT'S A LOT OF NOTES

[fringe summit]

Then: by prayers being answered, we know $\Vert f(A)\Vert\leq \sup_{Re(z)\geq \Lambda} |f(z)|$ for holomorphic $f$ bounded in that region

[fathom swallow]

Sharp, Archon of Severing

[fringe summit]

Why? Just fucking trust

[sonic field]

💯 LIKE RN

[fringe summit]

You really don’t wanna know

Now, as it turns out, $\Vert f(A)\Vert_{L^p \to L^p}\leq \Vert f\Vert_{L^\infty(Re(z)\geq \Lambda)}$ for $p\in(1,\infty)$

[hexed tangle]

I should use this in papers

[fathom swallow]

Sharp, Archon of Severing

[fringe summit]

Miraculous

[vast wraith]

i had a prof whose copy of greenberg’s euclidean and non-euclidean geometry was like this, she’s awesome

[fringe summit]

Turns out you’re chill at \infty to

For L^1: die

It fails

Straight up false

(Sometimes etc etc)

[fringe summit]

Well this is absurdly goofy stuff

[timid bronze]

This is him when somebody talks about oceanography

[fresh comet]

[fringe summit]

Anyway @velvet dagger it’s miraculous that spectra work out, I know how to make it work only assuming certain ellipticity assumptions, and proving that intermediary step is very very nontrivial apparently

Nontrivial enough I have seen whole appendices written about cases of it

In special nice settings

Fucking hell

Actual nightmare land

[velvet dagger]

Holy shit

When even the elliptic case is brutal...

[thorn wren]

which kind of spectra

[fringe summit]

Now, it being in an appendix isn’t a condemnation on its own

I mean, see appendices in early books

[thorn wren]

I hate that I can think of 2 that have an "elliptic" case

[fringe summit]

What makes it deadly is it’s a technical appendix in a specialized monograph

Specifically about these operators

I’m so fucked

[thorn wren]

oh like eigenvalues

[fringe summit]

Spectra of operators

Eigenvalue-ish

[fringe summit]

Lucky you: there are non-elliptic operators too

[latent edge]

tfw happy new year

finally

[solemn rivet]

6-7

[latent edge]

leave

[frosty scroll]

the server....is dead?

[solemn rivet]

He made a statement so trash 🗑️ even his gang clowned him 🫵😭

[frosty scroll]

He made a statement

[solemn rivet]

so trash

[sonic field]

you can just leave. thank you bye have a good year 😄

[solemn rivet]

This was tuff in 2025 😔

[timid bronze]

I forgot that I need to find a 2 credit class soon

Bruh 🥀 idk what to pick

I have my organic chemistry textbook now

[sonic field]

tfw u see 69/70 seats filled

[pastel needle]

Fuck

Which discussy is which

[slow pier]

This is 2

[slow pier]

Newton as a unit is definitely a green flag

[sonic field]

GET OUT OF MY DISCUSSY

https://tenor.com/view/slam-door-walk-away-fighting-angry-annoyed-gif-13863907

[hexed tangle]

Pandussy

[latent edge]

real

[timid bronze]

I couldn't fucking find a 2 credit class

So I went for a 3 credit one

😭

2 online classes and 3 in person

:p

[sonic field]

go ahead and pull that calendar out

[latent edge]

this is basically chemistry if u think about it

[timid bronze]

I can handle 16 credits at least

17+ credits I die

My friend did 24 and got all As

Idk how she did it

[sonic field]

i see an illegal symbol up there

[hexed tangle]

Also reminds me of wheat stone bridge

The structure

[latent edge]

is it over if the girl im texting has a book on cohomology of number fields

[timid bronze]

Why do I get the SAME physics textbook for physics II 🥀

[hexed tangle]

Cooked

[sonic field]

o that's how it is usually

the ones you need to watch out for

are those mofos who use different books

[latent edge]

which

[sonic field]

cuz you know some stuff bout to drop

[timid bronze]

I hate the textbook we use though

[latent edge]

oh yeah fixed

[timid bronze]

The format of it is so silly

[hexed tangle]

Ally is silly

[latent edge]

true

[sonic field]

you took the left parenthesis out?

[latent edge]

i wonder what field is real
draws the entire diagram
ah this one

okay ally so basically if you ignore Q(sqrt(2))

You get a square right

[timid bronze]

Let me show the cl*sses I'm registered for in a second

[latent edge]

This describes the symmetries of whatever compound has a square shape

actually keep the qsrt2

this is more or less XeF_4?

lmao

[timid bronze]

What are the group axioms in this case

[latent edge]

the square?

or for each field?

I can talk about each field it's more interesting that way

For Q(zeta_8) you have (Z/8Z)^x = {1,3,5,7}. So you are taking these numbers under multiplication modulo 8

[timid bronze]

@sonic field You know the other 2 cl*sses, but the electives I signed up for are:
Bioenergy & Renewable Systems
Epidemics, Agriculture, and Civilization
Modern Food Safety & Technology

Ngl I'm kind of excited for the first one

But yeah

[fringe summit]

[timid bronze]

I won't lie, I renamed the classes so some weirdo won't try to find the school I attend

[sonic field]

man bioenergy and renewable systems sounds SO BOMB

[timid bronze]

🤣

[timid bronze]

I can send you the course description

Check your pings in a bit

[sonic field]

K

[latent edge]

anyways going back

[timid bronze]

Dumb question but what does zeta_8 mean

[timid bronze]

Sorry for getting sidetracked

[latent edge]

https://en.wikipedia.org/wiki/Root_of_unity

in this case it's the 8th root of unity

Notice that 3^2 = 1, 5^2 = 1, 7^2 = 1 mod 8

All of these are in {1,3,5,7}

This means we can take each element and make a subgroup out of them

For example, <3> = {1,3}. 3^1 =3 , 3^2 = 1 mod 8 and it cycles as you add more powers so that's it

<5> = {1,5}, <7> = {1,7}

same story

all of these sit inside {1,3,5,7}

We can take the trivial subgroup {1}. This one is valid too

So overall we have 1 big group, 3 subgroups with 2 elements and a trivial subgroup

you can draw a picture of these things as a hasse diagram

[latent edge]

It's this but flipped (although in this case it doesn't matter because it is symmetric)

[hexed tangle]

Indeed

[timid bronze]

Ok

How do I know if a set is open or closed

[latent edge]

how is this related to what i said

[weak karma]

Hey guys i want to wish you all a happy New Year. Discord is full of copypasted messages, that people don't even read and just forward to other servers. I like to write what comes from my heart. Our friendships, from the are very important and will never be represented by a simple message copied from elsewhere. I would like to thank all of you. You are the best Minecraft Discord server I've ever been on. Lots of love.

[latent edge]

Now the real question is whether or not this message is a copypasta

[slow pier]

Just like this one

[timid bronze]

I've seen discussions on open and closed sets in the channels with topics that seemed similar to this (so I thought there would be relation), sorry. I semi understand what you're saying, but I don't have anything to say that would provide a productive discussion besides me asking more questions

[latent edge]

i mean it's fine I don't mind questions

Closed or open is related to this but I feel like it's not a good idea to talk about it

For this discussion I'm talking about set inclusion

is {1,5} a subset of {1,3,5,7}?

[timid bronze]

I think so

[latent edge]

right yeah

is it clear btw what I mean by multiplication modulo 8?

[timid bronze]

Yeah, you just perform the multiplication and subtract 8?

[latent edge]

wdym by subtract 8

[timid bronze]

I don't know, that's what Google told me 😭

[latent edge]

you divide by 8 and take the remainder

That's what I mean

for example 9 has remainder 1 when divided by 8

or another way to see this: 9 is 1 more than a multiple of 8

in general you take your number n and express it as n=8k+r for some k. the number r is the result you get upon taking n modulo 8

so 9 = 8(1)+1 so 9 modulo 8 is 1

[timid bronze]

Okay

[latent edge]

right we can make a group out of this business. You fix a number n then look at numbers below n that are relatively prime to it

well by "below n" I mean the range 1<= k < n

For example n=8
1,3,5,7 are relatively prime

2 is not because 8 = 2^3 so it shares a 2 therefore not relatively prime

Same story with 4 and 6

So overall you have {1,3,5,7}

Here's a question for you. List the elements for n=7

[timid bronze]

Going to need a bit for this but 1 surely has to be one of them right.....

[latent edge]

yes

In fact 1 is always there

[latent edge]

what numbers in 1 <= k < 7 share no prime with 7?

well 7 is prime so...

[timid bronze]

;-;

[latent edge]

right yeah

[sonic field]

you know everytime someone asks this question, i'm SO tempted to share my top troll book 🤣

[timid bronze]

I try man ;-;

Not like ik any of this

I already have to do a ton of googling for some of the definitions and symbols xd

[sonic field]

here, all u need is this passage

[latent edge]

yeah anyways that's it. I'm taking a group and writing out all subgroups

Galois theory then will give a correspondence to number fields

[timid bronze]

Taco sets is crazy work

Wait

You wrote this bruh

[sonic field]

yeah LOL

[sleek cape]

HAPPY HALLOWEEN 🎃

[latent edge]

There's something deeper that goes on when the group is the one we talked about

[latent edge]

mamma mia

[timid bronze]

Pure math is genuinely so complicated

Idk how you crackheads do this

I would not survive a day in this 😭

[sonic field]

girl ain't nothin complicated about tacos 🤣

[sleek cape]

I was talking to the biology and chemistry people and I think that if we consume meth for 81 days and take Narcan we become zombies.

[timid bronze]

Do you foodify all your math teachings

I'm serious though

[latent edge]

(Z/nZ)^x happens to be isomorphic to something called the the Galois group of Q(zeta_n) over Q denoted as Gal(Q(zeta_n)/Q)

[timid bronze]

Y'all are genuinely so damn cracked.

I fear I'll stay in applied math

My brain cannot 🧠

[sonic field]

you should see some of the games we play in class LOL

[latent edge]

if you do basic galois theory this says nothing deep really

BUT I claim there is something deep

[fresh comet]

I love this LOL

[last rose]

diamond$Gal (mbb Q(zeta_n)/Q); cong ; (mbb Z/n mbb Z )^\times$

[fathom swallow]

Oléagineux Distilliànus VIVII

[last rose]

just here to flex my latex bye

[timid bronze]

I fear I'm not smart enough to understand though

[latent edge]

https://tenor.com/view/absolute-cinema-absolute-cinema-femrover-rover-gif-14890473560168326644

[timid bronze]

Now I want to see how you teach diff eq to the kids

Do you foodify your teachings there too

😭

Let me join your diff eqns class since I'm not taking math next semester!

[sonic field]

i be comin up with all kinds of crazy stuff

we had the laplace transform guild association last class

[timid bronze]

Lap- what?

Nvm, I'm dropping the class before I even register for it

[latent edge]

The identification you do for the isomorphism is k -> zeta_n^k

[sonic field]

🤣

[latent edge]

In particular if you look at when k is prime

that's where shenanigans happen

[timid bronze]

So is this the galois group

[last rose]

diamond$(mbb Z/n mbb {Z})^\times ;xrightarrow{\ sim\ }; {Gal}( mbb Q(zeta_n)/ mbb Q)$

[fathom swallow]

Oléagineux Distilliànus VIVII

[latent edge]

yes the elements in Gal(Q(zeta_n)/Q) are maps sigma_k where you send zeta_n to zeta^k_n

you raise to the k power

[last rose]

diamond$k longmapsto sigma_k, quad sigma_k(zeta_n) = zeta_n^k$

[fathom swallow]

Oléagineux Distilliànus VIVII

[slow pier]

Wow

[sonic field]

omg your LaTeX looks so gorgeous

[latent edge]

thanks pure

[sonic field]

oh that's pure?

NO WONDER LOL

[latent edge]

yup ofc

lmao

[timid bronze]

I'm going to be sending an email tonight

[latent edge]

even if they change their pfp/name I can still recognize them from their messages

[last rose]

is that right

[latent edge]

yes i think so

[sonic field]

pure bout to flip the script fr now

[last rose]

i suppose FMTB is a big giveaway

[latent edge]

yeah ig

[timid bronze]

Is this what you enjoy studying most

[latent edge]

pure u gotta teach me your ways

[last rose]

start by practising portmanteauing

[timid bronze]

I have seen you talk about Galois a few times in the server xd

[latent edge]

lmao

[latent edge]

it's because the simplest case which is somewhat "presentable" to a layman

[timid bronze]

I'd mayybe consider taking discrete math at MOST if my calc 1/2 professor was teaching it

I still miss him

😔

[last rose]

[last rose]

what is that thing

[sonic field]

i'm tryin to find an opportunity to carve out my analysis texts. i need a semester where I'm straight teaching calc 1 series +

but I keep getting them in parts

and i always gotta teach calc 2 smh

[timid bronze]

You don't pick what classes you get to teach right?

[sonic field]

nah, we have little say in it

[timid bronze]

Aren't you also teaching calc 3 this semester

[sonic field]

not sure yet, it's possible. that one is actually my choice, idk if i want to yet

[timid bronze]

Oh

[last rose]

moice

[timid bronze]

Stokes theorem better not show up ever again

[latent edge]

pure can u do Gal(Q(zeta_n)/Q) -> C^x and (Z/nZ)^x -> C^x then attach these in a communist diagram

[timid bronze]

Wtf was that shit

💔

[sonic field]

LOL

[last rose]

communist

[latent edge]

yessir

[sonic field]

we definitely have stokes for sure

[last rose]

[timid bronze]

That was the last thing we did

[last rose]

uhm

i'll give you a commutative diagram

[sonic field]

yall didn do divergence theorem last?

[timid bronze]

We did like divergence of a curl

But that's all I remember

I already forgot what we did in that class

[latent edge]

$
[
\begin{tikzcd}
\operatorname{Gal}(\mathbb{Q}(\zeta_n)/\mathbb{Q})
\arrow[r, "\sim"]
\arrow[dr, "\psi"']
& (\mathbb{Z}/n\mathbb{Z})^\times
\arrow[d, "\chi"] \
& \mathbb{C}^\times
\end{tikzcd}
]
$

[fathom swallow]

nDeltoid

$
\[
\begin{tikzcd}
\operatorname{Gal}(\mathbb{Q}(\zeta_n)/\mathbb{Q})
\arrow[r, "\sim"]
\arrow[dr, "\psi"']
& (\mathbb{Z}/n\mathbb{Z})^\times
\arrow[d, "\chi"] \\
& \mathbb{C}^\times
\end{tikzcd}
\]
$
```Compilation error:```! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.61 \[
       
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.```

[latent edge]

absolute cinema

[sonic field]

this

[silent junco]

wait why did the error thing open

[agile fiber]

remove the $ and the \[

[last rose]

<tikz-cd>royalgold$\begin{tikzcd}
( mbb Z/n mbb Z)^\times
\arrow[r, "\sim"]
\arrow[dr, "\psi"']
&
Gal big(mbb Q(\zeta_n)/mbb Q\big)
\arrow[d, "varphi"]
\
& mbb C^\times
\end{tikzcd}$

[timid bronze]

Yeah, we didn't do this

[silent junco]

oh yeah oops sorry

[sonic field]

interesting 👀

[fathom swallow]

Oléagineux Distilliànus VIVII

[latent edge]

i dont like the background

[last rose]

tsk

<tikz-cd>gold$\begin{tikzcd}
( mbb Z/n mbb Z)^\times
\arrow[r, "\sim"]
\arrow[dr, "\psi"']
&
Gal big(mbb Q(\zeta_n)/mbb Q\big)
\arrow[d, "varphi"]
\
& mbb C^\times
\end{tikzcd}$

[latent edge]

this one is a lot cooler

[fathom swallow]

Oléagineux Distilliànus VIVII

[silent junco]

tbh this kind of gradient is always hard to get right

[latent edge]

hell yeah

[silent junco]

but i like this one better

[sonic field]

if math books were like this, i could read this ALL DAY

[last rose]

hmm I shall improve the gradients

[timid bronze]

Parameterizing (however tf you spell) line integrals was so stupid though

Why do we need to do all of this work

🥀

[silent junco]

i forgot everything i learned in calc 3

[latent edge]

i think I know how to get gradient stuff in latex

[timid bronze]

Calc 3 is the only calc I actually understood

[silent junco]

and now im relearning it in diff geo

[timid bronze]

Calc 1/2... Nope..

[sonic field]

that's why i hate teachin git, i need a few classes up for it to stick but everytime i teach it i always have to reteach myself. i don ever forget stuff in DE

[silent junco]

right

[timid bronze]

DE sucks

Too hard!

[silent junco]

like i took calc 3 twice, once in hs and once in college. both times i was in a particularly vulnerable stage in my life and barely passed

[timid bronze]

I hope things are better now

I'm sorry to hear

[silent junco]

thanks, yeah they are

[sonic field]

feels fr that's kinda how my calc 3 went tbh when i had it, i did good on the back end and pulled a B out

[sonic field]

naur

wait cuz now

[timid bronze]

THEY ARE

[sonic field]

you can do higher orders

[timid bronze]

DON'T GIVE ME A PROBLEM

NO.

[sonic field]

LOL

i got one waitin, it's fine. i can give it to you tmrw

[timid bronze]

My brain is already burnt by these questions so I cann't do any DE rn ;-; (btw thanks Deltoid for the teaching despite me failing miserably lmao because I'm slow)

[timid bronze]

;-;

Okay

[silent junco]

tbh i dont think an odes course is conceptually any more difficult than calc 3. in fact its easier imo, you just memorize a bunch of rules and learn how to apply them.

[sonic field]

yeh p much you just use the same mofo ansatz over and over again

[latent edge]

wdym just memorize this diagram

[sonic field]

till your de look different then u use subs then do the ansatz or a different one

[latent edge]

literally all of calculus 3

[sonic field]

i'ma show them this next class

gonna be on test 3

[latent edge]

no worries it's almost 2 am lmao

[hexed tangle]

Should I try making this in texit

[latent edge]

hell yeah

[timid bronze]

You are deaddddddddd wrong.........

[latent edge]

then do the pure shenanigans

[timid bronze]

My ODE calc 2 midterm cooked my ass tf up.

I was burnt, toasted, crippled.

Calc 3 went a whole lot better for me

Lmao lemme pull up my midterm 2 grade

Right at the median bro

[silent junco]

huh thats not even that bad lmao

[last rose]

<tikz-cd>diamond$\begin{tikzcd}[column sep=4.6em, row sep=4.2em]
Omega^0(mbb R^3) \arrow[r, "d"] \arrow[d]
& Omega^1(mbb R^3) \arrow[r, "d"] \arrow[d]
& Omega^2(mbb R^3) \arrow[r, "d"] \arrow[d]
& Omega^3(mbb R^3) \arrow[d]
\
C^\oo(mbb R^3; mbb R) \arrow[r, "nabla"]
& frak X(mbb R^3) \arrow[r, "nabla \times"]
& frak X(mbb R^3) \arrow[r, "nabla \cdot"]
& C^\oo(mbb R^3; mbb R)
\end{tikzcd}$

[fathom swallow]

Oléagineux Distilliànus VIVII
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[silent junco]

$\oo$

[fathom swallow]

rays
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[timid bronze]

YES IT IS 😭

[last rose]

hm ignore the too many alphabets error

[fathom swallow]

Achilleus

[sonic field]

they are categorically CRAZY

[turbid sedge]

hi fiscussy 2

I have returned

[latent edge]

peak

[last rose]

https://tenor.com/view/peak-mountain-top-mountain-mountain-range-wind-gif-12834632201688728871

[latent edge]

I did better on my year 4 math courses than my second year ones

[timid bronze]

Praying life gets better for me

[latent edge]

the reason for this is the second year courses just absolute suck

[timid bronze]

Tell me about it 😭

I don't have a fucking damn A in any science/math class, they're all Bs

[latent edge]

you go to the midterm and you have to compute gauss elimination for big matrices in every fucking question for 3 hours

[timid bronze]

It demotivates me because I'm really trying

[latent edge]

it's exhausting

[timid bronze]

Ikr

Wait

You're going to be a senior next year right

[latent edge]

yeah

[timid bronze]

God damn unc

[latent edge]

unc status fr

[turbid sedge]

this

[last rose]

wot

[turbid sedge]

Just grind son

[last rose]

you dare pong the great cooly

[timid bronze]

Don't tell me to grind bro

I've grinded too hard

☠️

[turbid sedge]

Oh...

Im a fat bum I cant relate to ts

[timid bronze]

Huh

What does your physical appearance have to do with grades xd

[hexed tangle]

Ally is a silly

Willy

[turbid sedge]

Oh nah

I mean

Fat bum is synonymus to a lazy person

[timid bronze]

I'm a WHAT

[latent edge]

in upper year classes the questions become more abstract and less computational

[hexed tangle]

Willy wanka

[timid bronze]

You're definitely drunk

[hexed tangle]

Yk i went to 3 parties

[timid bronze]

My nightmare

[turbid sedge]

verification

[timid bronze]

Drunkie

[latent edge]

It's actually not

[hexed tangle]

I can still do papers while being drunk

[timid bronze]

How many drinks did you have lil bro

[turbid sedge]

Good shit atleast I dont have to calculate the residue of some 1/sinz for no reason

[latent edge]

performance 🔥

[turbid sedge]

is that a skill

[hexed tangle]

https://tenor.com/view/i-am-the-milkman-milkman-psychonauts-milk-delicious-gif-15360002

[turbid sedge]

yes it is

[turbid sedge]

This would do numbers in 2025

[hexed tangle]

3-4

[turbid sedge]

no more mr nice guy

[turbid sedge]

beer?

[timid bronze]

Ik someone irl who takes tequila shots before an exam

[latent edge]

yeah in upper years the questions are like "prove X is isomorphic to Y" or "provide a counterexample"

[timid bronze]

Apparently it helps her focus

[hexed tangle]

Wine

[turbid sedge]

I guess bro....

I dont like being tipsy before exams

[timid bronze]

Bro, I was considering cutting out COFFEE before exams

[turbid sedge]

counterexamples are either too trivial or too deep

[timid bronze]

But I do that anyway since I'm on ADHD medication

[silent junco]

i used to do ts

[timid bronze]

😊

[turbid sedge]

thats tuff

[latent edge]

but yeah at the end of the day getting good grades is somewhat a gamble

[silent junco]

i didnt do very well, of course

[hexed tangle]

I be like magnus Carlos after being drunk

[timid bronze]

Must be difficult as hell

[timid bronze]

Bro why..

[turbid sedge]

didnt you say something about being drunk while attempting your hist paper

[silent junco]

idk i was stupid

[timid bronze]

You aren't stupid

[silent junco]

oh yeah i did

[timid bronze]

What is 2+3

[turbid sedge]

23

[timid bronze]

Ikr

[latent edge]

One of the people I know does drugs before exams and it helps them focus

[turbid sedge]

oh naw

[late fossil]

yoo

wsp

[latent edge]

i mean erdos was famous for doing something similar lmao

[hexed tangle]

$$
\dim_{\mathbb Q} H^1\big(\mathbb{P}^1 \setminus {0,1,\infty}, \mathbb Q\big) +
#{ \text{primitive 5th roots of unity in } \mathbb{C} } = 5
$$

[fathom swallow]

Achilleus

[latent edge]

real

[timid bronze]

The moment you said that, the song I was listening to mentioned drugs 🥀

[latent edge]

must've been the wind!

[late fossil]

agreed

[timid bronze]

Labubu comes back to haunt you

[timid bronze]

.

You're extra as fuck.

[turbid sedge]

we ALL have that one homie who beats up people before the exam

[turbid sedge]

Preuni math🥀

[timid bronze]

Girl what

[late fossil]

yuh

[timid bronze]

Do I need to call the cops..?

[turbid sedge]

my bad I stopped farming midway

[turbid sedge]

NO

[fathom swallow]

Achilleus

[late fossil]

yep

[hexed tangle]

MY WIFE IS MEAN TO ME

[latent edge]

casually pulling up the trace

[timid bronze]

This reminds me of vocaloid

[shell canopy]

HI👋

[timid bronze]

You're married?!

[sonic field]

OMG

my pork chops are so fkin tender

[hexed tangle]

Yes back in 1980

[sonic field]

i did exactly what that lady said and it worked

[timid bronze]

Unc ass

[turbid sedge]

Yash is a wife beater

[timid bronze]

Did you season your pork chops?

[neat lintel]

Hi all

[shell canopy]

HI👋

[latent edge]

,w 2026-1980

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by despairful_deltoid

[shell canopy]

Bruh these bots ....

[hexed tangle]

Nooo she beats me

[timid bronze]

Bro is TOO drunk

Achilleus go to sleep

[turbid sedge]

"waiter, my steak is too juicy and my lobster is too buttery!"

[latent edge]

what are u drinking btw

malt?

[turbid sedge]

We ALL want abusive wife

[latent edge]

no?

[turbid sedge]

dont sully me....

[neat lintel]

Nah, I want a lovely wife

[shell canopy]

Yeah mee too

[turbid sedge]

thats her love language

[hexed tangle]

A lot of stuff

[timid bronze]

Are you one of this TikTok kids that crave toxic relationships

[hexed tangle]

A*

[turbid sedge]

do NOT lump me with them

[hexed tangle]

I will sleep now

[neat lintel]

She better don't love me then

[hexed tangle]

https://tenor.com/view/sung-jin-woo-gif-12908384644153191582

[latent edge]

gn

[timid bronze]

You are one of them

[timid bronze]

Finally, shoo

Night

[neat lintel]

Gn

[dapper rose]

Meow

[turbid sedge]

I been an og here

[shell canopy]

Finally

[turbid sedge]

🥀

[shell canopy]

Really??

[turbid sedge]

anyway

topic change

[shell canopy]

Okay✨

[neat lintel]

Okay

[timid bronze]

[sonic field]

i sure did

[shell canopy]

Btw I'm new to this group can u guys tell me ur name's??

[timid bronze]

With what.

[sonic field]

ok i want you to guess on this one too

[timid bronze]

You seem afraid of seasonings

So I'm going to say water

[neat lintel]

No

[timid bronze]

Jk 😂

Let me think

[turbid sedge]

come back son I've sealed my inner desires🥀

[shell canopy]

Okay

[versed jungle]

discussion 2026

[timid bronze]

Salt & black pepper

and

Paprika
Thyme
Rosemary
Cumin
Garlic Powder

I feel like you'd use those 😭

Please tell me I'm close.

[sonic field]

salt, pepper, garlic and red pepper flakes

[timid bronze]

...

I'M DISAPPOINTED

[sonic field]

you'll be alr

[timid bronze]

THAT is barely any seasoning

[latent edge]

wait what

let me google

[timid bronze]

You definitely graduated from ryc culinary school

[timid bronze]

What

What are you googling

[latent edge]

oh this

[sonic field]

wtf is that worms??

[latent edge]

cumin

[timid bronze]

...

OK NAH

THIS IS A VIOLATION

[shell canopy]

What's ur plan for 2026??

[shell canopy]

🤣😂

[sonic field]

why is it zoomed in SO CLOSE

my cumin don look like that smh

I SAW THAT

[timid bronze]

LMFAOOO

[latent edge]

saw what

[sonic field]

o cuz it's a seed

nothin

[latent edge]

im ngl cumin is such an unfortunate name

[sonic field]

y

[latent edge]

i dont like it

[sonic field]

oh alr then

racist against cumin smh

[timid bronze]

Maybe's he's the real T######

[latent edge]

how do u say this word

[sonic field]

cu min

wym

like coomin

[timid bronze]

WHAT?

I say queue~min

[turbid sedge]

??

[sonic field]

ya that's how i've always heard it pronounced

yeh that's actaully closer

[latent edge]

i was saying kyuumin

[sonic field]

SEE I WAS RIGHT

[latent edge]

this does not make it sound better 😭

[hexed tangle]

CUMIN

[timid bronze]

DO YOU NEED ME TO SEND A FUCKING VOICE MESSAGE

I SWEAR MINE IS CORRECT

[latent edge]

NO PLEASE STOP

[hexed tangle]

Ally's voice is cute tbh

[silent junco]

queue min

[hexed tangle]

Be appropriate

I'm drunk and more appropriate than you

[sonic field]

bro let his inner thoughts win

[latent edge]

yeah im not letting my inner thoughts win at 2:30 am

[shell canopy]

Brotha I'm appropriate

[sonic field]

that wasn't even grammatically appropriate 🤣

[shell canopy]

Okay 👍👍

[timid bronze]

ANT is bad
NT is bad
Combinatorics is bad
Functional Analysis is bad
Group theory is bad
Probability is bad
Representation theory is bad
Spectral theory is bad
@velvet dagger

What you get for that DM you sent.

[latent edge]

what did the ants do to u

[sonic field]

somehow dami managed to curse all of mathematics with one rick roll

[timid bronze]

Analytical Number Theory

Is that different from Number Theory

🤣

[latent edge]

cute creatures

[timid bronze]

OMFG

**

**

NO

PHOBIA

NO

**

**

[shell canopy]

Yeah fr

[latent edge]

it's literally number theory it says it in the name

[hexed tangle]

Dami is a kind soul

[timid bronze]

Idk, there's a diff between Geometric Algebra and Algebraic Geometry, so I asked

[shell canopy]

ANTS ARE CUTE ✨

[timid bronze]

No

Stop with this shit

[latent edge]

ok spiders are cute tho

they are my fav

[timid bronze]

NO

[turbid sedge]

LMAO

[timid bronze]

OK I'M LEAVING THIS CHAT, GOODBYE

[shell canopy]

Yes

[sonic field]

nah no difference jus don say this at conferences

[hexed tangle]

You left your shoes

[velvet dagger]

Hi LEAVING THIS CHAT, GOODBYE
I'm Dami

[shell canopy]

Tarantulas are soo cutie pies ✨✨

[hexed tangle]

I'm so drunk goddddd

[sonic field]

you don lost yo mind

[latent edge]

https://tenor.com/view/spider-scary-sleeping-huge-sleep-gif-6188742989761831337

[sonic field]

bout to block you fr

[timid bronze]

Ok, I'm blocking you Deltoid

[latent edge]

wilted rose

[shell canopy]

Sorry just joking bro

[timid bronze]

You too

[shell canopy]

Why u have phobia to ants

[hexed tangle]

Do you know ally is a fish irl

[turbid sedge]

ally what your blocklist count now

[timid bronze]

Spiders make me cryyyyyyyyyy

I scream and have my brother take care of them for me

Or my dad

[turbid sedge]

holy shit man up

[latent edge]

fwiw I had a tarantula

[sonic field]

there's no reason for anything to be THAT poisonous

[shell canopy]

Why😥

[turbid sedge]

man up ally

[timid bronze]

🐟

[timid bronze]

Syfm

They're fucking scary

[turbid sedge]

resisting my urge to ragebait

[timid bronze]

I

[sonic field]

WUT U HAD NEED ONE OF THOSE FOR?? and what happened to it 👀

[timid bronze]

Got a <50% on a bio test (and refused to retake it) in HS because

[latent edge]

it died : (

[timid bronze]

It included pics of spiders in them and

I just clicked thru the answers

[turbid sedge]

based we ALL hate bio

[timid bronze]

Because I didn't wanna look at the pics on accident

😭

[shell canopy]

I also have an tarantula

[turbid sedge]

yeah ally you aint good son

[sonic field]

no you dont

[shell canopy]

Yeah I have in black color

[timid bronze]

Bro who needs a pet spider

[shell canopy]

Meee

[timid bronze]

Alr I'm blocking you too

[turbid sedge]

WHAT

thats racist

[latent edge]

I DO

They are genuinely nice

[turbid sedge]

I kill spiders indiscriminately

[timid bronze]

Hopefully I won't see any sp*der pics.

😄

[latent edge]

wilted rose

[turbid sedge]

thats racist

[latent edge]

tfw racism against spiders

[sonic field]

there is NOTHING you can do to convince me spiders are nice, i don got bit by a recluse and have been attacked my multiple widows

no racism THEY STARTED IT

[turbid sedge]

https://cdn.discordapp.com/attachments/1441200134401691860/1455440850287988756/q5rj7f6tj9rmy0cvdqb8yszss4_result__1.gif

[timid bronze]

So D*ltoid had a pet spider?

[latent edge]

okay yeah widows are evil sure

[jagged forge]

jay continuing the cycle of hatred… nothing ever changes

[shell canopy]

Sorry for annoying y'all

[latent edge]

They are widows for a reason

[timid bronze]

Tbf

[sonic field]

i do NOT care. you know spiders smarter than humans. those mofos sit on a wall for 72 hours lookin at you, you know they know your whole lifestyle and everything, there is no excuses

[timid bronze]

I haven't seen a huge spider in-person for years

But

[pure hollow]

Burn the cycles of homology.

[turbid sedge]

black widow

[timid bronze]

If I did any time now... I'd jump out my window

[latent edge]

tfw cycles over boundaries

[timid bronze]

Or burn myself alive 😄

[turbid sedge]

Ally blocked us for having a spider talk and shes still on this spider shi

[pure hollow]

Truly

[turbid sedge]

discrimination

[shell canopy]

PLS CHANGE TOPIC👍✨

[latent edge]

ally silly willy

[latent edge]

alright let V be a smooth projective variety of genus 1

[turbid sedge]

If it was another server, I'd have barged a canon of hate speech on you

[shell canopy]

Bruh😂

[turbid sedge]

you're safe here

[sonic field]

@jagged forge who spreadin the cycle 🤣

[pure hollow]

Boiiii ts tuff 😂 ✌️

[timid bronze]

Do you guys have new years resolutions

[turbid sedge]

YES

[pure hollow]

Survive

[sonic field]

dang bro it jus started 👀

[pure hollow]

Ts true

[sonic field]

u gud??

[pure hollow]

I have more cs next semester

[stuck crown]

I think i’m full of bitchiness in 2026 but i will not let it overcome me

[pure hollow]

The lab reports will be the death of me

[timid bronze]

Happy New Years to all college students
May our GPAs recover 🙏

[pure hollow]

Truly

[turbid sedge]

https://tenor.com/view/clash-royale-clash-of-clans-goblin-green-wah-wah-wah-gif-2173721757992636770

[latent edge]

may I get to publish something this year

[stuck crown]

I will be rich and happy

[timid bronze]

@sonic field

Are they done talking about spiders

[stuck crown]

And fat of course because skinniness is useless

[timid bronze]

Before I unblock

[timid bronze]

Hi Convy

[pure hollow]

Rep theory brainrot?

[sonic field]

yeh

[latent edge]

yes

[pure hollow]

Hello ally :3

[turbid sedge]

NO

[pure hollow]

Is NT related?

[latent edge]

no

[timid bronze]

I opened Lichtbatch's messages and they said "no"

[latent edge]

if it was I would be thriving by then

[timid bronze]

So I assume they're still talking about spiders?

[pure hollow]

Fair

[timid bronze]

Going to keep them blocked

[turbid sedge]

NO

I MEAN

weong reply

[pure hollow]

We be blocking licht before 2005 fr

[latent edge]

yeah when semester ended

my prof sent me an email "btw wanna work again"

🥀

[hexed tangle]

My wife is a spiderrww

[timid bronze]

@jagged forge told me about how one of his hats on Roblox is older than @solar hawk

😂

[turbid sedge]

whos WE

[hexed tangle]

Suremark plays roblox?

[turbid sedge]

convy you been my d1🥀

[hexed tangle]

I'm disappointed

[timid bronze]

WHEN ARE YOU GOING TO SLEEP

[hexed tangle]

I can't fall asleep

[timid bronze]

We all play Roblox I fear

[timid bronze]

:(

[jagged forge]

my 2007 visor is older than amukh yes

[latent edge]

who plays Roblox in the big 26

[timid bronze]

LMFAO

[turbid sedge]

anyone

how to comfort my hg she got dumped rn

[timid bronze]

@velvet dagger Can you get your monitor fixed

[turbid sedge]

serious question