serious-discussion

[torpid bay]

q_psi i viewed as a complex scalar, which psi as a complex vector, so a dot product wouldn't work, while the pseudo dot above does something similar but instead works over the real and imaginary parts rather than over the vector parts

[zealous garden]

Very odd

what is M?

[torpid bay]

oh

[zealous garden]

is M=B\gamma?

[torpid bay]

M = B

oop

[zealous garden]

Here's Joot's answer

[zealous garden]

T is the energy momentum multivector. Scalar part is the energy, Vector part is the momentum (divided by c).

[torpid bay]

whats the daggers?

[zealous garden]

I'll double check, but they should be reversion

There's not much use in G^3 for involutions other than reversion

main involution and clifford conjugation are far less frequent

[torpid bay]

my thing essentially does like (0,3) multivector times (1,2) multivector = 01 + 23 multivector

[zealous garden]

huh

wtf

tyg

[zealous garden]

alarm bells should ring

[torpid bay]

my alarm bells a wee bit slow

lemme write it out

[zealous garden]

The general geometric product between a k-vector and j-vector has terms of grades
|j-k|, |j-k|+2, |j-k|+4, ..., j+k

what happens if j=2 and k=3?

[zealous garden]

When you're done: ||Now what happens if the space is of dimension 4 or fewer?||

Unless you wanted that ||It's necessarily a vector, maybe you did now that I re-read things||

Reading through this, I'm reminded why I don't like physics

[zealous garden]

A different, delayed, alarm bell rang

This maintains the direction of the magnetic (pseudo)vector field doesn't it

But that's not the direction that the magnetic field will push a particle

[torpid bay]

the 1 part does,the wedge part wont?

[zealous garden]

This looks like it maintains the direction of B to me

[torpid bay]

yeah that does, but the equation before it has extra stuff

[zealous garden]

What is v

Velocity?

[torpid bay]

velocity of charged particle ye

it's pretty much taken from the usual maxwells, just modified a bit

[zealous garden]

so v^E will turn E into a (possibly 0) bivector field, and v^B will turn B into a (possibly 0) trivector field

But I think you want the bivector to turn into a vector term right

For forcing purposes

Where did you get the wedge from?

[gray glade]

forcing...

[torpid bay]

this was before i knew about GA, so the only reason its there is to replace cross product, i didnt undesrtand grades before

[zealous garden]

I'm guessing you thought "commutator->wedge"

This is only true if the arguments are 1-vectors

The proper cross product interpretation is as the commutator product

[torpid bay]

lemme take a lookt at my paper hold up

[zealous garden]

The commutator of two vectors is the wedge, which makes a bivector

The commutator of two bivectors, is a bivector!

(Just like the cross product of two pseudovectors is a pseudovector)

Fun fact, the commutator of any k-vector and a bivector, is a k-vector

[torpid bay]

ah here it is

original complex number formulation

$\vec{F} = k_{em}q_\Psi \cdot(\vec{\Psi}+\gamma\vec{\Psi}\times \frac{\vec{v}}{c})$

[fathom swallow]

Yeatte

[torpid bay]

what i heard vback then is just wedge = i cross

so i put it in

[zealous garden]

Ah

Cross product indeed is the dual of the wedge product, between vectors. If you have a pseudovector as an argument it's different

The commutator of a bivector and a vector, also known as the contraction or dot product between them, yields the vector projected onto the bivector, then rotated 90 degrees within the plane of the bivector

So thinking about it. We have a pseudovector, and a vector, then we project the vector onto the orthogonal complement of the pseudovector, then rotate it within this space until it is also orthogonal to its projection (and thus itself)

So this contraction, no imaginary number added, is the cross product

At least up to sign, I'm not sure about sign here

[torpid bay]

ig ill show the temporary curl notation i had to notate specifically acting on ijk instead of anything else

as well as that switching of E and B in the E+B gamma thing

,, E+B\gamma = \Psi_1 \ B+E\gamma = \Psi_2 \ q_\Psi_1 = q_e + q_m\gamma \ \text{etc} \ -c\gamma\nabla_{ijk}\times \Psi_1 = J_{\Psi_1} + \pdv{\Psi_1}{t}\c\gamma\nabla_{ijk}\times\Psi_2 = J_{\Psi_2} + \pdv{\Psi_2}{t}

[fathom swallow]

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

[torpid bay]

1,1 -> 2
1,2 -> 3

mm, thats annoyin

I also made one for split octonions as well

tho that one ended up having two equivalent ways to write the curl equation, and needed conjugates to do it

,, \Psi = E+B\gamma \ \Psi' = E-B\gamma \ \text{etc} \ -c\gamma\nabla\times\Psi = J'\Psi+\partial_t\Psi' \ -c\gamma\nabla\times\Psi'=J\Psi+\partial_t\Psi

[fathom swallow]

Yeatte

[torpid bay]

tho there is one other thing that's cool

$

,, (\partial_T + \gamma\nabla\times)\Psi = -J_\Psi \ \text{ curl equation above} \ (\partial_T-\gamma\nabla\times)(\partial_T+\gamma\nabla\times)\Psi = -(\partial_T-\gamma\nalba\times)J_\Psi \ \text{wave equation with charges included above}

[fathom swallow]

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

[zealous garden]

Axler is almost too good, but Roman is better

[torpid bay]

ig ill modfy the things a bit to make it work

[carmine zephyr]

Axler hates determinants, so I hate Axler

[zealous garden]

Does he really hate determinants when he gives them one of the best definitions possible?

[carmine zephyr]

He puts them at the end of the book! This is pedagogically terrible

His treatment of them is fine (it's the right definition, but I have seen it done that way earlier in other books), but the man literally wrote an essay called "Down With Determinants". He is not to be trusted

[zealous garden]

Nah

Determinants belong later in a book

you should introduce vectorspaces, linear maps, and exterior algebras first

And Axler proved his point that you don't need them for very many things

[carmine zephyr]

Absolutely you should do vector spaces and linear maps first, those are what linear algebra is about

But not exterior algebras, come on

[zealous garden]

Of course you should do exterior algebras

this is the only right way to define the determinant

They also give you a nifty way to talk about other objects in linear algebra and characteristics of linear maps, eigenspaces and eigenblades go brrr

And using the appropriate definition of determinant here also makes proving basic properties of the determinant trivial

and by trivial I don't just mean "oh it's just a computation" but "oh it's just this really easy computation"

And a lot of the properties of the determinant that people care about are actually just properties of the exterior product, whose structure underlies the determinant

So it's the clearer route as well

[carmine zephyr]

Introducing an entirely new and usually unnecessary abstraction is not the clearer route lmao

[zealous garden]

It's not entirely new? If you mean to the student, the entire subject is new to the student so that means nothing

Pretty sure I got it from a Dorst paper, gimme a minute

HERE YOU GO
https://onlinelibrary.wiley.com/doi/10.1002/mma.9754

[zealous garden]

I would hesitate to call it usually unnecessary too. It's unnecessary only really in the sense that it is not used

I could just as easily do everything with lines and lines of scalar equations, and refuse to recognize the linear algebra underlying it all, then call linear algebra itself "an entirely new and usually unnecessary abstraction". The point is in clarity, and sometimes conciseness.

And really exterior algebra is not that large of a jump up from vector algebra, at all

and it makes things like the cross product and determinant make infinitely more sense

I almost want to say the relationship is functorial, but I don't know what that means

What I can tell you is that by the universal property of exterior algebras, every linear map between vectorspaces extends uniquely to an algebra homomorphism between their exterior algebras

If you go all the way out to geometric algebra, there is a formula for the inverse of a linear map. It uses the determinant, dual, and an innermorphism (adjoint of an outermorphism)

"Why do I care, I have a formula for that, it uses the determinant and the adjugate, that's fewer parts!"

It uses a basis (matrix representations). Here we can see $$(\mathrm{adj }f)(x)=I^{-1}\overline{f}(Ix)$$

[fathom swallow]

wraithlord_kototality

[zealous garden]

where overline f is the innermorphism of f

Leo Dorst does some cool stuff, you should also check out his paper on oriented projective geometry through versors of R^3,3

There's a very nice construction in there of an oriented projective space in 3 dimensions, that doesn't start out from terribly weird territory at all

It lands you in a Geometric Algebra over the 6 dimensional space R^3,3, which is unexpected.

It really sucks that this construction only works in 3 dimensions

https://ivi.fnwi.uva.nl/isis/publications/2015/DorstAACA2015/DorstAACA2015.pdf

the TL;DR: If we start with the usual homogeneous coordinates model, with points in 3D space being represented in a 4D linear space so that we can use affine maps yada yada, we can assume no metric and take the exterior algebra, a clifford algebra

from this clifford algebra we look at the space of bivectors, which in 4D, is 6 dimensional

geometrically, these are lines

specifically, if we take two points, which are vectors (although you could probably take two planes instead and use a dual representation, where vectors are planes), then the wedge product is a bivector that represents a line through the two points (or the intersection of the two planes).

Since we are in 4D, we are really really lucky

We won't assume a full basis, but you might usually need one to find what I do want, let's assume we have a pseudoscalar I, so if you had a basis, just the wedge of all basis vectors. Then using the pseudoscalar, we can define a quadratic form on the space of bivectors

that is

taking two bivectors $b,c\in\Lambda^2\bR^4$, we can define a nondegenerate symmetric bilinear form $\langle\cdot,\cdot\rangle:\Lambda^2\bR^4\times\Lambda^2\bR^4\to\bR$ by setting $b\wedge c =: \langle b,c\rangle \mathcal I$

[fathom swallow]

wraithlord_kototality

[zealous garden]

This is the part that only works in 3D

but after that, we now have a quadratic form on the space of oriented lines through space

He then shows that the resulting clifford algebra contains all projective colineations, correlations, whatever other big words

It's also the mother algebra of R^3, which has a very different way of talking about all linear maps on R^3 and its dual space, at the same time

All this plus it's 6D, which is like right at the limit of where a lot of the theorems I've heard about the computational aspects of GA start to get nutty

Like I know at a certain point the inverse of a k-vector might not be another k-vector

-# regulus

[carmine zephyr]

It's only unnecessary in the sense that's it's unnecessary, is what you're saying here XD

Look I'm all for telling students that there is exactly one multilinear skew-symmetric normalized function from the n-fold product of R^n to R. That's true and great. BUT

[zealous garden]

what are you talking about

that's not my definition

that's not axler's definition either

it's defined through the outermorphism

maybe the old version is the weaker one

[carmine zephyr]

It's not from Axler, it's from Shurman's analysis book

[zealous garden]

in the latest edition, he defines it through the outermorphism

Well, that is still lame

It's not eevn an n-linear map on R^n!

it's a homomorphism From End(V) to the multiplicative monoid of F

[carmine zephyr]

You do not need to talk about exterior algebra more broadly to do this. That's what I mean by unnecessary. Doing so introduces a lot of clutter that's not at the heart of linear algebra. You can motivate all of those properties via volume, talk about multilinear functions because they will come up again later, but not delve into a bunch of abstraction that clutters the presentation

[zealous garden]

Wait hold on

someone has told me I'm weird for caring about this difference before

I don't care if I'm weird for it, I care about it

[carmine zephyr]

Yeah it absolutely is linear on its inputs with the others held fixed

[zealous garden]

because the difference is precisely the flesh connecting to the exterior product

[zealous garden]

but its input isn't N vectors

it's a linear map
-# tf did I smoke

You can use your extra structure, like a basis, to induce an ordered n-tuple of vectors, and then you can run that backwards to the determinant

but the determinant acts on linear maps

the wedge product acts on vectors and k-vectors

[hot lion]

yeah tbh I feel like the determinant is perfectly intuitive really idk what the beef is with it

[zealous garden]

My beef is with the coordinate representations of it

[hot lion]

sure the formula maybe feels a bit mysterious but also n-dimensional volumes are kinda hard to compute

[zealous garden]

Just wedge away

[carmine zephyr]

Introducing the determinant in a coordinate free way is absolutely asking for it even in a second course.

[zealous garden]

it's easy to justify the wedge product's properties from the properties of oriented parallelograms in 2D space

[hot lion]

idk I feel like that'd really confuse students

[zealous garden]

what do you mean?

$f(\mathcal I)=(\det f)\mathcal I$

[fathom swallow]

wraithlord_kototality

[zealous garden]

so clean

[zealous garden]

which part? the part where we introduce a product specifically for computing n dimensional parallelotope volumes?

then use that to do exactly what it said on the tin?

what's confusing

[carmine zephyr]

All of this is about the philosophy of how a linear algebra course should be taught, and how a textbook on the subject should be organized. Putting the determinant last lets Axler show off all his clever little tricks - which are no doubt great if you want to learn about minimal polynomials! - but they are not actually going to help you teach the subject

[hot lion]

I mean why not just introduce the determinant to do that

and then you don't have to mess with multilinear maps or any wedge stuff

tbh I was convinced at first by geometric algebra things but the more I think about it the more I think its just more confusing

[zealous garden]

what's confusing?

[zealous garden]

but yes you do!

You are turning the determinant into a multilinear map!

and you are stepping towards the wedge product

[hot lion]

but like why

[zealous garden]

why not just start at the wedge product and realize you had less steps to go through

plus it's then coordinate and dimension independent

[carmine zephyr]

Which is fine for a linear algebra course! Save the wedge product for when the student actually learns differential forms, geez

[hot lion]

abstraction is hard, I find math people (includiing myself) often overestimate students capacity for digesting new abstractions

[zealous garden]

that's precisely when you shouldn't

[hot lion]

mostly because abstractions are only easy and natural once you are familiar with the concrete thing you are abstracting away from

[zealous garden]

You should be familiar with the thing in isolation before you spread it across a manifold

[peak tide]

it's intended as a second course, why would you not want to learn about minimal polynomials

[zealous garden]

we are abstracting parallelograms???

how is that hard

[hot lion]

this goes for pure math students as well, not just like engineering math

introducing new notation, new rules, all sorts of things

[zealous garden]

it's literally as difficult as the vectors they just got a hang of

it's less difficult than the pseudovector bullshit

Yeah the biggest thing for Axler in particular is that he intends it a second course, so he has excuses to take weird routes

[carmine zephyr]

Of course I do, but not at the expense of the determinant

[zealous garden]

The wedge product is a very basic thing, if you can do a cross product you can do a wedge product.

It's that simple

and then after that, you can introduce the determinant

[hot lion]

yes but you're adding more notation and more rules to remember and for what

it doesn't really do anything until you do differential geometry anyway

[zealous garden]

To make the other rules easier to remember

[carmine zephyr]

I don't actually teach the cross product in linear, because it is specific to R^3

(And R^7, I guess, but ew)

[latent edge]

nah i dont care everyone finds relating things to motives natural so abstractions are fine

[zealous garden]

I don't use it \neq It doesn't do anything

[hot lion]

ya cross product I had to relearn to TA multivariable calc lol

the other issue I have with geometric algebra is that it relies a lot on the ability of students to comprehend this big abstract space and consider thigns like formal sums of scalars and bivectors

[zealous garden]

to make the other rules easier to remember

[hot lion]

ok like what though

[zealous garden]

this shouldn't be an issue for anyone who can reason about real (as in irrational) or complex numbers

[hot lion]

and even then it comes at a high abstraction cost

[carmine zephyr]

I promise you it absolutely is

[hot lion]

I really disagree with this to be honest

[zealous garden]

I know it is an issue, but it should not be

You've been taking formal sums for years before you meet GA

There are ways to show them what some examples might mean sure

and most things you encounter in practice will have meaning

[hot lion]

also the idea of having these formal sums is just really not quite that intuitive at all at least compared to just like vectors

[zealous garden]

Yeah but you don't get them unless you ask for them

Oh wait you meant geometric algebra specifically?

[zealous garden]

In that case, I would repeat this with an asterisk. The scalar+bivector objects you'll naturally meet are better explained as compositions of transformations, not as "adding a scalar and a bivector"

so the addition is wrong, you would factor it

the catch being there are infinitely many factorizations depending on which vector you start with

[hot lion]

ok but that's arguably even more confusing

[zealous garden]

It's only confusing if you don't know about the sandwich

you start with the sandwich

dot, wedge, gp, WHY? draw a triangle, make a sandwich, move on

[hot lion]

uh huh

[zealous garden]

What I'm referring to here is deriving through geometry exactly how you can reflect one vector across the hyperplane orthogonal to another one, how the GP is invertible, and how this "invertible dot product" lets us derive the sandwich product which handles transformations

this is a very basic task

What do you find funny

do you think it's not basic

Have you done it?

Have you seen it?

[carmine zephyr]

I think at this point you are either trolling, or I would hate to be in your linear algebra class

[zealous garden]

Someone else just told me they'd love to see people in linear algebra react to me

[zealous garden]

I don't know what makes you think I'm trolling?

[foggy meadow]

Honestly, as a programmer GA does feel very intuitive.

[zealous garden]

you get me!

[carmine zephyr]

All this stuff is great for grad linear algebra but I disagree strongly that it has any place in a second undergraduate course on the subject ¯_(ツ)_/¯

Usually a student's first proof-based course

(in lin alg)

So they've got plenty of abstraction to grapple with as is, and throwing wedge products at them is just not it

[hot lion]

for sure

[zealous garden]

go to 2D, draw 2 vectors, draw the line orthogonal to one

the reflection through this line is equal to the vector minus TWICE its projection onto the line

we learned projection thanks to normalization and the dot product

this gives us a workable form $R_v(u)= u - 2P_v(u)=u - 2 (\frac{v}{\norm{v}}\cdot u)\frac{v}{\norm{v}}$, we then use the most basic of properties of the GP, to get $R_v(u)= u - (vu+uv)\frac{v}{\norm{v}^2}= -vuv^{-1}$

[fathom swallow]

wraithlord_kototality

[hot lion]

problem with abstraction is that once you understand a particular abstraction it becomes very hard to understand what it feels like to not understand it

while at the same time often feeling much more intuitive

I've run into this a good bit when explaining things tbh, in my head something is just so clear and intuitive but when I start explaining it I realize that the only reason its so intuitive is that I've already fully internalized all of these extra abstractions

[foggy meadow]

This is literally anything?

[zealous garden]

This is genuinely basic

[foggy meadow]

Like anything in life .

[zealous garden]

The wedge product isn't complicated

differential forms are

[hot lion]

yes true, though I find it particularly holds in math

[foggy meadow]

"problem with learning how a toaster works is that once you understand it. That it becomes very hard to understand what it feels like to not understand it."

[zealous garden]

Like if you can take basic linear algebra, you can handle this

if you can draw the vectors and do the thing

you can do this

this isn't even a second course thing

[foggy meadow]

Again life in general just as strongly.

[hot lion]

idk to me math has a lot more concepts that feel like a completely different world before and after you understand them

[foggy meadow]

I mean if I always follow the instructions on the packet. Then I will never know truly how to cook.

[zealous garden]

k-vectors don't stop being non-simple until 4D

[hot lion]

there are plenty of things in life that I don't understand, then I learn them, and know I still understand completely what its like to not understand it because its just not that deep

[zealous garden]

multivectors aren't hard to grok until you add k-vectors and j-vectors instead of multiplying them

[foggy meadow]

Strange.

[zealous garden]

you don't add vectors and matrices do you? no? you multiply them?

so lets multiply the k-vectors and j-vectors

[hot lion]

have you ever taught linear algebra

[zealous garden]

Exterior algebra has them too!

I've never taken linear algebra

[carmine zephyr]

...

[hot lion]

ok I think we can be done here then

[foggy meadow]

Hi rakko

[zealous garden]

You the best

[foggy meadow]

How goes the math?

[zealous garden]

what's your point

[hot lion]

my point is if you haven't interacted with students you don't really have any idea what is or isn't easy or intuitive

you're just guessing based on yourself

[marsh cloak]

https://www.youtube.com/watch?v=Q1IcXuK0FwE

[foggy meadow]

Yeah, I had that moment for a bit.

[zealous garden]

Idk, my experience of people that don't get it is I explain it to them and they they tell me the right answers but insist they don't know them

not linear algebra, but generally speaking

[foggy meadow]

I mean you taught me a lot, and I thought that the exponentials were hard.

Or at least counter intuitive.

[zealous garden]

I don't know what it means! My sister is the biggest culprit, she'll ask me for help, insist she doesn't know, I'll look over her work and everything is right, I'll ask her some questions and she gets them right, I ask her what the problem is and never get an actionable answer

[zealous garden]

Yes you understood well, and I feel most people do, or can, understand

[zealous garden]

In this scenario I usually hazard a couple of guesses at maybe a gap in understanding of terminology or motivation, assure you that you can do it, and move on

Unless you want to argue with me

I'll argue with anyone for any reason and any length of time

[zealous garden]

Oh I forgot the part where I rant about things no one asked me about

[foggy meadow]

I liked the whole GR thing, which I sstill need to finish LAGA then read about GA GR.

[foggy meadow]

Hi yj.

How goes the mathing?

What have you been working on?

What's the difference between algebraic number theory and just number theory?

Cool stuff as in Landland's program?

Or cool stuff as in something else?

Honestly all this stuff is over my head, and it's cool you're into this stuff.

I want to understand some number theory more, because I feel like it'll be helpful or something.

The more I hear about primes the more weird they actually are.

I still need to learn about sheafs more deeply . I had a friend explain them conceptually, but I really don't get them fully.

Yeah my friend explained them like that.

Sounds like he gave me a good prespective. It's deals with every function or something around that. I forget the details, because I don't deal with them much.

Yeah, I deal with totally different stuff .

I mean it's a neat idea, but like idk.

[compact widget]

is it jover if i have a medical reason that im having trouble submitting my homework on time

i got bit by a dog in the weekend and that rlly messed up my weekend

idk if i should talk to my professor about it

i might just submit what i have done 😔

[compact widget]

i can get a doctors letter too

[silver basalt]

HELLO EMPTY VOID

AAAAAAAAAAAAAAAA

METH SERVER HAS NO AMPHETAMINES WHAT A SCAM

[hollow rain]

that sucks, how're you supposed to keep your ADHD in check?

[silver basalt]

i dont

[hollow rain]

[silver basalt]

sibel you made me sad

[hollow rain]

Dang it

[acoustic anvil]

need help with captcha

any1 can elp?

[silver basalt]

the clankers are asking for help

[limber thunder]

i thought clankers had rentahuman dot ai now

https://tenor.com/view/woman-fighting-robot-gif-2321323361045817386

[ionic tree]

Tell him that because honestly tho as long as you do your work and its done the right way professors will not care

[rich quail]

OMG WHAT ANIMAL IS THIS???
ITS SO CUTEEEEEEE

I think I know oit but i dont remember the name

[ionic tree]

i think its a chicken

[rich quail]

Lol

[long matrix]

furrer

[rich quail]

[restive mirage]

I hate Newton and his "PHYSICS"🚫

[knotty shell]

At least i dont have math anymore

[stuck tendon]

this is why ur name is a russian hello

[jaunty olive]

You don't mean sir Issac Newtown tho right?

Guy who invented calculus

While got fired Leibniz was watching

[still light]

...

May it always be truthful and always last, may the saddest days of your future be no worse than the happiest of your past. Us all blessing each other this way seems to be good math. . 🙂

[old oak]

Not the best taste in youtubers

[gray glade]

just the results from googling "crisis in cosmology"

[torpid bay]

ah sabine

sigh

[old oak]

sighbine

[hard oasis]

I've never watched her videos; are they good or bad?
(Now I'm a Mathologer enjoyer )

[gray glade]

they are rather pointless

[plush idol]

Finishing my masters and existentially terrified of the effect of ai on math careers

I’m irrationally worried there won’t be any PhD positions by the time I apply

For next cycle

Probably irrational but I have a lot of resentment towards cs bros because of this

[vernal lily]

Funny how it was thought that machines were supposed to take over manual labor so that we could allocate time and effort towards intellectual and creative endeavors

And it's exactly backwards

[plush idol]

Yep

A bunch of CS bros who think everyone hates their job think a world without work is utopia

It’s a world without purpose

Anyway

[sharp lake]

Hi people with ADHD. How do you study a math textbook without your brain dissolving your concentration?

[foggy meadow]

Because math is crack, besides this. Problem big fun, and coding big fun.

[sharp lake]

Huh?
Personally I think reading math can be very annoying at first, because you need to understand every word of the author. It gets okay with problems, because its your own logic, but reading others math (or coding) can be difficult sometimes.

It gets worse when theres so much distractions too. Thats why I always put phone away.

[sharp mulch]

#study-discussion

[sharp lake]

I apologize, but the channel was hidden for me.

[knotty beacon]

yo guys

whats 9+3

[quasi pumice]

928

[knotty beacon]

thanks

[quasi pumice]

Ur welcome

[quasi pumice]

https://m.youtube.com/watch?v=05fSXhZT028&pp=ygUbTGVhcm4gbWF0aCB3aXRoIGFuaW1lIGdpcmxz

[hallow fulcrum]

Hi

[shadow palm]

Hello nerds²

[latent edge]

peak

[small dust]

you can’t find purpose in life without a job?

[latent canyon]

exam tomorrow 😔

[pure stream]

Hi

[full hornet]

im loving these stickers

[mild ruin]

what's the best channel to self study ap calc a/b? (taking the exam at may 💔 )

[zealous bronze]

organic chemistry tutor if ur talking about youtube ig

or just khan academy

thats probably the best one

[willow juniper]

[plush idol]

I have no purpose in life without math

[small dust]

why would you need a job to do math

[plush idol]

What’s the point in doing math if AI solves all the problems

[small dust]

since when is ai solving all the problems

[zealous bronze]

if ai gets to a point where it can do that then the entirety of society is fucked basically

the good news is that it wont happen anytime soon

[vivid halo]

Because this isn’t actually the point lol

[plush idol]

It’s just depressing

[vivid halo]

Not really

Much to be excited about

More than ever

[plush idol]

Like the day an LLM does what it did in bio and some CS bro who drunk his way thru college and who’s only skill is getting investors to give him money to buy compute power wins a fields medal because he had a big enough data center to prove a famous conjecture

That will suck so hard

It already happened to the biologists

[vivid halo]

This isn’t likely to happen and even if it does it doesn’t actually matter

[zealous bronze]

the logical conclusion of ai-assisted math is independent ai math

[vivid halo]

These are all incredibly stupid takes

[zealous bronze]

i dont think this will happen, im saying if it does

[gray glade]

AI proving a theorem sounds exciting

Maybe not necessarily the good exciting

Maybe it will exasperate me

But maybe it will also be fun

For the hat tile, it would have been rather deflating tho, I'm glad that got proven by humans first lol

[zealous bronze]

the real problem is the effects of unemployment such technology would have. if you don't think that is an issue i don't know what to say

[gray glade]

We will move to a post-work society anyway

I wonder if people complained about machinery replacing menial jobs back in the day

[vivid halo]

I mean the usefulness of these kinds of AI tools is fundamentally quite limited here even if you grant oracle like abilities of deciding truth of mathematical statements, this does not actually put mathematicians out of jobs because this is not actually the job of mathematicians in the first place

[gray glade]

Of course, being a mathematician, programmer or artist is more fulfilling than ploughing the fields or doing rote work at the conveyor belt...

[zealous bronze]

if you're referring to teaching, those jobs would also be replaced if the technology got to that point

[vivid halo]

this is maybe a more realistic concern yes but I'm speaking to research mathematicians specifically

a lot of low level teaching jobs are already automated away from the hands of researchers through the exploitation of graduate students and adjuncts

if we could somehow remove the need for this busy labor that would be great

I'm a bit skeptical as to how well this can actually be done with these tools but whatever

but these tools will never be able to train people to do research, nor are they particularly useful for the parts of mathematics research which are actually interesting

[zealous bronze]

i mean right now of course. the idea is just that artificial intelligence could evolve further to a point resembling agi. that's the worrying situation

[vivid halo]

I really don't think this is a realistic thing to be worried about

[zealous bronze]

yeah i agree

if it does happen, it won't be anytime soon, maybe not even within my lifetime

[vivid halo]

yeah agreed

like if you extrapolate current trends, these models are becoming exponentially better at some less interesting mathematics tasks and yet they show virtually no signs of becoming better at certain more interesting tasks

the more interesting trend line here has slope 0 so like idk I don't find this so threatening overall

[small dust]

these people in the 1980s: nooooooooooooo computers are gonna do all calculations for us and i can't work

[vivid halo]

this isn't really how this works

these models don't just magically learn to reason able new definitions which are completely outside their training data

you can always train new models but this is far too expensive in practice for this to be a worry

[zealous bronze]

i also hate when people act like ai is not a fundamentally unique technology. its like the people who think that making ai generate them some image is the same as actual digital art tools

[vivid halo]

https://www.youtube.com/watch?v=jFJku8sxLWY

[zealous bronze]

yeah severely doubt LLMs will ever do interesting math

[vivid halo]

this is a very good recent interview between my PhD advisor and AI researchers on this overall issue

like fundamentally the issue is that these models are really limited in their ability to generate actual new mathematical insights and intuitions, this is maybe the most important job of mathematicians beyond merely deciding which statements are true

[zealous bronze]

well with the current models you can sometimes probe it to push a result like 2% further, thats about as far as its gone

basically what happened with the erdos problem thing

and even then thats in edge cases

[plush idol]

I never said my opinion was particularly rational (in fact I said the opposite). Nevertheless it seems like every week there is a new headline about AI proving an open conjecture. It scares me a lot

[vivid halo]

in particular these tools may become very good at solving open conjectures but they are rather useless for the task of generating new interesting conjectures in the first place

[vivid halo]

well this really doesn't scare most people who are actually researching mathematics

[zealous bronze]

i mean most difficult conjectures require interesting and/or new ideas, no?

[vivid halo]

it's very easy to get spooked about this sort of thing if you have some very narrow and limited view of what mathematicians are actually doing

[zealous bronze]

maybe some smaller stuff sure

[plush idol]

I suppose I just don’t know enough number theory to see how hard these conjectures being proven actually are

[plush idol]

In fairness I have done some research just not in number theory

[zealous bronze]

are you referring to the erdos problem thing or was there something else like this that happened?

[plush idol]

Last night axiom math published another thing

That’s what sparked my initial comment

https://x.com/axiommathai/status/2019449659807219884?s=20

Axiom (@axiommathai)

1/ AxiomProver has solved Fel’s open conjecture on syzygies of numerical semigroups, autonomously generating a formal proof in Lean with zero human guidance.

This is the first time an AI system has settled an unsolved research problem in theory-building math and self verifies.

X · Feb 5, 2026, 4:34 PM

This isn’t rlly number theory tbf and many ppl saying it’s just easy

So then I guess I’m overreacting

[zealous bronze]

well career wise you shouldn't worry about it

[plush idol]

Yeah fair

Acceptances at all grad programs are very down this year tho that’s prob more due to funding than AI

[vivid halo]

yeah this is largely a funding issue especially in the US but also in Europe to some degree

China is a completely different situation of course

for all the speculation and worry about AI completely cratering academic jobs, these kinds of political and economic issues are a much bigger worry

[opal pulsar]

So how’s AI psychosis treating this server? You folks seeing a lot of cases?

[old oak]

The mathematical community has been dealing with the crank phenomenon since well before the advent of GenAI; LLMs have just intensified it a bit, but I don't see it as a qualitative change

[gritty heath]

The quantitative changes though

[limber thunder]

before consumer genAI cranks just strung together random cool-sounding concepts into a few pages of gibberish trying to sound smart, after genAI it's that but now with a sycophantic bot that validates their crap and tells them plausible-sounding gibberish which they trust blindly

@vivid halo

[cinder lotus]

https://github.com/kaixennn/infinite-collatz-visualizer

[urban vigil]

That's why mathematicians won't disappear

Idk why common people cease to understand that

Like the fundamental reason they are scientists/mathematicians is "they are literally gaining new insights and connecting dots which llms won't ever do"

Like fundamentally, llms are just "guess and check" basically, it can never close the fundamental limit for "reasoning"

[urban vigil]

They have got the smartest leaders no joke

[wooden hound]

Hi Guys I’m. Alittle confused in limits

is limits like trying to find the slope at exactly one point, but can’t, so u find the slope by 2 points that are extremely close to each other?

[stiff turtle]

I don't know abt that

Even I saw a definition of limits like that from yt a few years back and ig it isn't that good

I pinged you in #calculus

You can read that msg of mine for limits if you have any other doubts I'm happy to help

[mint patio]

I don’t understand this. I’m pretty sure my professor uses the notation e_i e_j to mean e_i \otimes e_j. That’s how we defined the gradient. But then how does the expression (e_m \cdot e_p) \otimes e_q make sense? How do you tensor product a rank zero tensor (scalar) and a rank one tensor (vector)?

This seems like ridiculous abuse of notation

[long matrix]

misbracketed the 1st line?

[mint patio]

Where?

[long matrix]

if u move the last right bracket back one it makes sense

maybe.

[mint patio]

Doesn’t the tensor decomposition need the tensor product of the basis vectors?

[long matrix]

i dont know

[mint patio]

and even then you still end up with line two which is scalar otimes vector

[long matrix]

i dont know what ur doing, i can just see things

[mint patio]

this is my professor’s work and I too do not know shuwui 😔

[long matrix]

whats written there makes sense if what i said was true

i dont know any more

[mint patio]

Ya ig I will go office hours sometime

[agile crest]

e_m cdot e_p should be replaced by nabla_e_m e_p? under normal coordinates it is delta_mp

im wrong nvm

[wooden hound]

tyyysm

[mint patio]

ig you can tensor product a scalar and vector? it’s just scalar multiplication I think

[sharp mulch]

The notation looks fine to me

[stiff turtle]

Np :)

[agile crest]

i think its just scalar multiplication. im not familiar with your notations but the inner product probably comes from raising indices, which is in the definition of div

[mint patio]

Ya I understand it now, I didn’t realize that we define a \cdot (b \otimes c) = (a \cdot b) c

[spare topaz]

Bias variance tradeoff should not exist and should not be taught

[hollow slate]

Does asking for help with either past or practice (I forgot which) AP exam questions that my teacher assigned as classwork count as using help channels for a test

[night garden]

No i mean maybe ur allowed to ask for help for some but definitely not all

But they wont give answers ur just gonna be guided to it so ur basically still doing the work

[zealous garden]

based

[agile crest]

Fun fact: 'If 2^x and 3^x are integers simultaneously, then is x an integer?" is still an open problem. But we already knew that if 2^x, 3^x and 5^x are integers simultaneously, then x is an integer.

[night garden]

Well the answer is yes x is an integer

I have proved this rigorously

Via 🧠

[cosmic oxide]

Would an infinite space have no center, or would every point be the center?

[night garden]

Idk id assume every point is a center
If u define a center as the point equidistant from every edge.
so if a space is actually 3D infinite then no matter where u start no point will be from the edge
You could say every point is a center if it's from the observers pov

[cosmic oxide]

That's what I assumed

[void inlet]

Is anyone else just getting rejection letters from the graduate programs they applied to?

[torn remnant]

i haven't gotten any responses

didnt apply until like december though

[foggy meadow]

In your profile picture I keep seeing it as a weird dog.

Strong paradolia.

[torn remnant]

that low quality version looks more like a duck or something to me

[foggy meadow]

Yeah, I was listening to some music, and that's how I saw it.

@vivid halo I have a dumb question probably about q-pochhammer symbol.

$\sum_{n=1}^{N-1}\ln\left(1-aq^{n}\right)=\ln\left(\prod_{n=1}^{N-1}\left(1-aq^{n}\right)\right)=\ln\left(\left(1-aq^{n}\right)!\right)$

[fathom swallow]

DisOneGuy

[foggy meadow]

Is this true?

idk what n would be now on the left side, but I'm leaving it there.

[mild nebula]

You might have to explain to me where the factorial came from

[old oak]

What for?

[foggy meadow]

Well the fact of \sum_{n=1}^{x}\ln\left(n\right) = ln(x!). So, there's probably a way to relate the two because of that.

[vivid halo]

uhh

[urban vigil]

H

[foggy meadow]

Hi, I just was realizing you could do q analogue stuff and make it into sums. Which I found neat. I think there's a way to relate it to log gamma probably, but I'm not sure exactly.

[vivid halo]

I mean q-Pochhammer itself is basically q-gamma

[foggy meadow]

That makes sense. 🤷‍♂️ I guess I'm just going about showing that differently. Also would q-analog with sums be something interesting or not?

[vivid halo]

the log isn't really doing anything lol

[neat lintel]

Is anyone the best at mathematics here

[foggy meadow]

I mean it's making it into a sum. Otherwise I'm not sure exactly what you mean.

[vivid halo]

I mean sure but this has no extra content

[neat lintel]

I have a problem here please somebody help me, it will be appreciated

[foggy meadow]

No, yeah.
What it might let me do is make random sums into q analogs for free. Or take q analogs and just make them sums then integrate or derive them then put them as q-analogs again.

[vivid halo]

usually the natural form you want to write these things involves products and exponential form anyways

[vivid halo]

this is basically a way to guarantee garbage results

[foggy meadow]

I mean, has it been tried?

[vivid halo]

you don't just produce interesting q-analog identities by screwing around like this, they need to come from a deeper source than the original identities themselves

[foggy meadow]

Okay, wwell that's uninteresting.

Dang.

[vivid halo]

no you have it completely backwards this is profoundly interesting

[foggy meadow]

I mean what's interesting is up to the person.
I don't dis like it, but I would have to be in a different context to appreciate it fully.

[vivid halo]

usually these q-series with arithmetic significance are very hard to pull out of thin air, they need to come from some rather deep constructions

[foggy meadow]

Yeah, I got it when you said that.

[vivid halo]

the main place you go looking for these things is t-deformed q-difference equations

q-difference equations are very very hard to solve

[noble tinsel]

why is discussy 2 alive

[foggy meadow]

Yeah, you were telling me that.
I just don't think I'll really get into them ever, even though I do know about it some.

[noble tinsel]

heresy

[vivid halo]

usually once you have these q-series you are able to extract more classical special functions asymptotically

the appearance of Li_2(t) in the asymptotics for (t;q)_\infty in the limit q->1 is precisely why these things are related to quantum dilogarithms

[foggy meadow]

Yeah, but all that stuff I'd really have to learn and understand. Like I can see it and be like neat, but then I can't just treat them normally.

[vivid halo]

yeah I mean this is very hard and magical stuff

there is a standard story to learn about this stuff though

[foggy meadow]

Well if the sum log thing is ick, then like 🤷‍♂️ . Ugh.

[vivid halo]

like it is worth spending some time with the q-deformed version of the 5-term relation for the dilogarithm

you get a similar relation for the quantum dilogarithm and there are loads of very classical kinds of proofs for this

one such proof comes from the Jacobi triple identity for theta functions

https://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/978-3-540-30308-4_1/fulltext.pdf

pages 26 and onwards in this Zagier paper give a wonderful survey of this sort of thing

you have to remember that variables are no longer commutative in this setting

they are only q-commutative

this is why this setting is so rich and why the identities are so much harder to prove

@foggy meadow https://www.youtube.com/watch?v=pHL8E2lZ_eM

this is probably the single cleanest introduction I have ever seen for this sort of story

loads of very explicit computations and examples whole way through

[remote pendant]

Hello

[rich quail]

Heyyyyyy

[gilded gulch]

why are above chat closing?

like those # hate

[viral oracle]

because the helpees are done with their help session

#❓how-to-get-help

[gilded gulch]

wht are helpees

[viral oracle]

people asking for help

[gilded gulch]

im new

[gilded gulch]

ohkkk

[spice belfry]

UWU can I friend you? :3

[viral oracle]

no.

[spice belfry]

:3 why not

[viral oracle]

cuz I don't even know who you are

[spice belfry]

Your resolve reminds me of my former student

[spice belfry]

Can you teach me how to solve quadratic equations?

[viral oracle]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[spice belfry]

How do I solve x^2 +2x + 1 = 0?

[viral oracle]

did you read this prompt?

[spice belfry]

no

[fresh comet]

[odd spoke]

Hello

[worldly horizon]

,ui

[fathom swallow]

finestperfectionism (1311394031640776716)

​ ​ ​ ​ ​ ​ Name: Infinium³
​ ​ Nickname: None
​ ​ ​ Seen in: 2 guilds
​ Joined at: <t:1755056314:F>
Created at: <t:1732731102:F>

Roles

he/him, they/them, Helpful, Chess, Archivist, Meta, Undergraduate Math, Talks, Bot Enthusiast

Join order

250483.     ahmed_tk1
250484.     ayomidewealthbuilder
250485.     tranquil_n0va
250486.   > finestperfectionism
250487.     rom64
250488.     primehp05
250489.     famousrelic19

[worldly horizon]

pairs o²f tw

[wraith magnet]

wrong channel blud

[worldly horizon]

OH SHIT

[wraith magnet]

{{.}}

[worldly horizon]

[wraith magnet]

aura loss

[worldly horizon]

modz don’t ban me

[wraith magnet]

!topic

[worldly horizon]

…talking about aura itself is a fucking aura loss 😭

[quasi jetty]

Please read the channel description before posting, and stay on topic.

[worldly horizon]

I saw higher, hanako, and definitely car and my brain defaulted to bots.

[rancid cave]

does anyone know how to get helpful role?

because i've been here for like 1 years i think and i've been helping ppl in math help for pretty long time now

[fathom lance]

you get it if you’re a mod

[worldly horizon]

patience! ❤️
-# or you got noted, but unless you did something bad in the help channels you probably aren’t.

Progress towards helpful never degrades, and both the forums and regular chnanels count.

[fresh comet]

[rancid cave]

the thing is some ppl get helpful while not even helping

at least thats what i see

[brave flare]

you dont, but you do in essence

i am unworthy of #「helpers-lounge」 yet im there

[agile fiber]

the help channels are calling matroid

[worldly horizon]

Some people retire after getting helpful.

[rancid cave]

that doesnt mean they should come in and tell ppl to search it up because someone doesnt know something

and saying that we are not a search engine

[jagged idol]

you know like people who come back to their high schools as like volunteers or judges or coaches it’s lowk giving peaked in high school

[brave flare]

there was a time where i was somewhat active in help channels but nowadays i cant look at calculations anymore
if i ever come across a help channel like "how do i do this group theory exercise" i might hop on

[radiant sparrow]

Oi, @ me next time
-# (also mandatory hiiiiiiiiiiii though I'm about to sleep hope you've been good )

[worldly horizon]

Sleep well!

-# Will do. ❤️

[pure sapphire]

Which language should i start learning, python or c++?

[limber thunder]

do you have any goals or plans in mind after you've learnt programming? python is decent for data and ML though it has packages for basically whatever, it's a good all-around tool and often what people first learn when they learn programming, while C++ is mostly for low-level or embedded programming
we have a #1213610885277421588 forum you might be interested

[pure sapphire]

I feel like cpp might be a bit more versatile, but the steeper learning curver relative to python is putting me off for the time being.

[gilded gulch]

c++

start w java like for base then you will understand c++ and python very easily

[gilded gulch]

i mean i did this

[shadow palm]

Hello nerds²

[shadow palm]

Hey flux!

[rancid cave]

javascript is the easiest

there are no libraries for you to learn

[brittle jasper]

C++, earlier you try learn harder stuff the better.
When you segfault you'll realise why there's so many C++ replacements

[olive fjord]

Man wants to ask his crush out but is shy

His friend tells him, just be non chalant and say “You’re an 8 on a scale of 10”

The Man was confused by this advice, he didn’t know why this would work, but considering his friend has had luck with the ladies,

he cast his doubts aside, trusted his friend’s advice and went to her and said “Urinate on a skeleton”

[willow herald]

Depeands on what you wanna do exactly,
I'd recommend python if you wand to jsut do something
C (not C++) if you wanna know how computers work
And C++ if you want an inbetween (that imo isn't as good at eather but it does both good enough)

[rocky shuttle]

<@&268886789983436800> spam in several channels

[rich quail]

Lol

[gilded gulch]

hellooooo!

[worthy yacht]

Are you have any yt channel??

I mean Youtube

[unborn meteor]

<@&268886789983436800>

[mint patio]

Hola amigos! I do not speak the Calculus of Variations

Can anyone please explain why $\delta(N_I(x)u_I(t)) = N_I(x) \delta(u_i(t))$?

[fathom swallow]

feather

[mint patio]

Someone explained it to me as "in the context of the problem we are varying u, so that's how we know we take the variation of u only" but that is not satisfying to me

If I did not have context, how would I know? Does the variation operator obey any product rule?

Because then I could justify it as $\delta(...) = \delta(N_I(x))u(t) + N_I(x)\delta(u(t))$ and since $N_I(x)$ is a defined function then it can have no variation?

[fathom swallow]

feather

[long kayak]

The key point is that the displacement field is approximated as a linear combination of shape functions

u(x,t)=I∑​NI​(x)uI​(t)
where the shape functions 𝑁𝐼(𝑥) depend only on space, and the nodal values 𝑢𝐼(𝑡) dependo only on time
Now, the variation operator has two important properties. one of them being linearity:
(a+b)=δa+δb,δ(ca)=cδa
for any constant c
And also independent quantities do not vary, spatial shape functions 𝑁𝐼(𝑥) are fixed functions, so δNI(x)=0

now, applying this to your expression:
You can start with:

δ(NI​(x)uI​(t))
and using the product rule for variations:
δ(NI​uI​)=(δNI​)uI​+NI​δuI​
but since NI(x) is fixed,
δNI​(x)=0.
Therefore you get
δ(NI​(x)uI​(t))=NI​(x)δuI​(t)

[mint patio]

I'm the goat actually

Thank you 🤩

[long kayak]

Always!

[mint patio]

You study FEM?

[rocky shuttle]

Now I'm offended

[mint patio]

Why? 💀

[long kayak]

I did study it a while ago

[rocky shuttle]

Jk, but there's literally no difference to what I said about the shape functions being independent of u

[mint patio]

This makes more sense to me because now the variational operator is independent of the function you're taking the variation wrt

[mint patio]

May I add you to harass you with FEM questions in DMs?

[long kayak]

i'll try to help as best as i can

im a bit rusty

[mint patio]

My go-at

Thank you sir!

[long kayak]

no problem!

[velvet dagger]

Do goats usually have feathers?

[pure hollow]

FEM harassment moment
Hiiii feather :3c

[mint patio]

hi convyyy how you is

[mint patio]

This one do

[pure hollow]

I'm doing well actually what about you

[mint patio]

I am just alright 😛 not the worst

[pure hollow]

being alright is better than being the worst

I didn't know that you started your FEM arc tbh

[mint patio]

LOL You study it?

I’m taking a course for it and I guess I want to do something adjacent for it so it seemed right

[pure hollow]

I have the choice of working on FEM but I chose the TDA pipeline

[mint patio]

What is TDA?

[pure hollow]

Topological data analysis

[mint patio]

I GUESSED IT

[pure hollow]

Lmao

[mint patio]

ME GOATTT

What is that?

[pure hollow]

Definitely

[pure hollow]

It's more of using (algebraic )topological tools to do things with higher dim data

[mint patio]

What is higher dimensional data? Do you have an example?

[pure hollow]

Ig the most obvious one would be along the lines of Healthcare Data

[mint patio]

Go on

[pure hollow]

Yeah that's all I know I'm just in the early stages of learning it

[mint patio]

You will make big money in data analytics

[pure hollow]

If there's someone who will employ me

[latent edge]

big if and only if btw

what convy said

[royal crane]

yo chat does this order look right? ODEs + Calc 3 --> Lin Alg --> PDEs

[noble tinsel]

PDEs -> ODEs -> Calc 1 -> Calc 3 -> Lin Alg

[brave flare]

what!

[royal crane]

I already took calc 1, I KNOW thats not the order

[noble tinsel]

Calc 1 -> Lin Alg -> Multivar calc -> PDEs -> ODEs -> Calc 3

Pre-arithmetics -> Algebra -> Pre-algebra -> Calculus

[royal crane]

you need calc 3 for PDEs no?

[royal crane]

oh i looked at your bio thanks for the Lin Alg notes~!

[noble tinsel]

That's what the evil mathers will tell you

[analog abyss]

Actually it’s
Solve the Riemann Hypothesis -> arithmetic -> Complex Analysis
With no in between steps

[noble tinsel]

and then prearithmetics

[royal crane]

im on strp 3

idk where to do ocmplex analyiss

[noble tinsel]

Invent it

Reinvent it

[royal crane]

ohk give me a sec

done

now what

ah yes prearithmetics

[noble tinsel]

ofc

[royal crane]

that i finished with arthmetics

have I completed math?

[noble tinsel]

You still need Pre-Pre-arithmetics

[royal crane]

i did all the arithmetics with arithmetic

[noble tinsel]

You finished maths

I guess we can all go home now

[vernal lily]

Gödel turned over in his grave when you uttered these words

[old oak]

Very unlikely

[neat lintel]

HIIII, Does anyone have any tips on how to become better at understanding physics as someone who understands math better ?? Sorry i'm new if i'm not supposed to ask the question here

[vivid halo]

depends on your background and why you are interested in doing this in the first place

[neat lintel]

college i have toooooo

[vivid halo]

oh okay so not like actual research stuff

[neat lintel]

yes hhahah

[loud marsh]

Definitely no completion, but maybe they're more... consistent

[fresh comet]

[rocky shuttle]

[somber minnow]

hi

[dreamy crag]

Hellowo

[silent junco]

[latent edge]

the disappointment

[buoyant barn]

hey can i share a new thoery i found in group thoery?

with proof?

[alpine badge]

[fresh comet]

[shadow palm]

[snow ice]

[formal dagger]

[mortal cargo]

[west valve]

.

Oof wrong channel

[modest anchor]

Why you have not Even a Name?

[west valve]

I don't have ideas for a name

Idk

[modest anchor]

You should study hard buddy.

[night wyvern]

what's that?

[night wyvern]

yeah bro

[west valve]

I dunno bro

Too tiny for this

[fathom lance]

imagine having school tomorrow

[wicked oxide]

I have school right now

[fathom lance]

ew

I’m about to go to sleep though and get some lala land tmr at 10am

literally love it when I don’t have to go to that jail cell

[shadow palm]

@wicked oxide
Welcome to Mathcord, new nerd

[lethal knot]

@gilded vine

[gilded vine]

?

[lethal knot]

can we dm? if you're okay?

[gilded vine]

if you want to DM me, perhaps close this channel first, notify me in ⁠discussion-2 about what you want to discuss, then I'll let you know if I am comfortable discussing with you.

[wicked oxide]

Thanks

[sonic sleet]

hello

guys

sup

[balmy portal]

Not much ig

How to do. The helper thing idk how

[sonic sleet]

hmm

[fresh comet]

[rocky shuttle]

[fresh comet]

[rocky shuttle]

[fresh comet]

[rocky shuttle]

[fresh comet]

[fluid patrol]

[neat lintel]

[dull agate]

[fresh comet]

[viral oracle]

https://tenor.com/view/kitty-kitten-kittens-cat-cats-gif-23725952

[fresh comet]

https://tenor.com/view/cat-rabbit-cat-rabbit-cat-and-rabbit-cat-sleep-gif-5780726925060253864

[viral oracle]

https://tenor.com/view/holaroberto3-gif-15249034458188762381

[fresh comet]

https://tenor.com/view/bunny-bunnies-rabbit-kiss-bunny-kiss-gif-21363678

[viral oracle]

https://tenor.com/view/nose-kiss-cat-snuggle-nose-to-nose-kiss-gif-664372063405943849

[fresh comet]

https://tenor.com/view/cat-bunny-cat-and-bunny-rabbit-cat-and-rabbit-gif-26887571

[viral oracle]

https://giphy.com/gifs/fox-pet-gif-Gb7VsVFSfTYEE

[rich quail]

AWWWWW

[rich quail]

FOXYYŸŸYYYYYYY

[viral oracle]

https://giphy.com/gifs/moodman-dvBgr7pA6FTJOMOALY

[rich quail]

YAYYYYYYYYYYY

[grim flax]

Is that a fox

[viral oracle]

indeed

[pure hollow]

Foxes aren't real

[viral oracle]

rip @serene vault

[fresh comet]

[pure hollow]

Silly, the fox is in C rather than R obviously they aren't real

[viral oracle]

🦊

[solid yarrow]

Very true my convergent friend. Some might say I am partly imaginary

[solid yarrow]

Yes?

[pure hollow]

Smol epsilon ball in R

[rich quail]

Hii

[frosty zephyr]

Guys can someone tell me

Cool jobs

With pcm math stream

Also with high pay

I want sm like cybersec
Is anyone in cybersecurity?

[twilit knoll]

does anyone know how geogebra determines if two points, lines, etc are the same?

[fresh comet]

[mortal cargo]

[rocky shuttle]

[noble tinsel]

https://tenor.com/view/hiii-cat-wave-cat-wave-hi-gif-174708314057938083

[fresh comet]

[dusky rose]

i have just joined this server

what is this place

[cerulean oracle]

no idea, me new too

[dusky rose]

this place is really big and i'm scared

[cerulean oracle]

indeed

[elfin smelt]

yeah

i recommend staying towards more topic oriented channels..

it can be easy to get lost in the flow of discussion lmao

[cerulean oracle]

it feels like they're active 24/7

[elfin smelt]

ive seen discussion quiet for like, at most 30 minutes once at 4 am EST

[rotund girder]

PCM?

[fresh comet]

[frosty zephyr]

Math

[rotund girder]

What does pcm mean

[frosty zephyr]

Phy chem math

Its like

Stem

Science in hs

[shadow palm]

higher!

[rotund girder]

So are you just asking for math related jobs??

[frosty zephyr]

Ion know maybe

Other than tech

[real oriole]

Yeah

[mighty forum]

yo anyone got the discord server for gauthmath?

[eager knot]

Hi girls

[autumn thistle]

Hi guys

[gritty portal]

Hello

[plush oar]

Name: Rimjhim
Age: 17
From: Bangladesh 🇧🇩
Studies: A-Level Candidate (Edexcel)
Languages Spoken: English, Bengali, Hindi/Urdu.

Hobbies: Lit in all forms — novels, manga, anime, poetry, stories, VNs.

Anime: MHA, AOT, KNY, Assasination Classroom, Love is War, SpyxFamily, Dandadan, Kimi ni Todoke, Oregairu, Ghibli movies, etc.

Novels: Austen, Dostoevsky, Kafka, Brontë, Dazai, Orwell, Plath, Montgomery — traversing classic & contemporary.

Special Inspirations: Anne Frank’s diary & DDLC (both made me write), Danganronpa (favourite game series).

Music: J-Pop, K-Pop, Vocaloid, Classical, Bengali/Hindi/Urdu — mood dictates.

Beliefs: Capitalist-leaning, with socialist touches; individualist & idealist. Theist.

What I value in a conversation: I prefer a single, well-sharpened thought over a cloud of chatter. Grammar is the architecture of meaning, and I admire those who build with intention. Show me a clear idea, elegantly expressed, and you have my full attention. I listen longest to those who know how to shape a thought — not just share it.

Socials: I keep them quiet, even if installed. 🥀

If our interests align, feel free to DM! (I may respond).

[mellow wedge]

Arra bha

[viral flower]

I love my doggo

[noble night]

https://tenor.com/view/srinivasa-ramanujan-indian-mathematician-22december1887-gif-26648597

[noble night]

tuffest gif ive seen in a while

[acoustic iron]

gng plz lock in🥹 🙏

btw plz answer my question its in help-36 plz u samrt right🥹

[acoustic iron]

dont ignore ur day 1s 💔

wowies sucess rly changes some ppl thats crazy

now am broken frm inside

https://giphy.com/gifs/lassi-punjabi-memes-me-in-punjab-CoW0suMi3SqINSxqzS

ts me btw

[noble night]

nah id switch up

[acoustic iron]

is ts tuf in blr

[neat lintel]

hi guys

[kindred surge]

Is anyone familiar with the math used in machine learning? (Matrices, stats and probability, calculus) I already know the basics about stats and probability and i know a little calculus too, but i'd like to learn more if anyone is willing to help!

[hushed talon]

Its mostly linear algebra

And tensors

[kindred surge]

Can you recommend a good resource?

Or i'm down to just listen too if you wanna teach me

[hoary glacier]

Ooo

[kindred surge]

Well i think i do have some linear algebra resources already, but what i guess i'm really asking is: is it worth learning all aspects if linear algebra equally or can/should i just focus on concepts specific to ML?

[hoary glacier]

Oo ai ml

[hoary glacier]

I also wanna learn these things

[kindred surge]

Wanna learn together? What makes you interested in it?

[hoary glacier]

Sure!!
Honestly I am just super curious about how it actually works behind the scenes since its everywhere now

And tbh I am doing this from scratch

[kindred surge]

Yep that's exactly how i think about it too. Well it goes further but in order for you to not have to read an entire philosophical essay its pretty much that

[kindred surge]

Me too almost

[hoary glacier]

Yeaa

[hoary glacier]

:] ooo less goo

[kindred surge]

I only know a tiny amount about coding and the basic frameworks behind AI but that it when it comes to the technical details. But i have been doing a lot of philosophical research into it tho. In terms of technicalities i'm at ground zero basically

But i wanna ask do you know anything about matrices/linear algebra

[hoary glacier]

I know like a bit of python, html and game development.. I know how unity works and character design and stuff.. And talking about ai..
It's a total new thing for me
But learning things from scratch excites me :]

[hoary glacier]

Yea like only a little bit of linear equation not even linear algebra T-T

??

[kindred surge]

Then that's likely where we should start. let me look into how.

[hoary glacier]

Yea yea definitely

[hoary glacier]

Ello

I found something

A YouTube channel named

3blue1brown

[kindred surge]

Let me check it out

Oh yeah actually i already have completed a course on vectors i somehow didn't realize this is linear algebra, but i don't think i remember vectors very well

But i do remember them being easy compared to the rest of my math classes

[hoary glacier]

Yeaa

Check
Freecodecamo. Org channel too

[kindred surge]

Yeah i will

I looked into the very basics of matrices and that stuff seems relatively intuitive until you get to multiplication.

I mean not that multiplication is gonna be super difficult but its not caveman level

[hoary glacier]

We have to become caveman for that T-T lol

[kindred surge]

i think i partially understood why we use matrices for ML. I'll explain soon buy i'm gonna go in the sauna first.

[night garden]

Are u doing linear algebra?

[hoary glacier]

Yep

[hoary glacier]

Yep Linear algebra/matrices

[night garden]

Have u done singular value decomposition yet?

[hoary glacier]

Idk what it is..

[night garden]

A type of decomposition for any real matrix its used in a lot of applications

Like yk abt diagonlisation right

[kindred surge]

I think i understood why matrices are used in ML. Because a ML model is essentially just a program that can make adjustments, and the model transforms numbers with matrix operations because it's the most efficient way to compute even large amounts of data in a short time, because instead of having to compute each dataset one by one, you can turn it into a matrix. For example if you have 10 people and you want to know what grade they can expect to have based on their daily sleep and study hours, then you'll just make that into a 10x2 matrix with the people represented as the rows and the hours of sleep and studying as the columns. Then you create another matrix for the predicted value with the "weights" to predict the value from both variables. So you get a 2x1 matrix. Then now you just multiply the matrices with matrix multiplication

That's how i understand it now, but i might be completely wrong tho.

[real oriole]

energie strom ihr essen versorgung ist pollen also hoffe ixh sie trinkt ist rüsselt und dann setze ixh sie wieder raus und sie und ixh sind glücklich

❤️

[fresh comet]

[real oriole]

alpha external acsess gate 13 📌 ❤️

man kennt einen der einen kennt der einen kennt der einem kennt der einen kennt

[chrome cairn]

thats a philosophical answer right there if I have ever seen one

[kindred surge]

Idk what it says because it's too long for the translator

[chrome cairn]

something called piece by piece😔

[ebon pier]

My friend and I are arguing and I say that sorry is sry but my fiend says it’s srry
Someone resolve this

[true zinc]

<@&268886789983436800> user not speaking english

[hard oasis]

Please keep chat in English for moderation reasons!

Oh yeah I just noticed the text wall after you lance

[thorn wren]

Since you've received a past warning for this you'll also have a 1 hour mute.

Again it's just because we can't moderate chat if we can't understand it and have had a few incidents where bad actors abuse that to post slurs, hate speech, nsfw and other bullshit.

[bold terrace]

you know someone that knows someone that knows someone that knows someone that knows someone

[lusty zealot]

advice for someone taking discrete next year?

[rocky shuttle]

I know someone who knows everyone who doesn't know themself

[full hornet]

no you dont

[real oriole]

Trust me all know someone they think they knows them

[atomic drift]

Hello

[dull salmon]

I went to a cool talk about the model theory of the Farey graph today.

[vivid halo]

Nice

But also peep the Clausen IHES talk that dropped tonight

“One thing that is funny about Peter is he thinks number field shtukas exist”

[dull salmon]

The short version of the story is that the complete theory of the it has an extremely simple axiomatization with like 4 axioms. The models all look like if you glued a bunch of Farey graphs together by identifying a single point from each of them. Also you get an extremely nice characterization of the Scott ranks of these.

[vivid halo]

Oh nice

[dull salmon]

I’m wondering if I can find some number theory applications of this.

[vivid halo]

Weil anima

[dull salmon]

Will do!

[vivid halo]

Knots and Primus

[dull salmon]

My name is M_d.

[vivid halo]

Can’t wait to have better version of the Weil group so very soon

All the fucked up 2-torsion garbage finally fixed

Very exciting remarks towards the end of the first lecture about global Langlands and F_1 memes

Very exciting times

[dull salmon]

I’m thinking of straight up switching fields so I might just think about this stuff.

For the moment I need to prepare a lesson for my random matrix REU meeting tomorrow.

[dull salmon]

Everyone in my current one fled in fear when I showed up.

[vivid halo]

@dull salmon https://x.com/doxie_gay/status/2021363100918874128?s=46

doxie (@doxie_gay)

being friends with fellow schizos is so much more interesting than normies bc we talk about the patents they're using to control our central nervous system instead of complaining about your co-worker or whatever like bro i don't give a fuck

X · Feb 10, 2026, 11:18 PM

Us

[latent edge]

amazing

[pure hollow]

"number field shtukas " this sounds hilarious

[neat zephyr]

Any JEE aspirants or class 11 or 12 students?

[near crypt]

hello, who wanna discuss Maths with me

if you have any question, ask me

[rocky shuttle]

what kind of math

[near crypt]

we can discuss what you want

I like analysis most, but I am also good at algebra and differential equation field

[near crypt]

hey

[rocky shuttle]

how do you compute the arc length of the graph of the sine function from 0 to pi?

[near crypt]

haha, it's simple definite integral problem

[near crypt]

are u testing me? don't worry. i'm good at

[rocky shuttle]

please explain

[rocky shuttle]

no, i always wanted to know how to get the result

[near crypt]

for a curve y=sin(x), the arc length from a to b can compute like following

it's difficult to write the Mathtype, so I explain more detail

the formula is the following

Length of sin(x) = integral from a to b of square of (1 + square of cosine of x)

understand?

[rocky shuttle]

yeah, i understand so far

[near crypt]

are u uni student?

[rocky shuttle]

\[L = \int_{a}^{b} \sqrt{1 + \cos(x)^2} \, \diff{x}\]

[fathom swallow]

Zan (鹿乃 #1 Fan) ❀

[rocky shuttle]

right?

[rocky shuttle]

no, i am not

[near crypt]

yep

👍

length from 0 to pi is about 3.82

[rocky shuttle]

how did you get that

[near crypt]

you don't know compute definite integral?

[rocky shuttle]

please elaborate

[rocky shuttle]

i don't know how to compute this integral from 0 to pi

[near crypt]

how old are u?

[rocky shuttle]

why do you ask

[near crypt]

I'd like to know that you are hishschool student or not

[rocky shuttle]

no, i am not

[near crypt]

so, do u graduate the highschool?

[rocky shuttle]

i have already graduated from high school, yes

[near crypt]

you are not a minor

right?

[rocky shuttle]

i am not what does that have anything to do with the problem?

[rocky shuttle]

you said it was simple, can you please elaborate how you got 3.82?

[near crypt]

Calculate using the second approximation method

[near crypt]

it's curious

[rocky shuttle]

curious?

[near crypt]

no matter