#serious-discussion
1 messages · Page 130 of 1
I remember then learning to invert a matrix it's doing RREF
i will confess though that i never think about (a×b) @ (b×c) → (a×c) in terms of maps though
i just memorize it
even if the commutative diagram intuition is much nicer
oh
like AB I imagine the columns of B as vectors all being mapped, hmm I don't know if that's something I was taught
are we sure ab this
like for instance, rotation and then shearing seems easy to think of in terms fo maps to me
well maybe i shouldnt say rarely
but like
when its obvious then its easy to deal with
a bigger problem is when its not obvious
and your losses look fine and stuff
i have pretty poor visual intuition for linear algebra tbh
i still dont really get why determinants correspond to n-volumes
like they obey the same algebraic rules as volumes
thats great
but i still dont see the direct connection
yeah the formula is a bit whacky
I kind of pretend I'm taking the parallelepiped and then shearing and stretching it by the properties until it's a cube and that all just works out
the fact that geometry and algebra are related is just the fundamental weird part I think
like I'm good with the distributive rule and thinking like a(b+c) = ab+ac means we can cut an a by (b+c) box into two separate ab and ac boxes
and then work up from there lol
like triangles are bh/2 but doesn't actually matter where the point is for the top that you measure the height from, so you start learning intuition for shearing at a young age as well
yeah no i get why shears dont affect volumes, its more that i struggle to see the connection between the mathematical transformation and the geometrical warping of the plane
like i can derive it
but it doesnt come instantly to me
i need to think
I think another thing that I wish I understood sooner is, a linear operator means knowing where some basis vectors are transformed to tells you where all vectors are transformed to
instead it's like, "this is the definition of linearity: some axiom rules" which wasn't really helpful imo
yeah thats more of a central pillar of mathematics than of scientific disciplines in general
but it is still a good one
the notion of generators and bases
yeah, to be clear I'm saying that once you make the first claim, you can pull linearity out of that
sure
i think its obvious why linearity is "nice" even if you dont really understand that though
linearity is basically just saying "everything you want to do with this function from your high school classes, you can"
at least in R^n
it distributes, you can take inverses, etc
one kind of mystical thing to me is
well let's say I give you a matrix A, then when can I find another matrix so that when you look at all its rows, their dot products with the columns of A make 1 if they have the same index 0 otherwise, while also viewed as its columns, their dot products with the rows of A make 1 if they have the same index 0 otherwise?
sort of an obnoxious way of asking when does A have a left and right inverse

well yeah thats a case where the function composition definition makes way more sense
I still kinda wonder what makes gradient norm in ML problems vary so much even if the function is convex, I recently produced this graph
idk enough about ML to answer that
might be explained in the paper
Arki

Woah
more details pls
what details do you need
what is the function in reference
it's logistic regression
$-\log L(X;w) = \sum_{i=1}^l \log (1+\exp (-y_iw^\top x_i))$
Transparent Elemental
this takes entire data set per iteration
hmm idt ive ever paid attention to concavity, ive always just assumed the lr was high whenever i see similar behavior
is it documented/known that its due to convexity?
thatd be news to me
no I was saying Idk why it's happening if the function is convex
I just didn't observe this that much outside of ML problems
oh ic 
this is the kind of thing that usually happens (some random nasty function and LASSO regression)
(don't mind the peaks on the first picture)
right
o wait what, k is epochs/iterations right? do u remember if the peaks/dips were single points?
could there have been floting point issues? depending on the number of points its plausible
or maybe not, theres jagged behavior at the start as well

the peaks are there because I'm using restarted FISTA algorithm, which behaves much nicer if I restart it, the restarts happen precisely when the peaks do
(if you meant this picture)
(im referring to the original one, not that)
otherwise no, this kind of thing I've seen even when using more classical version of gradient descent
and I think on smaller problem too, this one isn't even that big as well it's like maybe a 100 objects with 6 features
hmm, i guess im not too familiar with that behavior when not using batches, as pretty much every problem ive ever worked on i use them
at least outside of intro classes where the fits can be perfect
What do you guys think of stack exchange?
Helpful sometimes, 90% of the posters are deranged
What, why?
Have you ever looked at a stack exchange post? You’ll get a 10 year old stuck factorising a quadratic and the top post will start with some grad level commutative algebra. Either that or you’ll ask a perfectly good question and someone will have a breakdown about formatting and or close your post because there’s a 13 year old unanswered question that’s vaguely related to yours.
I’m being hyperbolic obviously, stack has helped me a lot but like some of the people that use it are just weird
kawaii
ypoooooo
Does anyone know how to solve this integral? I assume using u-sub but I couldn't figure out the rest of the steps: https://cdn.discordapp.com/attachments/624371278672953345/1179032669233877022/image.png?ex=65784ebd&is=6565d9bd&hm=35671bf8f71aaa9b6af4900cbbe2257e0e3feabf650f5dd50218ee12ade51346&
Lmaoo
@cobalt reef use one of the help channels but i'll help for this time
Do yk about integration by parts?
https://cdn.discordapp.com/attachments/624371278672953345/1179033384207527936/image.png
https://cdn.discordapp.com/attachments/624371278672953345/1179033384207527936/image.png
@cobalt reef second image has the full solution so don't open unless you're confident you can solve by yourself
this is true

I want to try 1v1 on brood war but it intimidates me
Hm, I don't really see much of your first point on MSE.
Also the second, normally, if you post your question TeXed up, then no one should complain about formatting (atleast no one did on my 15 or so posts until now)
And regarding your third, questions can only be closed as a duplicate if the related question is answered
Most of the people who close the questions seem to search with Approach0 (https://approach0.xyz/search/), so after you search with that and Google, there shouldn't be any duplicates one can find
Except out of memory, of course
!nosols
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

Or just the answer with 0 explanation on how to get the answer
This is why wfa >> stock exchange tbh
how do you get the helpful role
like where does it get counted that you helped a person
Dm if u can help me
!help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
@ocean harbor my favourite gifs are gone. What did you do to my discord
What did you.
Can anyone help me with how to prove that the improper integral of root(cot x) 0--> pi/2 is convergent ?
!help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

My cs isn't here again let's go
I finished the linked list assignment

Idk what to do but imma do smth useful for myself
Sorry. Ignore the for
Oh alright
How many odd numbers over 40000 can you make with the digits 7 1 2 5 8 used each only once? Could someone run me through how to do this? Thanks!
does anyone know if there are any videos of serge lang giving a lecture or talking
i haven't been able to find anything, i want to see if he talks like he writes
that would be so funny
I'd fall asleep
Maybe I'll self promote here
Keep 5,7,8 one by one in the 10 thounsandth place ,and then normal permutation for the remaining
3 times 4!
@pulsar ravine I had seen in the Book Recommendations channel a thread about the historical intuition of algebra. Could you explain what you meant?
I don't think you meant that algebra was necessarily easy, but I'm curious.
Do you mean from an applied perspective (doing calculations) or from an intuition/motivation perspective?
Both though there are likely more intuitions and motivations. The other person on that topic knows more though, if you're curious it's definitely a fascinating subject
I can understand the applied version. I imagine pretty much anyone could be taught to do calculations in a few days with basic algebra.
It's a bit hard to imagine someone understanding the intuitions behind algebra in a very short time, though. You don't really understand basic algebra until your 3rd or 4th year of undergrad if you're a pure maths major.
I suppose it's possible we have different ideas about understanding, though.
Yes certainly, but the intuitions have revealed themselves through their discovery, regardless of application. With modern application though it's the difference between a gifted genius and talented student. Even if something takes more time to learn that doesn't mean you don't understand it, just that it takes more time. If it's so alien that is difficult, then the intuition is more foggy or closer to 0.
Where I can find someone how can explain some research papers in approximation theory
I don't think there's any doubt of, for example, non-euclidean geometry or topology being less intuitive than elementary algebra.
But students in high school and college are asking pretty profound questions during their algebra classes.
It's good enough to know what a variable is, how to add something to both sides of an equation, and that stuff is very obvious to everyone, I think. But as to why it works, that question isn't even answerable without abstract algebra and number theory.
Things like the Peano Axioms are non-trivial. Ignoring Godel's incompleteness, an absurd amount of work was being done in the 19th century to prove what numbers even are. I think you could reasonably train a monkey to do division, but "why does division work" isn't an easy thing to answer.
In Courant's book "What is Mathematics": "We learn in school the mechanics of handling fractions and negative numbers, but for a real understanding of the number system, we must go back to simpler elements."
Number Theory as a study only exists because while it's easy to say "take this, add it to that, and so, on," but it's much harder to answer why it's the case. Is it divinely inspired?
For example, in Principia Mathematica, it takes them something like 200-300 pages to prove that 1+1=2.

Apologies for the long writing. But a good deal of pure maths in the 3rd and 4th year is very non-trivial explanations of what is actually happening with an equation, why it works, etc.
Maybe I'm just stupid, but I didn't understand the "why" behind Algebra I and II until abstract algebra and, to an extent, real analysis. Maybe I am stupid lol.
But I distinctly remember asking in high school the why behind how algebra worked, why we are able to do thsee operations, why they work, etc., and I don't feel that I had those questions answered until my 4th year of college.
I would suggest that the criteria for understanding here are too strong
Hmm well sometimes we all have those 'aha' moments that teachers never give us
I really don't know how one can even try to understand why algebra works without field and ring theory. I think children are asking serious questions that are above their paygrade.
Understanding doesn't need to mean being able to give an axiomatic explanation for an idea
From a pure maths perspective it does, in my opinion.
But rediscovery through practice is definitely possible
Definitely disagree with that at just about every level
lmfao why is that poster so relatable every school had that poster
One can do calculations in calculus, but you don't understand calculus until analysis.
in that exact same font
Understanding to me has very little to do with seeing formal proofs
And in the context of the genius vs talented student, both will reach the same conclusion given enough time
maybe has to do with intuition
Engineers can do calculus for a very, very long time, with four classes of calculus, but it fundamentally isn't what calculus is. No matter how many times you rep out problem sets.
You can understand why something should work via heuristics, well chosen examples, having done lots of representative calculations, etc
In essence, math is man made, so it should be able to be understood by man
You can tell someone why riemann sums converge to an integral and are a good tool for defining integrals without doing any proofs
This is agreeable to me. I just personally don't think it's very easy.
Easy in the sense that difficulty varies depending on environment and intuition
Diet math isn't fun
You can't even rigorously define an integral without analysis. Pure math probably would not exist if it was enough to just do lots of problems.
You don't go to burgerking to understand why the burgers are made
And especially for basic algebra, you can definitely see why things like solving linear equations or completing the square of a quadratic or things like that work in a variety of ways, from geometry to agreeable manipulations to explanations by words
Pretty much immediately after the creation of calculus, people were unhappy and needed analysis to say "but why."
Rigor is a vehicle for math
Even abstract algebra is like a godsend
I would argue that rigor often stifles math
I cannot think of a single example in which that's true.
Bro 1000%
Why are the physicists so far ahead of mathematicians in developing mathematical physics?
The shit they come up with is all right
Yeah, but there's a lot in the intersection especially in modern physics and modern pure math
In just about any field of pure math
I'm a pure mathematician and I care about physics, but I couldn't care less if my research ever leads to something useful.
I think that's fine, but it's separate from whether or not one benefits from working on math with the mindset of a physicist sometimes
Published proofs should have been established rigorously certainly
Pleasure vs sport
But a lot of math happens in a different order from that, starting with heuristics, getting blocked into broad flavors of arguments and groups of conjectures and partial results
I'm absolutely confident that doing lots of calculations is valuable to a pure mathematician. I've worked through many engineering books. I think it's useful.
But mathematics is completely nonsensical without rigor. You literally cannot expand upon math without rigor. You must have rings and fields before you say "okay, now that we know what algebra is, let's do this with it."
this is a recent development in math
math was done "without rigor" for longer than it's been done 'formally'
Personally I think math should be made easier and more accessible
how can you make the math easier
the math is still the math
You can't viably use something so difficult it's alien

Okay, how about this. A lot of euler's theorems were conceived in the absence of any kind of algebraic or analytic formalism. Would you call all his results conjectures?
Of course it was. Yet Euclid's Elements became the second most printed book in human history because of its rigor.
Relative rigor.
Do what we've been doing LOL
because of?
that was the primary reason?
not... the lack of other written texts and a long standing tradition?
Amen
I would call anything a conjecture if it isn't accompanied by a proof. That's the definition.
this is ad hoc though
I think rigor is really important for learning math but it's not usually how one gets into understanding math that hasn't been explored yet
It isn't formalized until Euclid.
I think it's more apt to say that Elements is just straight up useful
sure but i disagree that its popularity was because it was "rigorous"
I'm assuming I'm the only pure maths major here lol.
???
lol what
Yes because im a pure math phd student...
im the only pure maths major in the mathematics server
only one in this discussion, not on the server
I'm leaving the library now, so I'll respond later. Take care
blud used his library time to argue on the internet... he's just like me frfr
I also will say we get a lot of undergraduate pure math majors (especially first and second year but with advanced background) who have a very strong fixation on rigor, one which tends to ebb away after they work on some kind of research project or maybe start preparing for grad school / start grad school
(and then there's the 10% of them that go into foundations)
Haven't left yet, but leaving now.. I've been here for 5 hours lol. I live in the library, so I pretty much only use discord here
anyway, I'll respond later
you can literally justify the most commonly seen number system (R) with the beginning of terrence tao's analysis book, which isn't even an algebra book
and even that is overkill for "understanding" basic algebra
That's actually the 10% of the 10% that does foundations but doesn't believe in rigor
Modus ponens is false
Anyway the rules of math are just culturally conceived, especially the proof theoretic rules, so it's kind of hard for me to buy any absolutist notion of mathematical understanding
rigor is cringy until you use your rigorpowers to outrigor treatments you disagree with
I'm not a math major, just CS but curious about its history and application
Especially when the evidence is that mathematicians force math to work a certain way rather than math forcing mathematicians to work a certain way. Plenty of people get plenty of good math out of nonrigorous argumentation
You hear things like "we don't need this" in school a lot and math quite literally ails students physically
I'm not good for rigor though as I burn all my books and notes
tbh, I still feel the same toward many topics in math
Category theory, logics, model theory, and to some extend, cohomology, are some in this group
What way is that
it's sad that we don't see so much motivation when it comes to math
All the alg toppies i talk to say that you can do as much hom alg as you want but you won't understand anything until you compute a ton of examples
I don't think that mentality is really there for like. Modern alg geo though
Field theory makes absolutely no sense to me until I understand Galois theory
Ring theory, the same, until applications to number theory, and intro to alg geo
some textbooks attempt to motivate stuff and play the role of historian, but i don't think there are individual stand alone books that are all exposition with titles like "History of Differential Geometry"
in some sense, I do understand why that approach is not popular. It's too slow for the usual pace, you won't get anywhere fast with that style. Plus, if you actually do Diff Geo the way Gauss did, or group theory the way Galois did, you will find it completely horrendous.
Usually it's like "this new thing we're going to study comes up in this other part of math you already know" or "this new thing has a picture that suggests why you might care about it" or "the results we are going to prove will end up being useful for understanding this other thing you've heard of"
But math courses usually take too long to get to the interesting stuff
People can do the interesting stuff themselves! Someone needs to force them to take their medicine
Why not both?
instead of building field theory from ground up, you can teach about field theory the way Galois did it originally, and draw parallel lines with modern field theory and how it has changed
That will teach the students more than the math. That teaches them how to think about something new
Where can I find how Galois originally thought about Group Theory?
🤷
that's a bit of the problem. the resources for learning about that sort of stuff are either lacking or obscure
I recently read a good book about Galois theory, gimme a sec
Galois theory by Stewart, 4th edition.
he didn't completely include Galois' original memoir, you can find translation of that online. But he did build Galois theory ground up, added a lot of historical context, and explained precisely what Galois actually achieved.
another problem is profs tend to teach something the way they learned it, and most never got interested in the historical context
Most ppl forgot what it was like when they were beginners
'ttends, t'es français?

yea seeing the historical context would be great
lmao i was in french mode sry
brain not braining properly
if you do speak french, feel free to look up Galois' memoir xD
is galois french
galois biggest loss was that he was french
oh
historians say that’s most likely his cause of death 😦
he probably surrendered in the duel
If only were he German, he would have thrived like Dirichlet or smth
or hungarian
,w galois
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I feel sympathetic toward him, I almost threw chalk to the examiners when I took the concours myself
Who was the mathematician who finally noticed the importance of galois' work?
Some say his methods were too original. Or could it be he was beans at everything but abstract algebra
That's it
the guy that did the 0.1010010001… is transcendental
there is a pattern tho
Also the best theorem in CA
Transcendentals can have a pattern
It's not a normal number
One of the few we can say is not normal iirc
Oh I mixed stuff up
for the time, definitely. No one thought about those objects like he did. Algebra was definitely a thing, but it was in no ways formalised until Galois came
Irrational and transcendental
most patterned numbers are transcendental
Is e patterned
well i said most patterned numbers are transcendental not the other way around
as long as the pattern doesn’t repeat yk
e has no apparent pattern in base ten
wait
whats a parrtern
cuz there is a rule for e
its sums of 1/n!
isnt that a pattern
tbh idk what we are considering maybe an arithmetic/geometric sequence
huh
i thought u meant the decimal
no yea but
there isnt a pattern in the decimal ig
but doesnt theother thing
count too?
idk the term pattern isn’t rlly precise
ok
wdym?
im confus 😭
Homophobic everywhere
Omg
Holomorphic
I was mixed up in my definitions
I'm thinking about a proof of FTA
It used Louiville theorem
what is the age thing for this server
@quasi jetty what is the age
/age restriction
13
Skibidi

how is the "x solutions remaining" score in wordle solvers calculated?
I'm looking into creating a wordle opening book of sorts, where the first and second move is "theory", essentially
obviously, I can't put down all 3^5 (243) possible results from the opening word(salet, in case you're wondering)
An idea is to treat greens and greys the same, but in order to even do that, let alone figure out if that's a good strategy, I need to figure out how "wordle eval" works
Math is too hard
Not
Yes it is
If I can do it anyone can tbh
Thats meritocracy bullshit
Math is too hard
External forces are to blame for peoples issues
I agree with you but you can also increase your chances of success
You know about self fulfilling prophecy
How can 'anyone' do it if they don't have access to internet or books or school?
Hm books are pretty necessary
hi
Okay so.
If you're motivated enough you can learn anything on the cheap
and the venticles are the lower chamber that pump blood to the arteries
Not if you are a refugee and don't have access to basic necessities
Are you?
No but you specified anyone
This is kinda accurate again
ok
So here's the thing
if you literally have nothing to learn from its hard yeah
He had books
he had stuff to learn from
wait accurate or inaccurate?
Atria will collect blood from different parts of the body.
That was auto complete
And Ventricles will pump it to different parts of the body
ok
Yeah.
Ramanujan wasn't a pow or a refugee fighting for survival without basic necessities. He had to deal with poverty but he had resources and time to learn
What's your point here?
Yeah
On the same side of the heart
That I'm wrong to say anyone can learn if I can?
You specified 'if I can do it anyone can' which is clearly false
The ventricle is bigger... So like... The right ventricle is bigger than the right atrium and same for the left
i think this more refers to skill/talent
not like
Exactly
being able to afford books
ok In what sense is blood flow in the body one way? (Think which direction blood moves around the body)
Okay... So tell me.
Where does the blood come in first.
Well you could also just tell me what is the direction of blood flow in the heart. That's pretty important
bone marrow?
o
There's many places different components of blood are made
one direction is the bloodflow in heart
I think that there is a discrepancy between poor and rich in schools due to school forcing competition when people have unequal resources and time and a myriad of other things
Where and how?
.
this has literally nothing to do with his point
wym by that
his point was that if he is bad at math and he can do it, anyone can do it
i disagree with him being bad at math but thats besides the point
So what chamber of the heart does the deoxygenated blood enter
right ventricle
I think here you also need to be acquainted with deoxygenated and oxygenated blood.
@hidden bough thanks homie
Read what you said about ventricles and atria.
i did
I don't think I'm super talented I just love it so I spend time at it
real
That point could be interpreted as 'if you are bad at math you didn't try hard enough because I can do it and therefore anyone can' especially he said it in response to me saying math is too hard
So does the ventricle pump blood out of the heart or recieve blood
pump
youre kinda tilting at windmills here
/oh so art
atria
Don't be such a Debbie downer
LMAO
it's such a great sketch
idk
Yes
?
What .?
Anyway math is too hard
You don't know?
nuh uh im stupid and i can do it
left?
No
I will say it's difficult to succeed at things you don't like. Because then you need toms of discipline
so right.
Fr this channel is talking today
Here we go again
It used to be shush here
so what is the conclusion
also "again"?
Im very stupid, but thats besides the point
He's going to talk about meritocracy now and the conversation will begin a new
MUHAMMED
Thats right
why did bro just dip
bruh
its not besides the point
if we're both stupid and i can do it
so can you
Meritocracy is fiction
how is this meritocracy 
this is basic logic
if i have low skill and can, and you have low skill, then you can too
(low skill=>can)^(low skill)=>can
It is not basic logic, there are millions of assumptions you are making here.
^
Those variables have lots of implicit connotation
name 1
Low skill implies a person has low skill in the material world
as opposed to what? the metaphysical plane?
the freaking spiritual demon land?
The variable has implicit assumptions that aren't defined within the logic
im asking you to explain those assumptions
what kind of skill is there other than in the real world
Is this just an exercise in pedantry
kinda?
You are giving an interpretation to those variables. Those variables are not just placeholders for true or false, but have implied meaning
It's not just basic logic because you aren't just saying a statement that is tautological within the syntax of the logic, you are using an interpretation of that statement to say something about the real world
Yes
Im trying to say that math is too hard and the other people are saying it's not too hard
anyone here good at Fourier transform? Just need some help
If it was too hard no one would succeed
No. It's hard enough to filter people out while letting the minority through
Which is too hard
What math are you studying btw
I don't study and i don't read or work out or do anything
Don't get me wrong it's difficult but that's why it's worth doing
It's difficult to sleep on a bed of nails, but it's not worth doing imo
Just because things are difficult doesn't mean they are worth doing
Have a listen to this track:
(Give me your opinions)
https://open.spotify.com/track/3j18z2KnqmnXanajoY4ecQ?si=EgpzzO78SUSCmKqmzBwGXg
Did you write this?
If math is so awesome, then why did grothendieck rip up his papers towards the end of his life and renounce mathematics and say that noone should study algebraic geometry or has the right to use his works
How cool
because he was old and bitter idk
Let me get headphones
Would appreciate if you guys could give it a listen and follow me
I'll critique your mix
It's pretty good
Good beat
Mix sounds pretty good on my beats too
If you don't already get it it's hard to make you get it
In my experience
Bro is setting a fire to his own temple
Wikipedia says that grothendieck wrote about how the mathematics community was "a guilded cage" and "governed by competition and status" because grothendieck had a "deep compassion for the poor and the downtrodden". And "the issue of military funding was perhaps the most obvious explanation for Grothendieck's departure from the IHÉS". To me it makes a lot of sense why grothendieck thought mathematics sucks.
Math teaches how to increase your chances of success and reduce chances of failure
It's worth studying for that reason alone
@neat lintel why are you in the math setver
It also sucks like any other tool but should be utilized to the extents necessary
This doesn't sound like an issue with math though, as any community has it's limitations
For someone who hates math you sure love grothendieck
He was my algebra professor's fave
You're worrying about the personal preferences of a dead guy?
All history
Do you like to study math or not
To the extent of aligning your own views with their own?
Study for your own sake not the opinions of relics
Your reasons probably aren't 1:1 with theirs
That's very ridiculous
Yeah ikr
Saying math is useless is like saying you aren't human bro
Never said that
I'm not sure what you're arguing then
Im saying math is too hard and sucks
I will
Breathing oxygen is hard
You're fucking right
There's no reason not to be able to use it with literal free internet and other alternatives
Breathing oxygen IS hard, and math is too hard.
Ok, why is math too hard?
Because they make it hard enough in schools in order to purposely filter out people from going to higher education
Is that your only reason?
It's a legitimate reason
I think you're confusing academic math with the pursuit of knowledge
Without a curriculum, there is only the math
In what way is this hard?
Because math is written by people and influenced by elitist culture
So you can't really escape the elitist element even if you say 'you are pursuing knowledge'
Change schools, change teachers, change books
Regardless of elitism each individual still has ultimate agency in the learning process
Theres not enough books about stuff like Langlands for example to have freedom of choice. You can't just 'change books'
You have to still interface with books
What is bro talking about
is that specific to math?
this happens in any field when you go deep enough
and langlands is definitely deep enough
Bro thinks academia = math
There are alternatives and you don't necessarily need any of those things to learn or practice math
How else can you read about Langlands besides from academia?
Very very sad world we live in
At any high level things become more constricted
Be the change you want to see
It's just the curse of awesome
It is still shitty dealing with math as it exists today. Math may not suck in the future, but today it sucks
how exactly do you want langlands to be translated for the lay person
or accessible for that matter
Arguably I think there are more PITA things than math
There are
because there's a heap of prerequisites before getting to it
But human production has always been constricted throughout history
Learning is hard, but teaching is even more so
I think AI would be the perfect solution for you
Theres a difference between having no prerequisites and being written with an elitist tone. Like when people write 'this theorem is easy' or 'its obvious'
Professors just write that because they are lazy
Mmm pita
Well I'm a reader and I don't think it's written for me
Well there you go, elitism
so technical literature = elitism
It'd be nicer if books were written more generally, but what do you expect out of select text written for select individuals with specific knowledge????
Everyone has technical knowledge, that has nothing to do with accessibility
the "this theorem is easy/obvious/easily verifiable" is endemic to mathematics because writing out theorems that mathematicians at that level should be able to keep up with obfuscates the central idea of the paper
Lack of ability is not elitism
this tangent was about specific tone and implicit culture like saying 'its obvious' which is not a necessary property of technical literature
i just explained why that comes with the territory
the point of a math paper/specialist text isn't necessarily to teach someone completely new to the topic and guide them along
it's to communicate results
To that end, there are still alternatives
You can write 'this theorem immediately follows' or 'with minimal additional deductions this theorem follows' or something
Yes they are
its literally just a more roundabout way of saying the same thing
See why math is elitist?
if your'e taking personal offense go to therapy or something
With a different tone
Math is much less elitist now than ever before in history
I think your concerns are too politically skewed
it's not some objective truth that these words carry the emotional charge you're assigning them
Therapy is a logical recommendation in this instance
You need some reprogramming to dilute some of these beliefs
Thats your own prerogative. I like the stanford rules
I don't have a goal though
you really took the word prerogative and ran with it
If anything I support you actually
You just said "You need some reprogramming to dilute some of these beliefs" which is your own prerogative
Yes I did
Great!
Since I'm one of those people that were 'transgressed' by the exclusivity of higher education
I'm glad that other people recognise these issues in mathematics
Uhh well yeah that's why I'm on this crusade at all
But I think you're going about it the wrong way
You should just promote more open learning and less 'it's obvious' methods in education
I bet there is evidence
cool, go find it
If the advanced book is really good they will even recommend suitable pre requisite material or a refresher chapter
what the fuck are you talking about
you’re expected to have the required knowledge
’its obvious’ is not an elitist tone
i think saying trivial/obvious/simple is fine
Yeah
[insert function that is obviously continuous]
this function is obviously RI because it is continuous
the solution for most mathematicians if they're unable to see the proof would probably be to email the author, "hey grand old buddy of mine who authored paper X, can you elaborate the proof for (3)?"
yes
these are your colleagues and peers afterall
who you are working with... to prove more math...
we literally have the internet
exactly, knowledge is easily accessible online
with internet connection you could master almost anything
Bro is stuck with tomes in Rome or something
he said "i assume is obvious to you" and i said "wait how is this trivial"
Funny story, we called them tablets back then too, imagine
moment he mentioned cacuhys theorem i understood
,w cauchy's theorem
which one 
That one?
cauchy mvt is honestly such a cool upgrade to regular mvt
rolles -> mvt -> cauchy mvt
satisfying direct upgrade
Oh boy here comes brad
They pinged me
that’s the subjective rule for that server
of course if they said it like
Well it's a good rule with a good justification
"is this not obvious to you?"
,w cauchy mean value theorem
yeah you are being a dick
If you’re studying deep enough in a field, you wouldn’t bother writing trivial things out
the case should be more subjective
Rad
Texting is elitist
but saying "this fact should be pretty trivial so let's not write down this part and get to the real meat and bones of the proof" is fine
Why is this fairly attractive woman sending emojis instead of reddit paragraphs
this is your own personal preference
why do you keep bringing up the stanford graduate math discord server
as if this is some supreme authority
bandwagon appeal? appeal to authority?
i like to use "it shouldn't be difficult" or "it is straightforward" because i usually really mean "it shouldn't take much work and if it is you might be doing something wrong"
it's unclear which one you're doing here
unfortunately this is a lot of words
I actually do think that "it is obvious" is almost never the best way to write it
Are you in university brad
and cool, you found other people that agree with you? i'm still free to disagree and think that the wording is not as deep as you're making it out to be. it's only ever harmful if it's actively detracting from the paper by hiding key things you're meant to recognize
bad writing \neq elitism
Saying 'I need therapy' implies that I am the odd one out. Does it not?
I usually use "it is clear" or "trivial" instead of "obvious", though I guess they effectively are the same
weird that you're using quotations when that isn't a direct quote
It’s synonymous
"if your'e taking personal offense go to therapy or something"
They really like Stanford I think
I think they were suggesting therapy cause you seem stressed about it
Okay?
yeah because it's ink on a book or lights on a screen about math. it's not offensive in any way
This sounds usual
How is that a prerogative
lmao
I think I remember why I hated math now
this person has me blocked btw
LOL
People still use the block feature?
this is kind of funny
Ikr
i use it but not to continue opening messages of the users i blocked 
I block too many people
I don’t block people unless they’re being annoying like DM spamming, blocking people in an argument proves their point as you can’t find an effective counter to their statement
When the ex contacts you
dealing with exes are amusing
Also i don't like being bombarded by sullys by mean people

I’m an online dating veteran, I date people online simply for their information while offering information in return




nice theorem
If you become a teacher
i personally find "it's obvious" rudin style of writing to be obnoxious when its in intro texts, but im also bad at math so
Also this conversation seems really unproductive
maybe it is obvious to someone
It's their right to think that way
does anyone in this server think they are good at math
Don't just tell other people to seek therapy because they think a style of talking is upsetting lol
If I become a teacher, I’d use ‘it’s trivial’ pretty often because I believe in condensation of knowledge
none of the ones that are good at math do
Oh g is the identity function for the special case of mvt
Yeah, it’s everyone’s rights too
I do
Like the typical professor probably
based
Im terrible. But im terrible at everything
i guess i did jump the gun here and should apologize @neat lintel
You're right, it was the templars who invented math
ye but thats someone elses fault
so its chill
the freemasons invented algebra
al jebra
al-jabr
smthn weird like that
weird?
to mechanical engineering
yeah, what a weirdo. he did algebra
I think al jabr was the name of the book
While the name of the person was al khwarismi (which is where "algorithm" comes from)

I'd like to get a copy
how do you turn khwarismi into gorithm
Idk
imagination
it's pretty similar, no?
i can kinda see it
kh sounds like g, s sounds like th
yeah almost exactly the same
El Algorithmo
the tongue placement is similar but it doesnt sound anything alike imo
i definitely see it now
Alkhwarismi -> alkhworismi -> algorismi (since you don't have the kh sound as much) -> algorithm
al-jabr means setting of broken bones
These naming schemes are too elitist
or idk probably some weird counting thing with bones
When math and death are closely related
I think it meant the whole from the parts
I mean the actual pronunciation of "Confucius" is more like Contzu lmfao
huhh
Our ancestors were woke beyond understanding
Hundreds of years of dialect changes and the telephone games between translating through multiple languages
bro temporal telephone js crazy
Wasn't Japan zipangu
ye ig
some dude couldnt do the s right and transmitted it as a th
contzu? 
Actually I dunno how it was pronounced back then, I know how it's pronounced now
Yeah no vowel would've really done it super well lmfao
Or I guess there's a technically correct way to transliterate but idk it + it has other characters I can't easily write down super easily 😛
I'll take it
Listen to Dolphincore by cali5nia on #SoundCloud
https://soundcloud.app.goo.gl/CAa65
Collection of jams made on a Korg Electribe EA-mkii and Akai Tom Cat
Made it on hardware synths
Isn't Confucius latinized name 
Yeah Eric knew that, and that's what I was alluding to
Just my transliteration made it seem sketch
What is damimark's latinized name
69
Incorrect
😭
420
80
do u single dog dare me??
What information format on the back-end is needed for plotting a diagram in a graphic library for Python? Like, only the symbols are needed and the front-end works from there?
Need a program handy for future me.
!help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
what does this even mean
I need to generate some diagrams, but at some point they get overly complicated to draw on paper and impossible to draw on ASCII screens. Although drawing on ASCII might work as a proof-of-concept for the future program.
what do you mean by diagram
Image meant to visualize something in maths.
Not that this is the correct definition, but I thought everyone would understand.
this is the least helpful description possible
do you have an example
is there potentially a language barrier
I had to draw on a monospaced notes app because my touchscreen did not feel like clicking the attachments icon:
.
c
|
a--b
\
\
\
b--c
\
\
c```
I made this to visualize a powerset. You can now guess it is a language issue because I was the "power of a set" guy.
One line links a letter to the rest of a set it is in; a is in {a,b,c}, {a,b} and in {a,c}, b is in {b,c}, c is included in every mentioned set.
i am lost
Hi d2
bees are fish
Hi Muhammad
The converse isn't true
not fish are not bees?
Hi HSF
That's contrapositive
I said the converse not the inverse
Okay well - cposi
I'm trying to call one of my HS friends but he's not picking up the phone
Since two days
were u able to understand

idk why it was like i woke up today and i had infinite energy
usually i just fuck around as much as possible a few periods into school but i concentrated for the entire school day (8 periods for me)
Are you undergraduate?
ye
Makes sense
I'm in highschool and there are like 9 periods
Your second message
?
undergraduate means high school or college right
as in "you have not yet graduated college"
they should get somebody to fix english what is this convention
high schoolers are underundergraduates from now on
also damn, which country?
Canada
normal people (don't have AP) in my school take 6 periods with 1 other period break
almost 7h total
Each period is like 30 mins
oh ok if its 30mins that makes sense
damn you start school late for where i live
(Made this in latex)
But its tiring when you get home
The time goes fast
For some reason
we start school at 7:15
even at ramadan we have late beginning and early end but that's still like 8:30 i think
Oh right ramadan
I think it's same time
It's not gonna be change
Had to make a new time management for next semester since im doing two math in a row
Something called night school
i feel you, i leave at 3:10, (normal is 2:00)
wdym
You blink and it's midterms
you take both uni and high school?
Nah this is my last year being in highschool
then how do you know how fast uni feels
But that's what I heard from my friends
ah okay okay
Night school is like 6pm to 9pm
i feel like the 1h period system kind of forces teachers to make breaks in class
Nah it's a course I'm gonna do next semester
In canada they call it advanced functions
I'm doing advanced functions and calculus at the same time
cool
I don't think I ever gonna done these math very well in a row since I have English and shit
But I'll see what happens
is night school for improving applications or is it just a for-your-own-sake thing or?
I have reasons...
... ?
I'm doing repeated courses cuz I keep getting strict teachers
I've went to three different highschool now
Strict teachers im getting like doesn't give a shit if you asked for help or smth else
I remember really
i'd say bad teacher lol
Don't*
Yeah and always like "university will be harder"
ye
I think my highschool experience was already messed up since the covid 19 come out
University was easier for me than hs because I got to choose courses I wanted to take
Chad
Ofc material is more challenging but I liked that
its not a myth?
Wdym
idk ive always been told don't think college is easier just because you get to choose/its less in-school time
ah ok
would you say the university itself matters a lot in whether you are going to enjoy your uni experience or not?
I'd say so
The culture can be really different
I went to party schools. But I was too old to party in grad school
example? and how can you really know about university culture as an hs student?
Maybe try visiting, asking students there
what if it's international? how could you contact students?
what about profs? would they be interested to answer? would they answer honestly?
I think you might speak to someone in admissions
admissions? that seems like the least likely to answer honeslty to me
in my mind i see them as more believing in university-ideals instead of university-realities, but maybe my idea is wrong
maybe
i honeslty don't understand how university culture would vary aside from study-more/less or socialize-more/less
well university is a lovely place to socialize and become a better person
Silly question: do theoretical physicists do any experiments at all?
I believe "theoretical" means not applied Ie. not working in industry
Like those at CERN are theoretical physicists
no people at CERN do a lot of practical stuff like analyzing data using statistics (most of modern physics is basically stats)
I know because I had to learn CERN's root package which they use for these kinds of things and watched a few talks about it
each has its own set of traditions
there aer also historical differences
in France for examples, ENS Ulm and Ecole Polytechnique are often seen on two opposite sides of political spectrum
the world is bigger than you would imagine once you get there
LinkedIn 
I tried, and it did work out tbh
Now I try to return the favour to anyone who asks
An safer bet is look for students who also graduated from your hs
then look for friends of friends
Or get drugged and kidnapped
hi, does anyone have an experienced opinion if the openstax intermediate algebra book is a sufficient preperation for a community college precalculus course?
pretty much every elementary algebra book will be sufficient
heck i think they are more than sufficient
For sure
i just reviewed its table of contents and it looks like it hits all of the expected cpntent for a 10th grade algebra class, which should be prepatory for precalc
Don't buy anything
thank you for that.
yeah i took 2 semesters of calc back in 2009 and im just finished the elementary algebra today... im going to speed through the intermediate algebra and hope to take precalc in spring2024 im excited.... been out of the loop for a while
Smart

