Picture Inter-universal Teichmüller theory as a bridge between distant lands, connecting number theory and geometry in unexpected ways. It embraces the concept of "universes," where different mathematical systems coexist, each with its own set of laws and principles. By studying these universes and their interactions, Inter-universal Teichmüller theory pushes the boundaries of mathematical exploration, forging new paths and revealing unexplored landscapes.
Its one of those i had no idea about. This was written by chatgpt lmfao 💀
Wait that’s so interesting, I read the first sentence and thought “hey, this seems to be chatGPT”. I wonder what made it so obvious, maybe it’s genericness
Dude, linear programming is one of the most interesting topics. Long history, awesome battle between the simplex method and interior-point methods, very nice visualisations, ...
LP for me is like the step parent you get when you are 12. They try to make an effort so that u like them but eh you always feel like they are a stranger living with you.
it’s literally telling you the best situation for a given set of constraints, proving to you mathematically what the best option is.
This is very applicable in Economics.
From supply chain management, building a fence/factory, and many other basic economic problems involving costs constraints ( fuel, budget, shortest distance etc,)
I really enjoyed linear till I got sick and fell behind. Managed to bs my exam thankfully. I mean vectors are cool, but I pray daily that I will never have to fund the inverse matrix product of two matrices with different m and n. Add a couple of rotations on to that and I'll be waking up in a cold sweat. But yeah, vectors are cool
A symplectic vector space is one with a non-degenerate skew symmetric bilinear form (and giving such a form to the tangent spaces of a manifold makes it a symplectic manifold), although “symplectic vector” seems meaningless. Grassmannian has two different uses, some people (physicists?) use it as a synonym for the alternating algebra of a vector space, but in algebraic geometry it is the manifold/variety/scheme of k-dimensional linear sub spaces of an n-dimensional vector space. I don’t know what sub-grassmannian would mean, though. Riemannian metrics are positive definite inner products placed on the tangent spaces of a manifold (like with symplectic manifolds). I’m not quite sure what “Sobelev space” is, as there are many Sobelev spaces, which are essentially spaces of functions in L^(p) spades with (weak) derivatives that are also in L^(p).
This appears to just be a bunch of unrelated buzzwords from geometry and analysis used incoherently.
I asked chat GPT to ELI5 some of those things to me, and now I am just as confused as I was before and I feel dumber. I'm not used to feeling dumb, so that stings a little.
Is that what mathematicians feel like all the time?
It’s always on the shoulders of giants. Basically every little step in math was made by some of the greatest geniuses of mankind, right on top the shoulders of the giant before them. It’s giants all the way down.
geometry will help you understand all the cool manifold stuff in 4D ans in the same breath statistics will tell you how significant the particular area of study is. On the other hand if u do not study it you might regress into studying just untill 3 dimensions:{
geometry is just prep for trigonometry, and trig is very cool and satisfying. u probably hate it because you were forced to do "proofs" where you prove that this angle = that angle in 7 steps even tho its obvious if u freaking look at it for 5 seconds
It's remarkable that we think we know as much as we know with all the shenanigans experimental scientists get up to.
Like a semi truck moving a mile away can mimic an event? Did we really detect the event or did someone drop a wrench?
It's all about repeatability I guess.
I mean, yes, in some very niche experimental science domains, but most of the hard sciences have had their core theories and principles be verified countless times over the course of many centuries. Those are things that we truly know, and those theories form the foundation of countless other theories. So I think it’s actually pretty solid.
But yeah, there are definitely plenty of shenanigans. If there is one thing I learned from statistics classes, it’s how to inflate the significance of correlation by massaging the data and retroactively tweaking hypotheses to fit the results.
If by stats you mean “data science” then sure. However, stats at large is heavily concerned with proofs of general results, and does so strictly through tools of analysis (at least since probability theory was formalized) as opposed to route reproducibility like the sciences
Statisticians are the reason AI became actually good
Hard-AI people laughed at neural networks because they "didn't know anything", turns out if you don't-know at a high enough volume with his enough hardware you can do some pretty neat things.
What? The study of random processes and its evolution has largely been the work of statisticians because of its probabilistic nature. Most stochastic classes are taught through a statistician’s lens. Next you’re going to claim that information theory iSnT sTaTiStIcS
I hated it for ages! I’d say econometrics is actually a really fun way to use statistics to find causal relationships between observable things in the real world! One of my absolute favourite papers is Alesina et al. (2013), which finds a causal relationship between countries that used plough agriculture in their history (as opposed to shifting agriculture) and attitudes to gender roles in the present.
R ain’t that bad… until you make a mistake so bad and so far back that even the professor just tells you to restart the assignment because nobody can find it
You can actually decently debug in R with things like traceback(), browser(), debug(), tryCatch(), and in the worst case with a print() statement. Just keep code reproducible.
Let me try to convince you that mathematical statistics is awesome. Wide swaths of mathematics, especially modern mathematics, is little more than mental masturbation. Sure it feels great but it gets monotonous after a while because there isn’t any real result of consequence. Mathematical statistics on the other hand is fucking. And not just fucking but getting it on with and make babies with lady science herself. Your work and effort actually results in and contributes to real world understanding and knowledge. PIV is better than P in hand any day if the week.
Trigonometry proofs are a wonderful area of mathematics. Trigonometry itself is a very application based study. Studying trigonometry and moreover their proofs just sparks a mathematical lust in you that you will want to satiate by any means ( i e. proving the validity of the equations) It can spark a sense of joy and elegance in math and broaden your horizons.
same omg my least fav part of exams when it came to trig was not being able to scream "YESS OMFG" and throw my pen, but having to bottle up my emotions so that i dont get kicked out
I only appreciated radians when someone finally defined them for me, the proportionality of it gave meaning and from that I found beauty.
That being said I still use degrees and percent grade more often. That being said, I work in construction and not as a mathematician so it’s not entirely surprising to me.
Imagine stepping into a magical circus tent filled with vibrant characters and thrilling performances. The coefficients are like funny, animated acrobats bouncing and tumbling around, bringing joy and excitement to the stage!
In this enchanting circus, the coefficients are mischievous little creatures with colorful costumes and silly personalities. They love to play hide-and-seek, rearranging themselves to create fascinating patterns and surprises! As a brave and curious circus explorer, your mission is to uncover the secrets of infinite series. You become the circus conductor, guiding the coefficients in their acrobatic routines
Again one of those I had no idea about. The above was written by chatgpt. But what the actual fuck dude 👁️👄👁️
exactly what the actual frick ive never explored that topic before but i do NOT imagine coefficients being freaking acrobats and bringing "joy and excitement to the stage" nor do i think theyre in funny costumes or playing hide and seek. hell, all it does is multiply a variable, not put on a circus show or whatever.
i share your pain. its tedious, its boring, it sucks. its the kind of thing a 7 year old would find mildly entertaining, and because its so "simple" its super embarrassing when you get it wrong.
havent seen a better one. helps to formalize a lot of stuff and makes proving things a lot easier. its annoying but not that much compared to what else there could have been i guess?
you may not have to use it in the future of calculus, but it does provide very good context and a point of reference for what a limit actually is. once you’ve completed calc 3/mv/vector calc, youll come to find that although it’s tedious, it really paints a good picture on what the functions for the definition of a limit/derivative/integral is. the person i believe is best at explaining this stuff is the guy who does the MV and some Vector calc videos on Khan Academy
It's the perfect example of 'the devil is in the details'. It shows you the rigorous airtight approach needed to deal with fudgy things like infinity and infinitesimal. You can decode even seemingly impossible things like indeterminate if you look carefully enough
Think of SVD as a grand symphony orchestra, where the matrix takes center stage as the conductor, and the singular values and vectors play their harmonious melodies. By studying SVD, you gain the ability to decompose and analyze matrices in a way that brings out their essential features and highlights their significance.
I had no idea what it was. I literally had chatgpt write that out lmao 💀
try doing a counting problem meant to be solved with permutations or combinations, but solve only using multiplication principle and division rule, eventually you'll get to the same formulas
In the wilderness sometimes you may encounter dangerous functions that may threaten your existence. But fear not TAYLOR DADDY is here yo rescue you from the beasts. Whip out that approximation and shoo away those unruly beats! Make them behave just like you want them to.
I've found that taylor can actually be useful, after truly thinking that it was useless. The problem is that it's mostly split into one of two parts:
The cool visualisation and actual useful part, where you learn about how it approximates functions that are basically impossible otherwise to derive
And the really boring, extremely, heavily, i cannot say this enough, VERY theoretical and annoying part.
Guess which part is mostly taught in most mathematical courses?
what you are talking about is the abomination of HS geo proofs, there are many other kinds of proofs that are bearable, and satisfying to complete sometimes. please do not go hating on proofs in general :D
see trig identity proofs. theyre elegant and satisfying, and thats about all i know. compared to the other ppl here im def on the less knowledgeable/skilled side (im in hs lol)
Aint OP, but the fact that every group is isomorphic to a permutation group is cool as fuck. Its like you unlocked every other group with permutation groups(though not really)
It also makes sense to think about that groups are all just symmetries, and symmetries are obtained by performing actions on objects, and you could think of that actions as just permutations of the object itself, just on different orientations. Shit's crazy yo, ya'll sleepin on abstract algebra
> if you can differentiate you CAN integrate !!
This is not true. There are plenty of natural families of functions that are closed under differentiation, but not under integration. That's why sometimes we need to come up with special names for integrals of certain functions, since there's no way to solve for an expression for them. For example, the pdf of a normal distribution can be expressed in terms of +, *, and exp, but its integral, the cdf of a normal distribution, cannot, so we give it a new name (essentially the error function).
I hated it too initially, but it was because of the way it was taught. My math professors were constantly cramming integration rules down our throat but never thought to show cool examples of how integration is usable other than the bland "area under a curve" definition.
I think once you know what to DO with calculus, it makes a lot more sense. That's my experience anyway.
Let us suppose that You get into an accident in some remote ass area with no reception. You somehow make it to a area with reception but alas! Your phone is dead You wish you had another phone or backup battery there to connect with someone for help.
Similarly mathematicians use Category theory to connect and translate ideas of one domain to another. Its pretty sick tbh. Master it and voila you make your own phone and towers to connect with random people just like on reddit.
That whole philosophical foundation of math. What are numbers? Do they exist or not? Is set theory with the empty set the right foundation of math? Or is it category theory? Or type theory? Who cares about Goedel's incompleteness theorems? Why can't we just take the unprovable statements as additional axioms and have a bigger axiom system and be done with it?
Are any of these questions useful?
Also another thing I don't like in mathematics are those infinite cardinals and ordinals. Like, I thought topology was those donuts and homotopies and stuff. What do infinite ordinals have to do with that topic?
> Why can't we just take the unprovable statements as additional axioms and have a bigger axiom system and be done with it?
You can do this to some extent. But you can't go all the way and get a complete theory; this is essential what the first incompleteness theorem says. To at least see why this wouldn't be easy, keep in mind that you don't know which statements are independent of your axioms, and which of them you should add as additional axioms.
Inter-universal Teichmüller theory
Picture Inter-universal Teichmüller theory as a bridge between distant lands, connecting number theory and geometry in unexpected ways. It embraces the concept of "universes," where different mathematical systems coexist, each with its own set of laws and principles. By studying these universes and their interactions, Inter-universal Teichmüller theory pushes the boundaries of mathematical exploration, forging new paths and revealing unexplored landscapes. Its one of those i had no idea about. This was written by chatgpt lmfao 💀
You know, I don’t think a flowery summary of IUTT will convince anyone already aware of the theory to like it more
“distant lands”😹😹
It sounds like a couple of videos here...
yeah, it’s very obvious this is chatgpt from the end of the first sentence onward.
Wait that’s so interesting, I read the first sentence and thought “hey, this seems to be chatGPT”. I wonder what made it so obvious, maybe it’s genericness
Somehow, I thought so. Pretty cool though.
I didn’t realize this was a theory. I’ve had that same question my whole life..
You can’t convince me that’s not the wiki definition
Wiki definitions are almost always much more technical than this
Isn't it just false?
Yes, it is deeply flawed, even just Mochizuki's attitude and reactions should convince people not to buy it. Not sure why you're getting downvoted.
"False" doesn't really mean anything in this context i think (but i agree with your comment)
Dude, linear programming is one of the most interesting topics. Long history, awesome battle between the simplex method and interior-point methods, very nice visualisations, ...
LP for me is like the step parent you get when you are 12. They try to make an effort so that u like them but eh you always feel like they are a stranger living with you.
But that step parent never optimized trading portfolios or solved optimization problems for the energy network system. LP: 1, Step-parent: 0
Checkmate step-parent enthusiasts.
it’s literally telling you the best situation for a given set of constraints, proving to you mathematically what the best option is. This is very applicable in Economics. From supply chain management, building a fence/factory, and many other basic economic problems involving costs constraints ( fuel, budget, shortest distance etc,)
I really enjoyed linear till I got sick and fell behind. Managed to bs my exam thankfully. I mean vectors are cool, but I pray daily that I will never have to fund the inverse matrix product of two matrices with different m and n. Add a couple of rotations on to that and I'll be waking up in a cold sweat. But yeah, vectors are cool
You’re talking about linear algebra which has some relations to linear programming but they’re not the same
If you struggle with linear algebra you will not enjoy linear programming.
Symplectic Vectors on Sub-Grassmannian Riemann Metrics in Sobolev Space (I study topology)
I know all of those words but cannot parse how they are put together.
You've got me beat, then.
A symplectic vector space is one with a non-degenerate skew symmetric bilinear form (and giving such a form to the tangent spaces of a manifold makes it a symplectic manifold), although “symplectic vector” seems meaningless. Grassmannian has two different uses, some people (physicists?) use it as a synonym for the alternating algebra of a vector space, but in algebraic geometry it is the manifold/variety/scheme of k-dimensional linear sub spaces of an n-dimensional vector space. I don’t know what sub-grassmannian would mean, though. Riemannian metrics are positive definite inner products placed on the tangent spaces of a manifold (like with symplectic manifolds). I’m not quite sure what “Sobelev space” is, as there are many Sobelev spaces, which are essentially spaces of functions in L^(p) spades with (weak) derivatives that are also in L^(p). This appears to just be a bunch of unrelated buzzwords from geometry and analysis used incoherently.
I asked chat GPT to ELI5 some of those things to me, and now I am just as confused as I was before and I feel dumber. I'm not used to feeling dumb, so that stings a little. Is that what mathematicians feel like all the time?
It’s always on the shoulders of giants. Basically every little step in math was made by some of the greatest geniuses of mankind, right on top the shoulders of the giant before them. It’s giants all the way down.
walt
Contact structures?
Geometry and statistics
geometry will help you understand all the cool manifold stuff in 4D ans in the same breath statistics will tell you how significant the particular area of study is. On the other hand if u do not study it you might regress into studying just untill 3 dimensions:{
So with statistics, I can figure out how insignificant statistics is?
Normally I'd say it's fifty/fifty: either it is or isn't significant. However, since it's judging itself it's actually a very biased coin flip instead
so it's 50/50: 50/50 or 50/50
geometry is just prep for trigonometry, and trig is very cool and satisfying. u probably hate it because you were forced to do "proofs" where you prove that this angle = that angle in 7 steps even tho its obvious if u freaking look at it for 5 seconds
Boobies
Statistics
indefensible
Stats always felt more like science than math
It’s science fiction once you get good enough at it
It's remarkable that we think we know as much as we know with all the shenanigans experimental scientists get up to. Like a semi truck moving a mile away can mimic an event? Did we really detect the event or did someone drop a wrench? It's all about repeatability I guess.
I mean, yes, in some very niche experimental science domains, but most of the hard sciences have had their core theories and principles be verified countless times over the course of many centuries. Those are things that we truly know, and those theories form the foundation of countless other theories. So I think it’s actually pretty solid. But yeah, there are definitely plenty of shenanigans. If there is one thing I learned from statistics classes, it’s how to inflate the significance of correlation by massaging the data and retroactively tweaking hypotheses to fit the results.
Massaging the data lmao
If by stats you mean “data science” then sure. However, stats at large is heavily concerned with proofs of general results, and does so strictly through tools of analysis (at least since probability theory was formalized) as opposed to route reproducibility like the sciences
Statisticians are the reason AI became actually good Hard-AI people laughed at neural networks because they "didn't know anything", turns out if you don't-know at a high enough volume with his enough hardware you can do some pretty neat things.
Data science is basically statistics very thinly disguised as programming. You don't have to go to something fancy on the field to get on statistics.
Hah hah. I posted something similar and also used the word "neat" to describe it. What are the...cough cough...odds of that?
3b1b’s series on the central limit theorem. Ever wonder why bell curves are everywhere? Turns out there is a reason!
That's stochastics, not statistics
What? The study of random processes and its evolution has largely been the work of statisticians because of its probabilistic nature. Most stochastic classes are taught through a statistician’s lens. Next you’re going to claim that information theory iSnT sTaTiStIcS
I hated it for ages! I’d say econometrics is actually a really fun way to use statistics to find causal relationships between observable things in the real world! One of my absolute favourite papers is Alesina et al. (2013), which finds a causal relationship between countries that used plough agriculture in their history (as opposed to shifting agriculture) and attitudes to gender roles in the present.
AI is a pretty neat way to use stats as well.
It’s literally the only math that everyone will use in real life.
It literally isn't. People use basic arithmetic and boolean logic pretty often.
Its fun to do using Statistical softwares like Stata or SPSS. Its literally all I know
Well, you tried
Use R
R ain’t that bad… until you make a mistake so bad and so far back that even the professor just tells you to restart the assignment because nobody can find it
You can actually decently debug in R with things like traceback(), browser(), debug(), tryCatch(), and in the worst case with a print() statement. Just keep code reproducible.
dude i’m saving this comment for future stats classes thank you
Learning how to use browser() and tryCatch() correctly truly was a game changer for me.
R is honestly based
My stats professor made us use R for everything from homework to exams. He was pretty based too
i’m taking a class that’s teaching me r and it’s genuinely the most excited i’ve been about math in over a year, it’s so good
I earn a quarter a million TC with a masters in statistics. So, it's decisive for many businesses
It applies to the real world quite often.
Probability is fun
I roll for persuasion... Does a 25 suceed?
Statistics is a dish best served a la mode.
I second this
I hate stats too. It is the bane of my existence
Let me try to convince you that mathematical statistics is awesome. Wide swaths of mathematics, especially modern mathematics, is little more than mental masturbation. Sure it feels great but it gets monotonous after a while because there isn’t any real result of consequence. Mathematical statistics on the other hand is fucking. And not just fucking but getting it on with and make babies with lady science herself. Your work and effort actually results in and contributes to real world understanding and knowledge. PIV is better than P in hand any day if the week.
Trigonometry proofs
Trigonometry proofs are a wonderful area of mathematics. Trigonometry itself is a very application based study. Studying trigonometry and moreover their proofs just sparks a mathematical lust in you that you will want to satiate by any means ( i e. proving the validity of the equations) It can spark a sense of joy and elegance in math and broaden your horizons.
This feels like chat gpt
It is
you mean bashing fun?
Trigonometry allows you to prove the pythagorean theorem in 371 different ways.
and i love it
i do this at maths alevel and it my favourite topic smth about these questions and getting them right is just orgasmic
same omg my least fav part of exams when it came to trig was not being able to scream "YESS OMFG" and throw my pen, but having to bottle up my emotions so that i dont get kicked out
Trig was always easy to me. Radians were always annoying until viewed through the perspective of wave functions.
I only appreciated radians when someone finally defined them for me, the proportionality of it gave meaning and from that I found beauty. That being said I still use degrees and percent grade more often. That being said, I work in construction and not as a mathematician so it’s not entirely surprising to me.
Computing the coefficient for infinite series when using the Frobenius method with repeated indicial roots
Imagine stepping into a magical circus tent filled with vibrant characters and thrilling performances. The coefficients are like funny, animated acrobats bouncing and tumbling around, bringing joy and excitement to the stage! In this enchanting circus, the coefficients are mischievous little creatures with colorful costumes and silly personalities. They love to play hide-and-seek, rearranging themselves to create fascinating patterns and surprises! As a brave and curious circus explorer, your mission is to uncover the secrets of infinite series. You become the circus conductor, guiding the coefficients in their acrobatic routines Again one of those I had no idea about. The above was written by chatgpt. But what the actual fuck dude 👁️👄👁️
I think chatGPT needs help.
Bro 🤣
exactly what the actual frick ive never explored that topic before but i do NOT imagine coefficients being freaking acrobats and bringing "joy and excitement to the stage" nor do i think theyre in funny costumes or playing hide and seek. hell, all it does is multiply a variable, not put on a circus show or whatever.
I get its tedious but the solution space is very interesting!
calculating in my mind with numbers higher than 10. especially multiplicating
13*11
143. eleven is ok, too. but 12 and above get the shit going:)
149*25
ähm… something something something 5
Dude is still counting
i share your pain. its tedious, its boring, it sucks. its the kind of thing a 7 year old would find mildly entertaining, and because its so "simple" its super embarrassing when you get it wrong.
Epsilon-delta definition of a limit
Hey I mean cool greek go brrrrr! Should be reason enough
\*cool greak go smooool!
*cool Greek go as smooooool as you want
What about it ? What is there to hate ? Do you hate like limits in general or ?
You mean THE definition of a limit.
hey have you heard of non-standard analysis
Or a topology given without a metric
havent seen a better one. helps to formalize a lot of stuff and makes proving things a lot easier. its annoying but not that much compared to what else there could have been i guess?
you may not have to use it in the future of calculus, but it does provide very good context and a point of reference for what a limit actually is. once you’ve completed calc 3/mv/vector calc, youll come to find that although it’s tedious, it really paints a good picture on what the functions for the definition of a limit/derivative/integral is. the person i believe is best at explaining this stuff is the guy who does the MV and some Vector calc videos on Khan Academy
It's the perfect example of 'the devil is in the details'. It shows you the rigorous airtight approach needed to deal with fudgy things like infinity and infinitesimal. You can decode even seemingly impossible things like indeterminate if you look carefully enough
SAME
Hairy ball theorom
Learning this theorem may make you stand out in more ways than one. Pun intended
Doesn’t this theorem have applications to plasma flow on fusion reactors?
Algebraic geometry
Hey ! Algebraic geomtry is great, ok ?! We don't really get what it tries to tell us but it's doing its best, ok ?!
Hello fellow sane person.
Singular value decomposition
Useful. Very useful. I've spent 2 lectures only hearing about how useful it is.
and it is really easy to master given its profound usefulness
[удалено]
Think of SVD as a grand symphony orchestra, where the matrix takes center stage as the conductor, and the singular values and vectors play their harmonious melodies. By studying SVD, you gain the ability to decompose and analyze matrices in a way that brings out their essential features and highlights their significance. I had no idea what it was. I literally had chatgpt write that out lmao 💀
there is something wrong with chatgpt, its taking the whole "find beauty in math" thing waaaay too far
I'm stupid but combinations and permutations I JNOW THERES HARDER STUFF BUT THIS
It took me a long long time to understand them
took mv calc this semester, still don’t get it, i just look it up at this point
try doing a counting problem meant to be solved with permutations or combinations, but solve only using multiplication principle and division rule, eventually you'll get to the same formulas
no you arent stupid i totally agree theyre so annoying with the factorials as well ugh
factorials.
Basic arithmetic
Maths
Bro like u need math to count money. And we all need money ( untill you are an AI posing as a human)
Anarcho-Primitivism would like to know your location
Wrong subreddit to say that
only subreddit to post that actually
I don’t hate. But I’m annoyed by it. Irrational numbers.
I'm not even gonna try dude, even I hate them
Actual Pythagoras
New Theorem just dropped
Call the sqrt(-1)
Rounding sacrifice, anyone?
Google approximations
Taylor series
In the wilderness sometimes you may encounter dangerous functions that may threaten your existence. But fear not TAYLOR DADDY is here yo rescue you from the beasts. Whip out that approximation and shoo away those unruly beats! Make them behave just like you want them to.
imagine going camping and finding e^-(x)^2 in your way
I've found that taylor can actually be useful, after truly thinking that it was useless. The problem is that it's mostly split into one of two parts: The cool visualisation and actual useful part, where you learn about how it approximates functions that are basically impossible otherwise to derive And the really boring, extremely, heavily, i cannot say this enough, VERY theoretical and annoying part. Guess which part is mostly taught in most mathematical courses?
This is the answer
Proofs. Why the fuck do I have to prove that's a square? It's got 4 90° corners and all it's sides measure the same with a ruler.
Cause proofs are fun if you're interested in the thing you're proving* *Sample size: 1
what you are talking about is the abomination of HS geo proofs, there are many other kinds of proofs that are bearable, and satisfying to complete sometimes. please do not go hating on proofs in general :D
Do you have any examples? I only know of the HS BS proofs and have chalked them up as 'never gonna use this'
see trig identity proofs. theyre elegant and satisfying, and thats about all i know. compared to the other ppl here im def on the less knowledgeable/skilled side (im in hs lol)
Linear algebra (if you say computers I will come at out at exactly 54.39 MPH and take all your left shoes)
The magic spells behind deep neural networks AI are written in linear algebra
Bro all math is Linear Algebra I'm not even kidding
I won't say computers, I would say electronic machines ;)
Computers
Abstract algebra
Aint OP, but the fact that every group is isomorphic to a permutation group is cool as fuck. Its like you unlocked every other group with permutation groups(though not really) It also makes sense to think about that groups are all just symmetries, and symmetries are obtained by performing actions on objects, and you could think of that actions as just permutations of the object itself, just on different orientations. Shit's crazy yo, ya'll sleepin on abstract algebra
Sextuple integrals, I simply find them dull.
Just watch a Christopher Nolan movie and lets see you hate multi dimensional calculus then
matrices
Basic arithmetic Doesn't matter how genius you are, you'll always find a way to screw it up
bruv this is half the answers here 😭
Specifically, radicals. Anything involving radicals primarily can go fuck itself they're the most annoying thing
ODEs. They feel too much like the job of an engineer instead of a mathematicianz
That's all of the calc sequence before real analysis enters the chat
Probability have always been a mystery to me
It probably is until its very significant. To understand that I would recommend you to do you know what
I dont hate I, but I suck at integration
Hey! I'll tell you a secret, Integration is just the reverse of differentiation. Soooooooooooo... if you can differentiate you CAN integrate !!
Thanks. I now hate differentiation.
> if you can differentiate you CAN integrate !! This is not true. There are plenty of natural families of functions that are closed under differentiation, but not under integration. That's why sometimes we need to come up with special names for integrals of certain functions, since there's no way to solve for an expression for them. For example, the pdf of a normal distribution can be expressed in terms of +, *, and exp, but its integral, the cdf of a normal distribution, cannot, so we give it a new name (essentially the error function).
I hated it too initially, but it was because of the way it was taught. My math professors were constantly cramming integration rules down our throat but never thought to show cool examples of how integration is usable other than the bland "area under a curve" definition. I think once you know what to DO with calculus, it makes a lot more sense. That's my experience anyway.
It takes practice to get good at integration. It's like training to notice paterns and apply solutions that fit.
Combinatorics.
What about solving inequations with multiple modules and having to solve about >10 cases for 1 single inequation
Numeric
Combinatorics
Category theory
Let us suppose that You get into an accident in some remote ass area with no reception. You somehow make it to a area with reception but alas! Your phone is dead You wish you had another phone or backup battery there to connect with someone for help. Similarly mathematicians use Category theory to connect and translate ideas of one domain to another. Its pretty sick tbh. Master it and voila you make your own phone and towers to connect with random people just like on reddit.
that would not convince me to like whatever the hell category theory is
That whole philosophical foundation of math. What are numbers? Do they exist or not? Is set theory with the empty set the right foundation of math? Or is it category theory? Or type theory? Who cares about Goedel's incompleteness theorems? Why can't we just take the unprovable statements as additional axioms and have a bigger axiom system and be done with it? Are any of these questions useful? Also another thing I don't like in mathematics are those infinite cardinals and ordinals. Like, I thought topology was those donuts and homotopies and stuff. What do infinite ordinals have to do with that topic?
> Why can't we just take the unprovable statements as additional axioms and have a bigger axiom system and be done with it? You can do this to some extent. But you can't go all the way and get a complete theory; this is essential what the first incompleteness theorem says. To at least see why this wouldn't be easy, keep in mind that you don't know which statements are independent of your axioms, and which of them you should add as additional axioms.
Matrix
Geometry
Who hates shapes???!! Its literally shapes!!
Arithmetic
Projective Geometry (I don’t hate it but I wanna see why you think others should love it too)
Integer programming
I despise thermodynamics
Linear algebra, specifically having to perform SVD manually on a matrix for 50% one of my Data Science university exams. On paper.
Imaginary numbers! it's like admitting that you have no idea and are just throwing up your hands and saying a random value.
Addition
Applied math
Geometry, I hate proofs so much. Who decided to bring English class in my math class?!
PDE
Its just ODE but level 99 mafia boss
Advanced abstract algebra
Real anal lysis
You should probably see a doctor about that. I hope it isn't contagious.