15:10

La mejor y más clara explicación que he visto. Cuando vi un poco de teoria de grupos en la universidad quedó como un tema totalmente oscuro para mí. Ahora todo hace sentido. Excelente video!!! Me encanta esta serie

I love this video!

15:43 well, all those group/ring/commutativity is terms directly from number theory, so it's weird claim they aren't related.

9:08 well, that was confusing. at 1:40 you said it was homomorphism, i.e. function for mappping is character, but here you pick one one permutations and call it a character.

amazing, if i become a patreon in some time, will the video still be available? ik zag trouwens laatst in je Q&A dat je vlaams bent, en ik had me al afgevraagd waar je accent vandaan komt, want vaak en zo ook nu kan ik een vlaams accent niet herkennen in het engels en daar had ik het toevallig die dag zelf nog met iemand over gehad. maar goed, ik kijk al je video's zodra ze uitkomen! hopelijk kan ik binnenkort eraan bijdragen :) als je nog eens een Q&A doet ben ik benieuwd wat voor muziek je luistert

Very cool!

4:12-;

goldmine, have been trying to understand the mobius function for the last few days, absolutely beautiful explanation, thanks

1:11-;6:46-6:56;8:10-8:22;9:03-9:15;

Amazing video!! A really great introduction to some core ideas in representation theory :)

Before going deep into the math of these symetries and their applications. Where others failed, you succeeded. Deep explanations and intuivie. Really good content. Thanks !

Honestly, the looks/animations of the videos are just a bonus - I stick around because your explanations are the most clear and elucidating I've ever seen, often exceeding 3b1b

a division by zero is a contradiction in most cases, and everything follows from a contradiction

I AHVENT' WATCHED THE VIDEO DID YOU COOK IT UP SHOULD I FINSIH IT

Fourier was great video

I'm also a software dev, undergraduate in computer science and ending a Physics one. Your teaching amazing and passing is just as good to have us thinking the subject until the next one comes up. I think division by zero is a zone of trasition, it's a degenerate state, where either you lose dimensionality information as in linear algebra projection transformations or have an ambiguity as in geometry with unknown polar/azimuthal angles at the origin/poles, also in algebra they're related of to a curious pythagorean triple involving dual numbers, imaginaries and reals, the division by zero is not possible in scalar or row vector algebra, by an incompletude, but you can work around it using dual numbers matrix representation or poles and residue theorems from complex calculus, with some clever tricks. Spoilers: you arrive at differentiation operations. Borrowing again from LA, zero is the kernel of any morphism in math, so itself acts as a pivot, that makes any sum, product or exponential with it meaningless since you get the original operand, zero or one. The unique place where it changes anything is when divided by itself since 0 = k0, so k = 0/0, where k is literally anything you can put in an equation involving inverses, be it number, vectors, matrices, tensors, shapes, sets, etc.

The preview resembles a thing I did with pixel shaders, while exploring various fractals(Mandelbrot, Julia sets, Ducky fractal etc) I repeatedly applied projection matrix, using homogenous coordinates (x,y,z,1), somehow assigning z value(probably with a parabolic function z=const*(x^2+y^2)) so it was something like: take a picture, project it on parabola, take a picture again, project on parabola and so on(about a hundred times in total). If the projection plane was tilted(or shifted) a bit, it looked very similar

> why div by 0 allows this obisously, because it's uncertain and following the definition of division you can grab any result from it making reasonable equations into useless math. Wonder if category theorist have category for those.

Thought you used manim as well.

One fairly obvious (but not deep) reason for division by 0 being problematic is that multiplication by 0 is many-to-one, whereas multiplication by k for k != 0 is one-to-one. So if we define the function mul_k(x) = kx then the inverse function div_k(x) = x/k exists for all k except zero k since mul_0(x) = 0 for all x Because of this, an implication like: a*(x-y)=b*(x-y) => a = b is false if x=y (since the multiply is non-invertible), and if you can hide such a step in a proof then you can apparently prove nonsense like 2=1

KZbin as a learning resource is *hugely* under-appreciated. I’m glad you’ve jumped into this as a content creator.

I am Dutch, and I had absolutely no idea you speak Dutch. Also, "right" and "straight" are both correct translations from "recht" in Dutch.

Your channel has been incredible! ❤ I am a math/physics undergrad in America. Most of your videos have left me with new perspectives and appreciation for the intense beauty of mathematics. Your animation quality and the clarity of your explanations rival that of 3blue1brown. Keep up the good work! I am excited to see what you make next! I believe that this channel will eventually become very popular

Beautiful <3

NOTE: had to reverse image search(may be inaccurate) half of them, but they match the icon and general content. List of channels displayed from 2:00-3:00 TOP ROW - 3blue1brown - Mathologer - khanacademy - MathTheBeautiful - rationalityrules - ron-math - eigensteve BOTTOM ROW - (Eigen Chris) UCN8wTUlSAroLslWyf87E2pw - mathemaniac - Aleph0 - PhysicswithElliot - RichBehiel - SanderKonijnenberg - sudgylacmoe

Division by zero breaks everything because 0 doesn't have an inverse in all rings except the {0} ring. You can prove that if you have a ring where 0^-1 exists then that ring is {0}. Also, in a ring one of the first things you prove is that 0*a = 0 for all a in the ring.. but by definition of inverse, you would have 0 * 0^-1 = 1. So you conclude that 0 = 1 , so for all a in the ring, a = 1*a = 0*a = 0, and that leads you to the ring being just {0}.

The way I do things these days is to ask AI what it would do in my situation: "- Ask AI." It replies. "- Thank you very much!"

I've also always loved math! Too bad that this love isn't mutual.

Very clearly explained.

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The best video of number theory I've seen! Thanks!

Does more dimension will yield bigger sign group? like with 3D space which has 4 diagonals it become sign group of that size?

Also please don't gradient plane points (like 6:18). Group coloring doesn't look like turns into gradient.

Are we gonna study whole table of groups including sporadic ones?

Wow!

Hey, isn't isomorphic the same as saying an homomorphism exists?

BEAUTIFUL ! Love your work ! THANKS !

these matrix representations reminds me a lot about functors, could there maybe be a correlation or could be that I'm just confusing things...?

May you also share the python manim code that you used for making this video. that would be really helpful

Late happy birthday to your dad! I'm israeli but I recently moved to the netherlands for a master's degree in logic in UvA. Working hard on giving you some future content :)

WONDERFUL ! Thank You ! 👌

THANK YOU ! WOW ! You're a GREAT Teacher !!

Sedenions (16D) lose alternativity and they have zero divisors. Trigintaduonions (32D) lose distributivity as well. Power associativity is presumably lost at the sexagintaquatronions (64D).

Excellent presentation. The graphics are great and the pace is pleasant. And mist if all the subject matter is fascinating. Thank you

This makes me want to dive back into shilov chapter 1!

Man I just found your channel as a self-studier and I can tell it is a gold mine!

Great video, intuitively informative, nice graphics and animation. Thanks a lot!

I didn't understand the proof that the set contains only one neutral element. I think you didn't explain this well. Why does the neutral element get this mini-commutativity, where the operation results in the same output if the neutral element is either input? Because associativity ore closedness doesn't prove it, it's not a result of the definition of the monoid like you said, unless you also put that property into the definition of what a neutral element is.

cool video