Episodes 1-10: “Ah this is quite easy and relaxing” Episodes 11-12: “Um what are we even doing?” Episode 13: “HOW THE HELL AM I SUPPOSE TO VISUALIZEE 4D SURFACES IN A 3D WORLD ON a 2D SCREEN IN MY 1-D BRAIN?!”
@@fatitankeris6327 man that was so long ago. But no. Multidimensional funtions implies several inputs. She you reach tre inputs you can no longer representate the output on a grafic.
It took me over thirty years, two math degrees and a decade of teaching math to even know of this shadow's existence, much less the meaningful layers behind it. This was incredibly humbling and illuminating.
I believe Riemann hypothesis can be proven using something similar to a 3d magic cubes like magic squares and could predict them easier but what do you think?
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v". >>>With same meaning of the notations as stated.
I actually had tears in my eyes at the conclusion of this series. For the nearly two decades I've been studying mathematics, teaching, and using "lateral" numbers...I never truly grasped their meaning until the very end of this video, which ends where the entire series began. Thank You so much, this was gorgeous and very well made.
8:18 This is exactly similar to how you CAN return to a place you have been to previously, but CAN NOT return the same _time_ AND _place_ simultaneously.
@@khytron06 Actually we are all moving at the speed of light in spacetime. This video ua-cam.com/video/au0QJYISe4c/v-deo.html visualizes it perfectly. This is the best channel I know of regarding visualizations of physics- ans math-concepts.
This. Is. Always will be. My favorite video series I've ever watched. I'm in university now working for a degree in Mechanical Engineering. I never enjoyed math. That has always made working for this degree difficult. Ever since following this series, math is the most beautiful thing I've ever seen. Thank you, Welch Labs. You gave me something I've been desiring my whole life.
Dude, I don't know why, but some of the people still using this pepe meme are the worst commenters on youtube. Btw, hope you're doing great on your degree man
good luck mark! I have a professor who teaches analysis II which is basically differential equations. He always says that we have to love math. He gives a particular example "imagine if you are a dr. and you are doing heart surgery and you tell the patient ooh man i hated anatomy, but its ok i can operate you " lol it is the same thing for engineers you have to love math lol
Numberphile, 3Blue1Brown and Welch Labs did the same for me. I started in Mechanical Engineering and now wish I had started in Mathematics and Computer Science. I guess I'll be a self-taught Applied Mathematician because that's where my heart is now.
This series deserves a field's medal. This is Graduate level Math for toddlers. You guys just exploded the power of imagination. This is education AS REAL AS IT CAN GET !! Thanks a ton !!
Best educational series I saw. Strong plot. Many catchy moments. Tons of history and examples. Astonishing visual effects. I want to rewatch this with every of my friends. Thank you.
Oh My GOD!!! You are amazing! I actually felt emotional at the end of the story "Imaginary Numbers are Real". This video series is beyond this 3d space we live in! :P All the efforts you put into this videos series is truly apreciated.
I have never seen a better series of on any subject anywhere else on youtube. This series was just perfectly made. I recommend this to anyone even if their field is not math related.
Indeed, it was brilliant and - what i find the most surprising - it was very entertaining. It's amazing what a valuable content can be found on youtube underneath all that meaningless, popular bullshit.
watching this series after 6 years of its release, and i'm really impressed of how beautiful this is, one of the most fun and amazing series I've ever watched
It took me 2 days (with work and stuff) to finish this series because I just got so into it, i took detours to learn more and more about math and science (as well as do sample practice problems as you went over certain topics) to deepen my understanding. College really just felt like regurgitation of methods with no context, storytelling, or passion; just some tools to memorize and redo and pass. But now you've single-handedly rekindled my old and BURNED OUT passion for mathematics (which I tutor regularly) and made it my favorite subject again. It's 4 AM and I don't even think I can sleep. I just want to keep learning more and more
I really wish college math classes could be longer than a semester. So much knowledge is missed out on. Every week is just a cram to get all the homework done without being able to enjoy the intricacies. I get that college is expensive and nobody wants to spend an extra 2 years on a bachelor's, but I would love it. My favorite math class ever was AP calculus in high school. It was everyday for a whole year, totaling 180 hours. My teacher really went out of his way to make sure we understood WHY everything worked. If people didn't completely grasp something he would just spend a whole day re-explaining it. Now at a large uni with 150 students in each class, it's just not feasible to get so deep into it.
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v". >>>With same meaning of the notations as stated.
because we can really understand those concepts in a level that we can see the beauty it has? much deeper than men? of course you wanted to keep your privilege of being so pathetical in the past :D but now all that you have is sweet male tears
Little Bey You're the one crying sweetheart, and I seriously doubt you understand mathematics as deeply as you say considering this video describes basic entry level concepts...Besides, it was a man that first described the beauty of mathematics that lesser people constantly copy in order to appear intelligent....It was also a man that made this video that made you cry so take your box of feminist tampons and fuck off back to the princess tea party...
What an amazing experience to binge watch this series, can't even imagine the people who had to wait after all those cliffhangers!! Math is really beautiful, and that storytelling was on point, I got the chills in the end of the video. That's an awesome piece of work, keep up with it. Love from Brazil.
After all these years, this series is still the greatest I’ve ever watched. It’s breathtaking. If this was the only video on your channel I would regard you as a math phantom.
That's the best storytelling about complex numbers I've ever seen so far! A special thanks for episode number 11, 12 and 13 that are really awesome! Thank you. Can't wait for the.....following!!?
I usually don't comment on UA-cam. But, I couldn't leave without expressing my gratitude to your effort in this series. I spent almost two minutes trying to find out the right words to describe your work but there are none. Maybe, they reside in 4D space just like complex functions :)
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v". >>>With same meaning of the notations as stated.
I have a final exam tomorrow (not mathematics), but here I am watching all of your 13 videos about imaginary numbers. These videos were great, I finally understood what these "lateral" numbers I've been using all along. I never imagined (lateraled?) I would escape from studying for my exam, by studying something else. You managed to grab my attention throughout the whole 13 videos. You deserve a cookie (and a nobel prize) #subscribed
Watching this ~1 hour series will save you hundreds of hours trying to study and comprehend Complex Analysis. That is how mathematics are ought to be taught. In fact every teacher in every school everywhere should already start using these videos. Thank you for creating this masterpiece and sharing it with us for free. It really is the most amazing educational project I have ever seen!
This series was probably my most beautiful discovery of 2018. The final parts in specific where all you had tought us came into a shadow of a 4D plane were really emotional for me :') Thank you for all the effort in making a short and understandable explanation of imaginary numbers. You have earned yourself a happy sub
I had rewatched this series twice but I didn't still get that gut feeling understanding. I ended up writing a small article on it to improve my understanding. The end result is that I finally understood the whole series and I ended up using the article as my math project. Making a 17-year-old comprehend these things clearly shows how great the videos are!
Well done. I feel like i binged through a season of House of Cards. Except this was actually useful and opened my eyes to lateral planes. Thank you, good sir.
This should be compiled into a movie.. and should be released in theaters so that other people will know how much interesting mathematics really is.. 😀
I wish so too, but while you and I would find this interesting the majority of the "general audience" would be looking elsewhere. There is a reason "reality t.v." was so sucessful.
Waaaaay late, but this series was certainly one of the best things I've seen on UA-cam. I have no words to express, mate. Someone said below "I actually had tears in my eyes at the conclusion of this series.". I am happy I was not the only one. Congratulations!
The beauty of math is that it conveys a simple truth. It's based on a set of very few principles that we can all agree on (axioms), and from there on, impressive discoveries can be made by simple logic. Nevertheless, it requires both creativity and perseverance to make the correct logical leaps to discover the truly impressive and beautiful relations - such as, for example, e^( i * pi ) + 1 = 0 - a relation between the most commonly used constants and identities in mathematics (0, 1, e, i, pi), which also happens to involve the basic operations addition, multiplication and exponentiation once each.
to me math is not beauty, but it's greatness because it permanently extends the reach of our thought. It's touching because of how great it is and what math has accomplished in engineering and science.
It shows the power that a well crafted script and narrative has especially when applied to a carefully chosen subject. We are curious story-tellers, all of us. You satisfy those two things, and you satisfy totally.
Mate, I came to UA-cam to watch a chemistry video for my test tomorrow... Ended up here learning about how imaginary numbers are represented in 4D and then casted down to 3D which I then watched simulated on a 2D screen. All I wanted was to know more about redox reactions and now I'm questioning existence, thanks -.-
I've been having much more fun watching this series than watching a Netflix series. Even though I haven't understood what's going on here, it's been an immense pleasure to be a part of this journey.
I have watched it atleast 5 times already, each time with a little more understanding of underlying concepts of mathematics that i havw been learning in school This is truly amazing
Never in my life have I ever had tears in my eyes from watching a video/film/series. It had to be math. Thank you so much for this journey, besides that it was very well made and very effective, I think I've truly learnt to see numbers different for the rest of my life.
Simply Magnificent. Guys I want you to know that I rarely post any comments on videos, but this serie deserve one. It was wonderful, yet mind blowing, because we barely know the capacity of "lateral numbers (I'll stick to that name) and those numbers could provide a huge advantages, both cultural and scientific, to the human race. If the Number Universe was big enough, now has double it's size. I want to congratulate you for the explanation, it was clear and easy, yet clever and logical. Thank you very much
This is one of the most beautiful mathematical realizations Ive ever seen! I would have never imagined that the standard Cartesian graphing techniques I learned in grade 9 had such a completely hidden world just under the surface!
There exist no words on this planet to express the awe, surprise and beauty of something so fundamental, elegant and yet so complex as complex numbers and a humble expression as the square root of negative one. I LOVE maths and this playlist made me feel like a student at my school desk just wanting to keep learning. I didn't learn complex numbers in my school due to the restrictions of the syllabus and now I know what I missed out on. My jaw was left hanging open and my brain was itching for more upon the end. That 'i' in the end was literally smiling at me. I now feel that I finally understand an iota of advanced mathematics. Thank you Welch Labs, thank you so much for the beautiful explanation of a humble but all powerful concept
This is a masterpiece. When I asked myself at the beginning which one I should watch, this series or a movie, I opted this series and I am dumbfounded. This is purely amazing.
I just wanted to let you know that your series has given me such a fascination with mathematics that I have switched my majors from CS to Computational Mathematics.
I've watched this three times over the last few years. The final scene brings me to tears every time. Thank you so much for this beautiful series. Special thanks for the incredible visualizations too. These are, hands-down, the best math visualizations I've ever seen.
this is by far one of the best mathematical series on the internet, your diligent work is much appreciated sir, thank you for this eyeopening outstanding series!
12:32-13:49 It could've been a plain lecture but instead it's a movie's finale recapping over critical events leading up to the resolution The soundtrack fits
Riemann was a genius. He had pure imagination. I admire him. I cant imagine how advanced the science/mathematics today would be had he not died too early :(
Hello, man from the past! I'm sorry to disappoint you, but we nowdays have only way more flat Earthers and anti-science activists, rather than geniuses like Riemann...
I am still in High school and I still found this follow able. You guys deserve an award. I have always loved math but this... This is beautiful. How knew we could graph in 4 dimensions on a 3 dimensional plane.
This is fantastic. As a math teacher I’ve only known surface level concepts of complex algebra but this is what I’ve been looking for. The historical background is amazing and leads well into the graduate level branches. This has given me a great idea of what I might study for grad school. Thank you and I’m sure this will help my students
It was like watching a movie come to an end. I mean, these type of things aren't meant to be free, you're doing a great service Stephen. Thank you so much for inspiring us and introducing this whole new world of complex numbers. I will never be able to look at it the way I used to before. You've given me a new dimension (pun-intended) of interpreting and solving complex numbers. Once again, thanks.
hey, i don't know how to thank you. I love to study beyond whats i'm having in school. I was having some problems with complex numbers and I hit into your videos and know I learned even more. Hope youre making more of this, because you got a new subscriber :)
+Henry Smith Hey Henry, I noticed we concur the same maths channels so I went through your subscriptions in case I missed any of them. Maybe you've checked it already but I thought you'd like one called hackerdashery. Cheers
Hi, do you have any other math channels to reccomend? The ones I'm already subscribed are numberphile, mathologer, 3blue1brown, and njwildberger, in case you don't know them yet. I'd also suggest the Banach-Tarski video from vsauce.
Hi! 3blue1brown is my personal favourite, but if you like mathologer and njwildberger you may as well like Mathoma (or even XylyXylyX). More divulgative/entertaining, there's a couple of videos about possible curvatures of the universe on Zogg from Betelgeuse, explained by an alien. Much more arty (you may know this one) is ViHart, who plays around with fractals and other cool mathematical concepts. You can find them on my subscriptions as well
There is no way I can thank you enough for what you are doing to people who always had problems with math but still need it and love it in a weird manner, like me. I wish I can do something like this in my country soon, once people here are right now crossing a major collapse of educational system (and self esteem), and most of them can't understand english. Keep! rocking! And, again, thank you very, very much!
Welch Labs This series was awesome! There was a question on the last ACT that asked the distance between 2 complex numbers, and thanks to you I was one of the few people to get it right.
When I was having a bachelor's degree in physics back in 2014, there were no visual study materials. I passed my math courses blindly. After 10 years you opened my eyes. This playlist is 8/9 years old, and I have just found the gem at the end of 2024. It feels like I am having a rebirth. Should have found this long before. My heartiest gratitude to you for your tremendous magical efforts.
I pretty much never comment on videos. However, an exception must be made for this series. I have never had a subject so thoroughly, consicely, and clearly explained to me. It really felt like a wonderful journey through math, and I was as enraptured by the journey and each new revelation as I might be watching a movie or reading the climax of a story. So much obvious care and work was put into this. It is a shame this does not have several million views. Thank you, truly, for the knowledge. I hope you continue to share. Have yourself a fantastic day.
This series actually time travelled to the past from a 22nd century math classroom. You were born a century before when you’re supposed to be born. After a century if UA-cam will still exist, I believe people will echo my comment. This was an immense pleasure and privilege to enjoy something that belongs neither to our time nor our dimension. Hats off for the efforts put into this series. You are a true hero of entire mankind.
UA-cam suggested part 1 to me, then 2, then 3. I never thought there were 13 parts! I've watched them all at once and now my head is spinning. But wow, they are amazing. Made from a deep understanding, very clear explanations, clever visualisations. Thank you!
I wish I could have seen these videos 20 years ago when I was in school. Brilliant stuff. I loved the way you used color to help with the visualization of 4D space. I really couldn't stop watching.
Wow. So well explained and visualized. Even a regular guy like me can understand that (I think). I wonder how a guy like Bombelli, who pondered a lot of time about those things, would've reacted if we could have shown him this.
Wow this was amazing! I watched all 13 episodes today and will probably watch the entire series a couple more times. Thank you for making this! And like the others I never really leave comments, subscribe or like but videos and channels like this deserve it.
Still one of the best math series on UA-cam. I come back and watch the entire thing about every year and I always understand it more than I did the last time I watched it. Words can't do justice to describe how much I appreciate this series.
It is incredible all the effort you put in this. But dude! Absolutely worth it! Everything on these videos are just perfect! I love it! This are the things that no teacher will care to explain you, but are the really important things. This are the things that make you love maths and knowledge in general, which schools and colleges lack of. Im an engineering student and eventhough ive done a ton of shit involvin lateral numbers the teachers never cared to explain this things. Please, keep up this amazing work! I love this so much!
yes you are right! these mind blowing problems make learning interesting. but I think we should also appreciate what our teachers are doing, even though they sometimes hide/are forced to hide what's really interesting..
I wouldn't even say that. I think at school you learn what you really don't like, so you can find something you like to do as a job. and in these other subjects you get knowledge anyway because you have to in order to finish school. and general knowledge is always good
What makes you think that teachers know how to explain such concepts to start with! I'm sure the fast majority of people involved in these calculations teachers, engineers, physicists etc don't really understand it themselves! And the comments on this video are only a testimony of that... Truely understanding any topic (quantum mechanics, relativity, evolution etc) is not the goal or the point of all education systems that I dealt with in multiple countries, the only goal of them seams to be just cloning half capable professionals to fill certain jobs in the educational institutions and in the society in general.
Best mathematics series on youtube which I hv seen so far....fantastic work. You have this amazing skill of explanation complex concepts in most lucid, interesting and enjoyable manner.... good job! keep it up!
A beautiful presentation! I had mugged up on complex numbers for my exams, but now after watching all the videos, I clearly understood their significance. Thanks a ton, welch labs.
Oh boy, that went from junior level math to master level in just 13 parts and I actually fucking understood quite a lot of new things. And I've Engineering and MBA degrees, I feel like I wasted "years" learning through crude methods what was otherwise possible in these 13 parts. THANK YOU!!!
You've done a great job in explaining a simple-to-calculate-but-hard-to-visualise complex functions. Many confusions are cleared. I've watched episodes 11, 12 and 13 over and over again. 10 out of 10. Thank you!
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/tr.png)
Wow, this is super well done.
Woah, thanks 3Blue1Brown! I love your channel!
3Blue1Brown You both people doing great job for mankind Sir :)
3Blue1Brown omg , I came here aftr a marathon in your algebra playlist!!
You're both sooooooo amazing!!
Coming from you who makes awesome visualizations too, hats off all the more to imaginary stuff
3Blue1Brown ha I was literally just watching some of your vids!
Episodes 1-10: “Ah this is quite easy and relaxing”
Episodes 11-12: “Um what are we even doing?”
Episode 13: “HOW THE HELL AM I SUPPOSE TO VISUALIZEE 4D SURFACES IN A 3D WORLD ON a 2D SCREEN IN MY 1-D BRAIN?!”
TO 0D ATOMS?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!?!??!?!?!?!!?!??!?!?!?!
@@gabrieldoughty6239 nah my 0D understanding
lol - your not.
0D: Wtf are numbers and lines? Wtf is an angle?
1d brain lol
Episode 1: what is a number
Episode 13: *COMPLEX MULTIDIMENSIONAL MATHEMATICS*
This is a multiverse extra-complex-mathematics. As predicted.
@@RobertoArteaga The real jump was after episode 10. Whe you saw the hell introduced by multidimensional funtions.
man i binged the shit out of those videos. what a ride!
@@eduardopablo7123 Aren't Multifunctions called that way because of several outputs for an input?
@@fatitankeris6327 man that was so long ago. But no. Multidimensional funtions implies several inputs. She you reach tre inputs you can no longer representate the output on a grafic.
It took me over thirty years, two math degrees and a decade of teaching math to even know of this shadow's existence, much less the meaningful layers behind it. This was incredibly humbling and illuminating.
I believe Riemann hypothesis can be proven using something similar to a 3d magic cubes like magic squares and could predict them easier but what do you think?
more proof that degrees are worthless lol.
Me too!
I rate this series *i out of 10*
uh, thanks?
Its actually an "i" instead of an 1 xD
Its a rate in a whole new dimension
That's very lateral thinking
Why not -10i^2
Fahrul Razi All those in favor, say "i"
Watching the series feels like a top detective-documentary about math. Brilliant work, stunning storytelling.
Thanks for watching!
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v".
>>>With same meaning of the notations as stated.
I actually had tears in my eyes at the conclusion of this series. For the nearly two decades I've been studying mathematics, teaching, and using "lateral" numbers...I never truly grasped their meaning until the very end of this video, which ends where the entire series began.
Thank You so much, this was gorgeous and very well made.
Exactly, so many things we 'know' but in fact don't know.
Me too !!!!!
Psychodelics were involved
I had tears in my eyes
@@timpower9742 why are people crying lmao
8:18 This is exactly similar to how you CAN return to a place you have been to previously, but CAN NOT return the same _time_ AND _place_ simultaneously.
Yeah!! Nice understanding......👍👍
Very well framed
Does this suggest that even if we're not moving, as long as time is a concept, we always move on 1 specific direction in 4D?
what about same time and different place?
i exists in math, not in science.
@@khytron06 Actually we are all moving at the speed of light in spacetime. This video ua-cam.com/video/au0QJYISe4c/v-deo.html visualizes it perfectly. This is the best channel I know of regarding visualizations of physics- ans math-concepts.
4D visualization in 3D + Bass in the background? you guys need some oscars man!
On a 2D screen
With a 1D time line :D
Now it's complete
Aman Mahendroo guy.... Imagine all this is done by one guy! (Except captions)
Delivered by 0-dimensional photons to our eyes.
Yeah, remined me Interstellar a little bit :D
This. Is. Always will be. My favorite video series I've ever watched.
I'm in university now working for a degree in Mechanical Engineering.
I never enjoyed math.
That has always made working for this degree difficult.
Ever since following this series, math is the most beautiful thing I've ever seen.
Thank you, Welch Labs.
You gave me something I've been desiring my whole life.
Matt Bob no u
Dude, I don't know why, but some of the people still using this pepe meme are the worst commenters on youtube. Btw, hope you're doing great on your degree man
Try "Essence of Linear Algebra", by 3Blue1Brown
good luck mark! I have a professor who teaches analysis II which is basically differential equations. He always says that we have to love math. He gives a particular example "imagine if you are a dr. and you are doing heart surgery and you tell the patient ooh man i hated anatomy, but its ok i can operate you " lol it is the same thing for engineers you have to love math lol
Numberphile, 3Blue1Brown and Welch Labs did the same for me. I started in Mechanical Engineering and now wish I had started in Mathematics and Computer Science. I guess I'll be a self-taught Applied Mathematician because that's where my heart is now.
This series deserves a field's medal. This is Graduate level Math for toddlers. You guys just exploded the power of imagination. This is education AS REAL AS IT CAN GET !! Thanks a ton !!
This is nowhere near Graduate level
@@thedoublehelix5661 it’s still like 3rd or fourth year dumbed down to the point that I a high school student can understand it… mostly
@@jameson1239 it's not that either. If you wanna learn complex analysis, pick up a good textbook and start going through it
@@jameson1239 2nd year at my uni
I had to pause and cup my hands over my mouth multiple times while watching this video. Thank you for such a beautiful explanation.
They are astounded by the beauty of mathematical elegance
Best educational series I saw. Strong plot. Many catchy moments. Tons of history and examples. Astonishing visual effects. I want to rewatch this with every of my friends. Thank you.
Thanks for watching!
Oh My GOD!!! You are amazing! I actually felt emotional at the end of the story "Imaginary Numbers are Real". This video series is beyond this 3d space we live in! :P
All the efforts you put into this videos series is truly apreciated.
Thanks for watching!
I have never seen a better series of on any subject anywhere else on youtube. This series was just perfectly made.
I recommend this to anyone even if their field is not math related.
Thank you!
Check out 3Blue1Brown! His serie on Analysis and Linear Algebra, as well as all his other videos, are just mind blowing!
Indeed, it was brilliant and - what i find the most surprising - it was very entertaining. It's amazing what a valuable content can be found on youtube underneath all that meaningless, popular bullshit.
watching this series after 6 years of its release, and i'm really impressed of how beautiful this is, one of the most fun and amazing series I've ever watched
Te recomiendo la serie de algo está pasando con phi
I binge watched all the 13 videos, amazing.Hats off to the creator.Every math class should show this to the students.
Thank you!
It took me 2 days (with work and stuff) to finish this series because I just got so into it, i took detours to learn more and more about math and science (as well as do sample practice problems as you went over certain topics) to deepen my understanding.
College really just felt like regurgitation of methods with no context, storytelling, or passion; just some tools to memorize and redo and pass. But now you've single-handedly rekindled my old and BURNED OUT passion for mathematics (which I tutor regularly) and made it my favorite subject again. It's 4 AM and I don't even think I can sleep. I just want to keep learning more and more
I really wish college math classes could be longer than a semester. So much knowledge is missed out on. Every week is just a cram to get all the homework done without being able to enjoy the intricacies. I get that college is expensive and nobody wants to spend an extra 2 years on a bachelor's, but I would love it. My favorite math class ever was AP calculus in high school. It was everyday for a whole year, totaling 180 hours. My teacher really went out of his way to make sure we understood WHY everything worked. If people didn't completely grasp something he would just spend a whole day re-explaining it. Now at a large uni with 150 students in each class, it's just not feasible to get so deep into it.
@&rnie To the revolution comrade!
i vfinnesed in like an hour and a half
no way on earth anyone can explain complex number better than this. thumbs up, hats off, thank you.
I just watched all parts in a row :D
Teacher: This will be on the test so pay attention *shows part 1*
Test: *part 13*
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@@isaniruch ...
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v".
>>>With same meaning of the notations as stated.
i'm really crying at the end 😭😭😭
that was so beautiful
because we can really understand those concepts in a level that we can see the beauty it has? much deeper than men? of course you wanted to keep your privilege of being so pathetical in the past :D
but now all that you have is sweet male tears
Little Bey You're the one crying sweetheart, and I seriously doubt you understand mathematics as deeply as you say considering this video describes basic entry level concepts...Besides, it was a man that first described the beauty of mathematics that lesser people constantly copy in order to appear intelligent....It was also a man that made this video that made you cry so take your box of feminist tampons and fuck off back to the princess tea party...
bitch, go cry in another place and fuck you
such a poor crybaby
go home so your mama could clean your tears :)
why you need so much attention of a woman?
ask some psychologist, maybe they could help with your frustration with them lol
That... was.. the... best... series... of... episodes... of... imaginary (ops... lateral)... numbers... ever.
You misspelled "oops" as "ops".
I agree
What an amazing experience to binge watch this series, can't even imagine the people who had to wait after all those cliffhangers!! Math is really beautiful, and that storytelling was on point, I got the chills in the end of the video. That's an awesome piece of work, keep up with it. Love from Brazil.
Thanks for watching!
"… can't even *imagine* the people…"
@@SreenikethanI no
After all these years, this series is still the greatest I’ve ever watched. It’s breathtaking. If this was the only video on your channel I would regard you as a math phantom.
I need season 2 of this
yes season 2 please
season 2: 0/0
Learn complex analysis! You might have to learn a little more math first though.
only season 2i available
That's the best storytelling about complex numbers I've ever seen so far!
A special thanks for episode number 11, 12 and 13 that are really awesome!
Thank you.
Can't wait for the.....following!!?
Working on it! Thanks for watching!
Great! subscribing right now for notifications 😜!
I usually don't comment on UA-cam. But, I couldn't leave without expressing my gratitude to your effort in this series. I spent almost two minutes trying to find out the right words to describe your work but there are none. Maybe, they reside in 4D space just like complex functions :)
Thanks for watching and for the kind words.
Very well put.
MaShaAllah
Thanks for this - I enjoyed learning more about complex numbers
Hi i love your channel as well
Can someone please get me the equation of that plane (hyperplane actually, projected in 3-D Plane; I guess) in terms of "x,y,u&v".
>>>With same meaning of the notations as stated.
I have a final exam tomorrow (not mathematics), but here I am watching all of your 13 videos about imaginary numbers. These videos were great, I finally understood what these "lateral" numbers I've been using all along.
I never imagined (lateraled?) I would escape from studying for my exam, by studying something else. You managed to grab my attention throughout the whole 13 videos. You deserve a cookie (and a nobel prize) #subscribed
Ahmad Aldulaie I agree
the power of lateralisation
Watching this ~1 hour series will save you hundreds of hours trying to study and comprehend Complex Analysis. That is how mathematics are ought to be taught. In fact every teacher in every school everywhere should already start using these videos. Thank you for creating this masterpiece and sharing it with us for free. It really is the most amazing educational project I have ever seen!
Wow, thanks for watching and for the kind words.
This series was probably my most beautiful discovery of 2018. The final parts in specific where all you had tought us came into a shadow of a 4D plane were really emotional for me :')
Thank you for all the effort in making a short and understandable explanation of imaginary numbers. You have earned yourself a happy sub
Woohoo!
I had rewatched this series twice but I didn't still get that gut feeling understanding. I ended up writing a small article on it to improve my understanding. The end result is that I finally understood the whole series and I ended up using the article as my math project.
Making a 17-year-old comprehend these things clearly shows how great the videos are!
Well done. I feel like i binged through a season of House of Cards.
Except this was actually useful and opened my eyes to lateral planes.
Thank you, good sir.
Awesome, thanks for watching!
This was fantastic!
I never knew imaginary numbers had such a rich history. Could a programming-literate child do this? Is the programming easy?
Me too! And I'm not even math professional! Very good job Welch Labs!
This should be compiled into a movie.. and should be released in theaters so that other people will know how much interesting mathematics really is.. 😀
That is exactly what I was thinking!!!!!!!!! I WOULD WATCH THAT
they should put it in netflix, so people would spend their time watching something actually meaningful
I wish I could understand what you do! It may as well be Latin
I actually ended up closing Netflix so I could completely watch this instead...
I wish so too, but while you and I would find this interesting the majority of the "general audience" would be looking elsewhere. There is a reason "reality t.v." was so sucessful.
For the first time in my life, I got the feeling I grasped what imaginary numbers are about. Thanks for creating this!
Waaaaay late, but this series was certainly one of the best things I've seen on UA-cam. I have no words to express, mate.
Someone said below "I actually had tears in my eyes at the conclusion of this series.". I am happy I was not the only one.
Congratulations!
This is amazing,no words to say how happy I was watching this whole series.
Thank you,Welch lab.
Thank you for the kind words.
Why am I crying? I know nothing about math, but I love this series. How can math evoke so much emotion???
guess the music also helped
The beauty of math is that it conveys a simple truth. It's based on a set of very few principles that we can all agree on (axioms), and from there on, impressive discoveries can be made by simple logic. Nevertheless, it requires both creativity and perseverance to make the correct logical leaps to discover the truly impressive and beautiful relations - such as, for example, e^( i * pi ) + 1 = 0 - a relation between the most commonly used constants and identities in mathematics (0, 1, e, i, pi), which also happens to involve the basic operations addition, multiplication and exponentiation once each.
to me math is not beauty, but it's greatness because it permanently extends the reach of our thought. It's touching because of how great it is and what math has accomplished in engineering and science.
It's mostly the BGM
It shows the power that a well crafted script and narrative has especially when applied to a carefully chosen subject. We are curious story-tellers, all of us. You satisfy those two things, and you satisfy totally.
Mate, I came to UA-cam to watch a chemistry video for my test tomorrow... Ended up here learning about how imaginary numbers are represented in 4D and then casted down to 3D which I then watched simulated on a 2D screen. All I wanted was to know more about redox reactions and now I'm questioning existence, thanks -.-
I've been having much more fun watching this series than watching a Netflix series. Even though I haven't understood what's going on here, it's been an immense pleasure to be a part of this journey.
I just finished watching the whole series for the second time, a breathtaking journey to the most real imagination...Well done.
I'm here in my second time too, simply amazing
I have watched it atleast 5 times already, each time with a little more understanding of underlying concepts of mathematics that i havw been learning in school
This is truly amazing
My second time too, one of the best series on youtube
@@underfilho Complexly amazing.
Me too
Never in my life have I ever had tears in my eyes from watching a video/film/series.
It had to be math.
Thank you so much for this journey, besides that it was very well made and very effective, I think I've truly learnt to see numbers different for the rest of my life.
SAMEE!!!!!!!!!
It’s just beautiful
Simply Magnificent. Guys I want you to know that I rarely post any comments on videos, but this serie deserve one. It was wonderful, yet mind blowing, because we barely know the capacity of "lateral numbers (I'll stick to that name) and those numbers could provide a huge advantages, both cultural and scientific, to the human race. If the Number Universe was big enough, now has double it's size. I want to congratulate you for the explanation, it was clear and easy, yet clever and logical. Thank you very much
Thanks for watching!
Me: watching all parts in 70 minutes
Well that escalated quickly
IKR!
I too did that lol 😂
It's because he left cliffhangers at the end of every video. Clever way to keep attention
Yes
shit, has it already been 70 minutes? i just watched all of it and had no idea that much time passed
This series should have billions of views. It's the best thing I've seen on UA-cam so far. And I've seen a lot.
Did I just binge watch a math series? Yes... yes I did.
You couldn't *imagine* how interesting it was!
Yepp
I was just wondering if I had done the same thing....and then I find your comment!
While I'm meant to be working on an assignment? Yes... yes I did.
Ditto! :-D
This is one of the most beautiful mathematical realizations Ive ever seen! I would have never imagined that the standard Cartesian graphing techniques I learned in grade 9 had such a completely hidden world just under the surface!
Thank you!
There exist no words on this planet to express the awe, surprise and beauty of something so fundamental, elegant and yet so complex as complex numbers and a humble expression as the square root of negative one. I LOVE maths and this playlist made me feel like a student at my school desk just wanting to keep learning. I didn't learn complex numbers in my school due to the restrictions of the syllabus and now I know what I missed out on. My jaw was left hanging open and my brain was itching for more upon the end. That 'i' in the end was literally smiling at me. I now feel that I finally understand an iota of advanced mathematics. Thank you Welch Labs, thank you so much for the beautiful explanation of a humble but all powerful concept
I just watched this whole series and learned more than I did in the past 2 years of math class.
Triamcinolone Acetonide I want to like. But you have 69 likes
True :D man true
Classes are really more about memorizing then actually understanding the subject,
This is a masterpiece. When I asked myself at the beginning which one I should watch, this series or a movie, I opted this series and I am dumbfounded. This is purely amazing.
Thank you for watching and for the kind words.
I just wanted to let you know that your series has given me such a fascination with mathematics that I have switched my majors from CS to Computational Mathematics.
Woah, really?!
I've watched this three times over the last few years. The final scene brings me to tears every time. Thank you so much for this beautiful series. Special thanks for the incredible visualizations too. These are, hands-down, the best math visualizations I've ever seen.
this is by far one of the best mathematical series on the internet, your diligent work is much appreciated sir, thank you for this eyeopening outstanding series!
Incredible. BEST explanation of any mathematical concept ever. This is teaching. You should be proud.
"Thanks for watching"
*holding back tears*
No Sir *snif* Thank you
12:32-13:49
It could've been a plain lecture but instead it's a movie's finale recapping over critical events leading up to the resolution
The soundtrack fits
Riemann was a genius. He had pure imagination. I admire him. I cant imagine how advanced the science/mathematics today would be had he not died too early :(
A lot like Ramanujan, another brilliant mathematician who died too early...
@Noor Wachid Better question is what if we had 100% focus for extended periods of time?
Also dont forget Galois. He kickstarted the foundation of a whole new field of mathematics (pun intended, lol) before he died at age 20
@Noor Wachid would people eat more or less bugs ? I don't know...
Hello, man from the past! I'm sorry to disappoint you, but we nowdays have only way more flat Earthers and anti-science activists, rather than geniuses like Riemann...
I actually teared up a little at the end. I have no idea how you made a video series about math so powerful, but man I applaud you.
Thanks for watching!
I am still in High school and I still found this follow able. You guys deserve an award. I have always loved math but this... This is beautiful. How knew we could graph in 4 dimensions on a 3 dimensional plane.
This is fantastic. As a math teacher I’ve only known surface level concepts of complex algebra but this is what I’ve been looking for. The historical background is amazing and leads well into the graduate level branches. This has given me a great idea of what I might study for grad school. Thank you and I’m sure this will help my students
Watching the 13 videos of the series in a row has been such an enriching experience. Every single second was worth it. Thank you very much.
I'm so sad it's over. Didn't think math could almost make me cry.
It was like watching a movie come to an end. I mean, these type of things aren't meant to be free, you're doing a great service Stephen. Thank you so much for inspiring us and introducing this whole new world of complex numbers. I will never be able to look at it the way I used to before. You've given me a new dimension (pun-intended) of interpreting and solving complex numbers. Once again, thanks.
One of the most beautiful educational series on youtube! Seriously underrated - although it is a quite niche topic, this deserves more recognition
Next serie: Laplace transform, please.
That would be an interesting to visualize
hey, i don't know how to thank you. I love to study beyond whats i'm having in school. I was having some problems with complex numbers and I hit into your videos and know I learned even more. Hope youre making more of this, because you got a new subscriber :)
Woohoo! Thanks for watching!
I'm grateful for internet access I have. This has answered every question my profs couldn't answer me satisfactorily. Kudoss to the work you put in
Yeah, this is why internet was created in first place, even though pop socials use it for showing off asses on IG haha
The first and only time I've shed tears from the beauty of maths
This is so fantastic! Thank you so much for making this
+Henry Smith Hey Henry, I noticed we concur the same maths channels so I went through your subscriptions in case I missed any of them. Maybe you've checked it already but I thought you'd like one called hackerdashery. Cheers
Wow, I've never seen such a well put explanation of the P vs NP problem. Thanks for the suggestion, I subscribed.
you're welcome!
Hi, do you have any other math channels to reccomend? The ones I'm already subscribed are numberphile, mathologer, 3blue1brown, and njwildberger, in case you don't know them yet. I'd also suggest the Banach-Tarski video from vsauce.
Hi! 3blue1brown is my personal favourite, but if you like mathologer and njwildberger you may as well like Mathoma (or even XylyXylyX). More divulgative/entertaining, there's a couple of videos about possible curvatures of the universe on Zogg from Betelgeuse, explained by an alien. Much more arty (you may know this one) is ViHart, who plays around with fractals and other cool mathematical concepts. You can find them on my subscriptions as well
Stunning visualizations and terrific explanations. Great video.
Yeah I tried finding how to do th be reimann graph by myself, but found something almost completely different! :D
What did you find?
There is no way I can thank you enough for what you are doing to people who always had problems with math but still need it and love it in a weird manner, like me.
I wish I can do something like this in my country soon, once people here are right now crossing a major collapse of educational system (and self esteem), and most of them can't understand english.
Keep! rocking!
And, again, thank you very, very much!
Thank you, and thanks for watching!
Welch Labs This series was awesome! There was a question on the last ACT that asked the distance between 2 complex numbers, and thanks to you I was one of the few people to get it right.
When I was having a bachelor's degree in physics back in 2014, there were no visual study materials. I passed my math courses blindly. After 10 years you opened my eyes. This playlist is 8/9 years old, and I have just found the gem at the end of 2024. It feels like I am having a rebirth. Should have found this long before. My heartiest gratitude to you for your tremendous magical efforts.
I almost cried at the end. Amazing series!
After Episode 10, this series getting more "complex" for me.
Top class education! Thank you Sir
Thank you!
This could do well in classrooms!
For free, shoud I add
Congrats for finishing this journey. Here's some views/likes statistics as of August 2020:
1. 5,330,727 / 111K
2. 1,557,435 / 29K
3. 1,020,456 / 22K
4. 877,545 / 18K
5. 842,658 / 20K
6. 706,350 / 16K
7. 621,010 / 14K
8. 521,989 / 12K
9. 486,186 / 15K
10. 440,908 / 14K
11. 587,091 / 13K
12. 348,950 / 8,6K
13. 738,382 / 31K
WHAT...
5:50
the danger of visualizing high dimensional mathematics concepts.... Going beyond my brain limit.....BRILLIANT WORK.
I pretty much never comment on videos. However, an exception must be made for this series. I have never had a subject so thoroughly, consicely, and clearly explained to me. It really felt like a wonderful journey through math, and I was as enraptured by the journey and each new revelation as I might be watching a movie or reading the climax of a story. So much obvious care and work was put into this. It is a shame this does not have several million views. Thank you, truly, for the knowledge. I hope you continue to share. Have yourself a fantastic day.
This video made me cry. There couldn't be any way better to describe and visualize this things. Just perfect
This series actually time travelled to the past from a 22nd century math classroom. You were born a century before when you’re supposed to be born. After a century if UA-cam will still exist, I believe people will echo my comment. This was an immense pleasure and privilege to enjoy something that belongs neither to our time nor our dimension. Hats off for the efforts put into this series. You are a true hero of entire mankind.
That was beautiful.That terrible feeling of confusion i have when thinking about complex numbers has been eased ever so much!!!
Woohoo!
UA-cam suggested part 1 to me, then 2, then 3. I never thought there were 13 parts! I've watched them all at once and now my head is spinning. But wow, they are amazing. Made from a deep understanding, very clear explanations, clever visualisations. Thank you!
I wish I could have seen these videos 20 years ago when I was in school. Brilliant stuff. I loved the way you used color to help with the visualization of 4D space. I really couldn't stop watching.
Awesome, thanks for watching!
From now my biggest dream ever is to become that capable one day that I could understand each n everything from this entire series...
Wow. So well explained and visualized. Even a regular guy like me can understand that (I think). I wonder how a guy like Bombelli, who pondered a lot of time about those things, would've reacted if we could have shown him this.
Norbert Harrer don't worry, the guy who made this video is probably Bombelli reincarnated.
Wow this was amazing! I watched all 13 episodes today and will probably watch the entire series a couple more times. Thank you for making this! And like the others I never really leave comments, subscribe or like but videos and channels like this deserve it.
This was absolutely beautiful... Thank you!
Thank you!
Still one of the best math series on UA-cam. I come back and watch the entire thing about every year and I always understand it more than I did the last time I watched it. Words can't do justice to describe how much I appreciate this series.
It is incredible all the effort you put in this. But dude! Absolutely worth it! Everything on these videos are just perfect! I love it!
This are the things that no teacher will care to explain you, but are the really important things. This are the things that make you love maths and knowledge in general, which schools and colleges lack of.
Im an engineering student and eventhough ive done a ton of shit involvin lateral numbers the teachers never cared to explain this things.
Please, keep up this amazing work! I love this so much!
yes you are right! these mind blowing problems make learning interesting. but I think we should also appreciate what our teachers are doing, even though they sometimes hide/are forced to hide what's really interesting..
Teaching system is fucked up. Not teachers fault. They gotta bring bread to the table.
I wouldn't even say that. I think at school you learn what you really don't like, so you can find something you like to do as a job. and in these other subjects you get knowledge anyway because you have to in order to finish school. and general knowledge is always good
What makes you think that teachers know how to explain such concepts to start with! I'm sure the fast majority of people involved in these calculations teachers, engineers, physicists etc don't really understand it themselves! And the comments on this video are only a testimony of that...
Truely understanding any topic (quantum mechanics, relativity, evolution etc) is not the goal or the point of all education systems that I dealt with in multiple countries, the only goal of them seams to be just cloning half capable professionals to fill certain jobs in the educational institutions and in the society in general.
You have just earned a Graham number of thumbs up
haha - maybe one day.
very wonderful work ! it makes math beautiful , not some absurd boring rules!
Thank you!
no, thank you! this is EXCELLENT
This is Nirvana! With enthralling background score, I felt like I am watching "A Beautiful Mind" again! Well done.
Best mathematics series on youtube which I hv seen so far....fantastic work. You have this amazing skill of explanation complex concepts in most lucid, interesting and enjoyable manner.... good job! keep it up!
wow. I have to rewatch the series to let it sink in
I've just opened the you tube and found myself completed this series. Im so impressed its amazing man!
I think its only the second time i hit a like for a video
woohoo!
Same. Binged all of them in 1 go.
Everything was going great but then i lost you at this part. Awesome series regardless, thanks for making it
A beautiful presentation! I had mugged up on complex numbers for my exams, but now after watching all the videos, I clearly understood their significance. Thanks a ton, welch labs.
Sweet!
Oh boy, that went from junior level math to master level in just 13 parts and I actually fucking understood quite a lot of new things. And I've Engineering and MBA degrees, I feel like I wasted "years" learning through crude methods what was otherwise possible in these 13 parts.
THANK YOU!!!
I can't put into words how amazing this is, thank you for making this
You've done a great job in explaining a simple-to-calculate-but-hard-to-visualise complex functions. Many confusions are cleared. I've watched episodes 11, 12 and 13 over and over again. 10 out of 10. Thank you!