The way this entire video beautifully transforms right from a single point in euclidean geometry to the shape of the entire observational universe itself is so fascinating
a book call Quran (1400 years old ) talk beautifully about the shape of the universe and what will happen to it the verse says : "" On the Day when We fold the heaven, like the folding of a book. Just as We began the first creation, We will repeat it-a promise binding on Us. We will act. ""
I am a high school student rn , and I know nothing about geometry BUT i wanna study it from the very basics to the most advanced level there is , would it be possible for you to provide me with the roadmap and perhaps a guide book too if possible ? (please!)
I have a question that I have been wondering. If we were able to communicate, only using math, with another human civilization, would we be able to define the difference between a person's left hand vs right hand? Or would we first need to show them a picture of what we mean by these relative terms? Is there some fundamental difference that we could use as a beginning point?
This is a fast-paced video. It doesn't give the opportunity to deepen and enjoy the beauty and the importance of these discoveries. Don't let yourself be derived by animations, a double-edged sword tool.
@@feynman_QED it's a perfectly paced video. It's not supposed to make you understand everything about the subject, just to introduce it in an interesting way and make people interested to learn more about it on their own. If it was longer and dived deeper, less people would care about it in the first place
@@n1ppe First flaw of your comment: I have never said that a video should let you understand EVERYTHING. Second, the reason why people cannot catch this aspect is the same behind the many thumbs-ups received by an illogical comment: you don't want a more articulated video but you want "to dive deeper". Please, make a decision and select which one you wanna pursue because it's not possible to satisfy that requirement simultaneously. I love this guy and how he produces videos. But videos are very often aimed at knowledgeable audiences who can keep up with a shortage of details and the fast pace. And it is absolutely not true that one requires 3 hours to make a more articulated video. If you indeed are interested, you just find a few slots of time during your week and you watch it carefully. Finally, I don't believe you're going to search a book and then study the topic in-depth. You're simply in the "infancy" stage when you are impressed easily by animation and hype, but you haven't developed an internal and sincere urge and interest for learning something more deeply. It's what happens with children: they are excited by toys, but after playing for a while they get annoyed.
Yeah, I wholeheartedly agree. I took freshman Algeria 4 years in a row and graduated with a cumulative grade of a D- . So believe when I tell you, of everything that I think I know, there is only one thing that I know for certain and that is that I don't know anything. 🤣
This video combined 3 best kinds of videos you make: 1. History of science & math 2. Visualization of difficult concepts especially those of physics & mathematics 3. The current great curiousity of humanity
So Flat Earth were way ahead of curve and Meant Flat Universe??? Also a side note... Euclid Book was one of the things demanded by Arabs ...after one of those Byzantine Arab wars...
Man I used to think I hated math even though I was really good at it...every Veritasium video about math that I watch makes me feel more and more like they just trained me wrong as a joke
I saw Professor Kontorovich this morning at the DMV and I couldn't remember where I had seen him. I even asked him if he was on TV because I recognized him. I found you professor, you are too humble, you are famous in my eyes!
Your Standard Model of Cosmology is a dead and stinking. The BigBang-to-BlackHole sex-and-death cult has no scientific verification. It's all false assumptions for a foundation for a house of cards. The god of gravity is dead. Long live the Electric Universe Model. Good luck in your search for a better understanding of reality. Best wishes, Charles A Campbell III
Haven't seen the video yet, just the introduction (0:55 now). And I must say: it sounds extremely fishy for now. Don't get me wrong, I very much like Veritasium and I appreciate is work. His means to get the public interested in sciences, even the fishy ones, I see them as a good ideas. Doesn't change the fact that suggesting Euclide already knew about "Hidden Universes" (modern science ones) is, at best, sketchy. I know a bit of history of sciences and Euclide most certainly is one of this genius among geniuses. A mind like that would probably (hard to prove) make discoveries ahead of its time in any era. But still. It's very confusing to suggest that, since it leads to a very inaccurate understanding of what was the state of science (philosophy) back then. It's a great way to introduce the concept. But I don't think you should repeat this idea at lunch time, you'll propagate a misunderstanding or pass for a fool. Well, maybe not, I have to watch the rest of the video to now ;-)
it hurts to imagine that many great minds and their works were lost to arson in burning the libraries at Alexandria , Nalanda , Takshashila and Baghdad...what have we lost?
I find it so wild that mathematicians can do crazy things like predicting one supernova appearing 5 times spaced 1 year apart, but do things like spending 2000 years arguing about 1 sentence Edit - How did this start a war. I just exagerated some stuff to make a point
To call Euclid just "Father of Geometry" is an understatement. The major branches of math are built from Axioms, and Euclid pioneered that. He might as well be called the Father of Pure Mathematics itself.
Euclid had a great merit in consolidating in the Elements most of the mathematical knowledge of his time. But he is by no means the "father of Geometry". At least 2 centuries before him, other pioneers like Thales of Miletus and Pytagoras of Samos had already devised the logic-deductive Method, on whitch rests all of Mathematics.
@@gilbertogarbi4479Greeks are famous in history for just stealing all the other countries best ideas of cultures, inventions, math and making it seem like research was just like inventing. Greek alchemy is just middle eastern alchemy etc they've never come up with anything only debated other cultures creations they stole from and improved the original idea. Pythagore was a cult leader who stole sumerian math and has gone down in history as it's inventor.
I took a geometry course in college where we started from Euclid and went on to derive essentially everything that you covered in this video to end with the shape and dimensionality of the universe using relativity. It was the best class that I ever took and this video was an amazing refresher on it.
iI loved my geometry course in uni and we did almost the same up to spherical and hyberbolic geometry, but your ending on the dimensionality of the universe sounds brilliant
I am a physicist, and this is one of the best explanations of curvature of spacetime I have seen on youtube, starting from absolute basics! Thank you so much, and keep up the good work. 🙂
This video surpasses your usual Veritasium content in a unique way. The layered storytelling, which included extra details beyond just non-Euclidean geometry, enriched my experience. It felt like a 3D exploration rather than a linear journey, giving me a deeper and more nuanced understanding. I think this is one of the best ways to explain a topic yet. Good job!
Great observation. In the 2nd episode of Cosmos, Sagan opens with a recounting of a 12th century Japanese battle only to segue into a discussion of selection/evolution: there's a magical quality to that scene that I've rarely felt elsewhere. This has a similar feeling, and "layered" captures it perfectly.
Yeah, you are absolutely right:) I really love the butchering of Greek and Arabic names, the misuse of the Latin Roman spelling for Greeks and those fantasy images of some material, where we actually have real historic content available. Stock Photos ... it's just a blessing ... Also getting Εὐκλείδης Axioms ignored and the purpose of Postulates confused is rather embarrassing. Well ... he had ONE JOB to do. I guess nobody's perfect?:) (Talking about "Journalists" here ... better consult a historian next time)
Being able to observe and predict a phenomenon as large scale as light bending around an entire galaxy to make a cosmic lense is insane. What a time to be alive.
This is I think the 3rd or 4th time having professor Alex on the channel and I’ve loved it everytime. He seems so enthusiastic with his explanation to the point where it’s infectious.
I find his argument about definitions ridiculous back then that language most likely lead to a specific understanding.. otherwise, why does everybody else agree and well mathematics as well. Seems Alex was the only one who didn't understand.
@@Cameron-ls3qtNo. At first, I too wasn’t buying it. However, I heard him out (and digested his whole argument), and I can now see it. It’s actually pretty brilliant. If you write a definition, the definition is made up of things that also could be defined, of which all are composed of even more things to define, and so on. It’s either a cyclic (circular logic, flawed) or never-ending (no useful definition) problem. Instead of establishing definitions, the professor suggests to establish relationships. As in, given this thing (regardless of how it could be defined), here’s how it relates to other things (regardless of how they could be defined). It all of a sudden makes this never-ending definition problem into a finite relationship problem, and it has much more rigor this way (as the postulates now only need to establish relationships, which then could be used to demonstrate other relationships, proving theorems). Yes, one could certainly understand Euclid’s definitions (and they don’t invalidate his results). However, his definitions are hand-wavey and non-rigorous… and most importantly (as the professor explains), unnecessary.
So you are saying that your university course was only superficial and just taught you some history and only explained concepts, but didn`t teach you how to calculate the stuff?
@@maythesciencebewithyou "Foundations of Geometry" sounds like your typical survey course for students aiming to one day teach high school mathematics/geometry. So, ironically enough, there's likely little in the way of teaching them how to actually "do" geometry.
Take a look at the game Hyperbolica. It's set in a world with hyperbolic geometry. It takes a bit of adjusting to go back to moving around the real world after playing it for a while. Appropriately, the first tag to show up on Steam is "surreal".
I love how some things went unsolved for millennia and then multiple people have the same idea at the same time. This has happened over and over in the history of science and mathematics.
It's because individual geniuses are utterly meaningless to the history of progress. Humanity has always had plenty of smart people, what matters is the opportunity. If one famous historical person didn't discover something, someone else would've, and for the same reason that person did: Not specific individual intelligence, but individual intelligence applied to the sum of human knowledge at that point in time.
Makes you wonder if there was something about the time period of the 19th century (more mathematical geniuses?), or if older versions of the idea are lost to time. Possibly during 2000 years countless mathematicians came up with non-Euclidean geometry but never published it because they feared ridicule.
@@cereal-killer4455, isn't that the bizarrest thing - he claims the universe to be essentially flat after just describing the reason why mathematically any sphere can be seen as essentially flat when zoomed in enough!
Gauss never ceases to amaze me. There isn't a single math or science class I've taken where his name hasn't come up. Someday I'd love to spend some time learning about all of his greatest discoveries and trying to connect all of the dots of the contributions he's made.
The German author Daniel Kehlmann wrote the superb novel "Measuring the World" on C.F. Gauss' and Alexander von Humboldt's (yes, THAT Humboldt) lives. It was an sensation, depicting two crude geniuses in a absolutely entertaining, readable and intelligent way. The moment you open the book, you'll read it in one go, accompanying both Gauss and von Humboldt getting old, and even more strange. Gauss did not publish all his findings. He published only if he decided that he treated a subject in it's entirety. E.g. he did not publish his vast and deep findings in mathematical knot theory for he just wanted to complete some details, as we learned from his duaries.. Decades after Gauss' death, other mathematicians began to devolop the very same ideas, that Gauss already had knew.
Don't sleep on my boy Euler. Lots of things are named after the person who discovered them after Euler, otherwise almost everything would be named after Euler
Hey Derek, you probably won't read this but I just wanted to say that I've been watching your videos casually for many years when you first started. I just need to say that your production quality and ability to keep audiences engaged has evolved so beautifully. I watched this 30min video and it felt like only 5 minutes had gone by... and I'm not even that interested in mathematics let alone history. All I'm trying to say is well done. Thank you for all your years of educational content and thank you for continuing to impart the same level of passion in every project. I hope you continue for many years to come.
28:35 It's so mindblowing to me that Euclid's work was mostly based on the 2D plane. Then as the Earth was proven to be spherical, the math became more complex and humans had to adopt these new models of geometry to keep up. But apparently on a large enough (i.e. universal) scale, it's all apparently a 2D plane still. It's as if Euclid's genius came from some arcane, otherworldly knowledge.
I don't get that part. The universe is flat? Like it is wider than it is tall or something? Cuz theres definitely an up and down dimension with stuff scattered in every direction. So how is it flat?
@@zwenkwiel816 I'm not gonna pretend to understand the math behind it, but yes, the data presented in the video points to the universe being flat. This next part is only my understanding, but yeah I think that that's what it boils down to - the universe is so unfathomably wide and expansive that the "up" and "down" (z axis) are nowhere near significant enough compared to it's length and width (x and y axes).
@@Grimlo9icFlat: as in that it doesn’t curve around in dimensions higher than 3 and meet itself on some other end like a hyper sphere or some other hyper shape. If you keep traveling in our 3D universe, you won’t come back to the same point. In this universe, parallel lines really are parallel.
I am a physics and maths enthusiast and a game developer myself, and I generally love the explanations you provide also the small little details in the video, like moving the eyes of Gauss when the explanation texts goes from left to right of his picture. I mean ofcourse its not necessary but knowing that you guys put in the efforts into even the minor little things in video production makes me respect your efforts infinitely.
If someone had told me this when I was in highschool (I was fascinated with astronomy as a kid, so maybe even earlier), my relationship with math would be completely different. This is fascinating
@@firstnamelastname9215they didn't necessarily want to torture you, there aren't many teachers as good as this channel but there are a lot of honest people trying their best
The system wanted to torture them is the point. And in a system like the best Finland lot of those honest people would be unable to qualify to be a teacher which is harder to do then get in med school. @@alecmartin8543
@@alecmartin8543 I love math and had a good teacher, but there are a lot of teachers who hate/mistreat children or aren't good at their job. I've definitely had more teachers that made me dread going to school than good ones
I feel like I finally understand a bunch of stuff that I've always heard, in relation to math and physics, but was never able to fully grasp and connect together, for example what people meant exactly by the curvature of space time caused by gravity and such. This video's narrative is absurdly good and really helps tie it all together in a very comprehensible way. Just wow... this channel never ceases to amaze me.
I had a math teacher with Elements sitting on his desk. I have dyscalculia, numbers are extremely confusing (if not downright nightmarish) and math was always my worst subject. Straight A's with a D- in algebra. However, glancing through that book a little bit every class period, I found that the THEORY of math fascinated me. Sadly, schools only cared on if you could find answers to questions, and they didn't give a damn on if you knew WHY math worked. In college, after struggling for 3 years with "self paced math" meant for people with learning disabilities, my campus came up with an experimental "Algebra for Liberal Arts Majors" class, where we had the option of doing 30 math problems, creating art projects to illustrate the math theory, or writing essays on the theorems, how mathematicians came about discovering and proving them, or how this particular type of math applies to the real world. THAT I could do with ease, and it was my very first A in a math class. Numbers are still a mystery, something I just cannot sort out with my weird brain, but I love the history of math and what went into the geniuses who came up with these ideas.
check out "fractals" that's probably how your brain is trying to operate. like mine, in reality, not fictional numbers. this thousand year old stuff is cool, but new thinkers might benefit more from realizing 3d math exists but is just way too complicated for most to even fathom. i figured it out on my own but then learned somebody already did in the 70s, thank god, cuz i wasn't trying to write that book myself. the way i understand it is every atom is 3 parts. and reality is base 3 number system. everything in 3s, based on that simple postulate. expanding out in all directions, continuously. interesting rabbit hole, but that's the real infinite realm. base 10 makes sense on paper, and counting on our fingers, but that's not how god designed the universe.
@@Sorrowdusk It was brand new when I took it back in 2004, a test program for students who don't need advanced math in their given major, especially folks like me with a learning disability that nearly prevented me from getting a degree. It was humiliating during matriculation when my counselor exclaimed, "How can you be in the top 1% in English and Logic but the bottom 1% in Mathematics?" Dyscalculia. That's how. It's because my brain cannot process numbers, so it compensated by using logic. (Also part of being autistic.) Yet the California education system refused to give me a pass on the math requirement, even though it had NOTHING to do with my major. Struggling with numbers doesn't mean that I can't have a successful career; in fact, the way my brain works is THE IDEAL for my job.... it just means I have to hire someone else to do my taxes, because my brain can't process numbers in the right order. If this sort of program didn't catch on at other colleges, that's a real shame. We need an education style that evolves with our growing understanding of neurodiversity. I've begun to work with Umbrella US, a NPO trying to change this sort of thing and get society to realize that not all brains work in "typical" ways. There are talented people out there being held back because they can't pass a course designed for neurotypical students. Look at all the scientists over the generations who struggled in school, because their brain danced with numbers but struggled with language, or danced to the music of etymology but fell flat with numbers. Imagine if they lived today, where they had to pass all these frivolous classes mandated by the federal government, but have nothing to due with their interests, or else their ideas and theories are disregarded due to not graduating from the "right school." One day, hopefully, programs like what I took become the norm. Give students the option to show the teacher that they truly understand a subject, even if the way they do that is not neurotypical.
Me too i hated math growing up but now that i am learning it's history and creative applications, I am really starting to appreciate it more and more. I'd say it's just a beautiful subject taught in an ugly manner
Brother/sister; math is just about seeing coherences and expressing these coherences with symbols we call numbers. Art and music are ALSO about seeing coherences and expressing these, but NOT in numeral symbols but having the coherences expressed in form and colour; or in the case of music: sound. You too are a mathematician, you just use a different language to describe the coherences you see.
My goodness, man, I think that quite often but I have to say this is one of your best videos to date. The level of storytelling and the way you managed to tie ancient knowledge all the way to the very edge of our current understanding of the universe was absolutely mesmerizing. And poetic, even, because just as in culture, arts, music and so forth, the new doesn't necessarily destroys the old, but rather builds higher grounds over earlier foundations. Chapeau!
I am sad for Bolyai as he thought his hero Guass would appreciate his work. Still, when Guass replied that he didn't do anything except repredicting his work Bolyai would have been crushed deeply. I definitely see Bolyai as a legend doing such great work at the age of 23 in just 5 years while Guass had spent nearly decades finding out about it. "Appreciation can make someone's day, even change lives. So even if the work is small or the best it is incomplete without a 'Good Job'." - A Wise Man.
He didn't really say that the work was unimpressive or bad, the sentence is taken out of contex, we don't really know if he followed it up with praising
summary: drawing lines on a sphere or a bendy shape follows different rules than on a flat surface. that's literally it. the spacetime stuff is pointless because we're inside whatever shape the visible universe is, it's the fishbowl problem, you can't be confined to a fishbowl and know the architecture of the house across the street
I used to hate math class in school, but the topics that Veritasium covers are so interesting I always find myself going down a mathematics rabbit hole after i watch one of his videos.
because this isn't math, it's a history lesson and a story. You just hate making an effort which is what math requires and listening to a story does not.
No he hates the dry boring way that math is normally taught. A very valid point. And he actually states the story gets him interested in doing that effort you describe. Your opinion is why so few like math. @@zwan1886
the greeks already knew the earth was round, and used spherical geometry as well (Eudoxus of Cnidus, Autolycus of Pitane, Hipparchus, Menelaus of Alexandria, Theodosius of Bithynia, Ptolemy...) they wrote books and theorems on spherical geometry, since the time of Euclid in fact. It's not true that it took 2000 years to figure out these things...
I love the historical backgrounds upon which you base many of your videos; this greatly sets the stage for the upcoming knowledge that is so expertly and well delivered. Thank you.
Hyperbolic geometry is more than just a giant cosmological thing. You know how the outside edges of some types of lettuce and kale go all crinkly, just like with the crochet model? The cells in them are effectively living on a hyperbolic plane, and studying the shapes and sizes of the cells there - how they fit together and exchange resources and such - requires some of this geometry.
Leonard Mlodinow's Euclid's Window is a good book for those who want to dive deep into the history of geometry. Thank you, Veritasium, for animating the history and concepts. I am a math teacher and have always wanted to incorporate historical development of mathematics into math curriculum. I want to dilute the goal of math education from only problem solving to explaining math concepts. I want to tell stories like Galois' duel, Zeno's paradox, Newton & Leibniz's letters/rivalry, the centuries of proving Fermat's theorem (and Langland's program), al-Khwarizmi's completing the square, the discovery of the formula for cubic & higher (and the affairs) ....etc. Veritasiim and 3blue1brown are my favorite youtubers who have great influence to our online math community. Now we find THOUSANDS of math explainers on youtube who actually teach better than professors and grade school teachers (myself included).
The kind of mind you must have in order to actually want to teach math to the kids..... I commend you, and appreciate your drive to teach difficult things to difficult peoples.
THANK YOU !!!! I wish I had been exposed to your video 58 years ago. The WORK they have put into ALL of this is incredible. The puzzle pieceS you've given me are overwhelming. Awesome. Thanks !
If only my teachers in high school had had this ability to present math in this way.... I'm grateful to finally be able to understand/grasp these concepts.
Teaching is live vs having an editing team for a content creator on social media w/millions of views. First relies on a fraction of the income and does their own prep. Not saying this channel didn’t take effort to build just not a fair comparison.
@@zwojack7285 When Farakas cautioned his son Jonas Bolyai with a father's concern that he should come to nothing as he himself failed there being a teacher in the field. But when he later realized his son's originality and brilliance he accepted his mistake, when 1) he made his son's work as an addendum to his own and 2) he sent it to his old friend Gauss. So Farakas did the best thing and was not responsible for what happened next, viz. Bolyai's frustration due to Gauss's fear of "Bootier".
@@-astrangerontheinternet6687might be true for him, definitily isn’t for others. People have been hanged or imprisonned for stuff they discovered. Or people like Kafka who has been depressed his whole life, thinking it amounted to nothing only to be successful after his death. It is tragic
he definitly has a production team working on the videos with him, but that doesnt take away from the passion he puts into explaining the topics he covers
I honestly believe that learning to sew could have given insight for those mathematicians that spent 2000 years trying to understand the 5th postulate. All fabrics are essentially planes, but our body isn't and, depending on culture and time, it needs to closely follow our body's format - that is definitively non-euclidian.
This concept is what confounded me the greatest. We know the universe must have thickness so it can't be a plane, much like a tabletop, which is flat but you can still measure its thickness. So how "flat" is the universe? Is it a sheet of paper or a tabletop or ...?
@@LeeNotSa the universe is not “flat” in the sense that it can have “thickness,” it is flat in that, if you move in one direction forever, you will move further and further from your starting point and never circle back around to your starting point, which is exactly what would happen on a spherical planet. Another way to think of it is: On Earth, you and another person start on two different locations on earth and head north. No matter where they start, they will always end up at the true North Pole, in the exact same spot. In space, that doesn’t happen, instead they just head straight in the same direction for eternity, like two parallel lines never crossing paths.
@@AaronSkone OK, but wouldn't the same thing happen if the universe were hyperbolic? Wouldn't a straight line still cause you to never return to your starting position?
@@LeeNotSa yes, however the difference is that in a hyperbolic universe, the parallel lines would grow infinitely further apart. There’s theories for either or and we’re not really sure! The universe is so massive that even measuring the small section of space-time we occupy would be inadequate (similar to someone looking at the open water and saying “looks flat to me”).
I know, I know... Hungarian is a pretty difficult language, but if you just tap listen in the Google translator, you will be amazed, how big the difference pronouncing Bolyai János in English and in Hungarian. As a proud Hungarian, I thank you for this video!
The most impressive of all is how far ahead Euclid was that it took mathematicians thousands of years and forced them to invent a whole new field of mathematics and non-Euclidian geometry.
@@devshankarnair6344 I don't watch that much pop science channels, I know Dr. Becky is astrophysicists delivering news on astrophysics. From math I know few, 3 blue 1 brown, mathologer and flammable maths
Hi Derek! I send you greetings from Göttingen. Right now, while I'm watching this, I am sitting at the Gauss Tower in the cities forest east of Göttingen and I am deeply touched by the emotional gravitas and the history behind the place and it's meaning for human society in conection with the 2000 years of history of the topic of your video. This is truly an intense moment for me it will probably stay in my mind for many, many years to come. Thank you very much ❤
As soon as he started to talk about Gauss and Göttingen, I thought about going to the Gaussturm to admire the stars and get high on my curiosity about this universe we live in :)
Your passion for what you do is contagious. It's evident that you genuinely love creating content, and that enthusiasm translates into an enjoyable viewing experience for your audience. Keep that passion alive!
Thanks for the video! I love reviewing and scrutinizing the foundations of math. It is very exciting stuff! Is their any book like Euclid's for today's maths? Or is there any book that gives an exhaustive overview list of all the branches, fields, subfields, sub-subfields, sub-sub-subfields, and so on in maths?
Sword fights, geniuses, spurned admirations, secrets of the universe, and arguments about parallel lines. Only in Veritasium video could it coellese into something so crystal clear. It's shameful other educators leave out the history and context. It dymisyifies the subject and let's the mind feel safe to play with the ideas. It's brilliant you're teaching this way.
As usual, a wonderfully interesting and informative video! I absolutely love how the story evolved from a simple, dry, millennia-old mathematics axiom we learn in high school, to an almost incomprehensible explanation of the structure of the entire universe.
@@sumathipitchaimani actually, there is no difference between an axiom and a postulate in modern mathematics but euclid differentiated between them as such: Postulates were specific to geometry but axioms were general mathematical statements holding for all forms of maths
Mind continually blown. Thank you Dr. Muller (and cohorts) for your efforts to make this extraordinary topic accessible to aspiring minds like this one.
Fantastic video. Im shocked that i actually understood that. It helped that ive been watching videos on similar topics, but this one really made everything click for me.
It just blows my mind how everything has adds from the past body of work of mathematicians to the current body of work in different fields. During academics we just know mathematics is in the core of everything but this channel just initiates and finishes the stories we never knew they needed to be told. Thanks @Veritasium
How is this video available for free? the production quality, the storytelling and the animations are all perfect. Veritasium is truly levelling up every video.
Far out ! This blew my mind away and Math is not even my strongest suit. So compelling, easy to understand, seamless narration and nicely presented. Thank you for this .
This is my third video I’ve watched from this channel (yes I subscribed) and it’s masterclass. The guy who had to cheat to pass math because it just doesn’t sink in spent 30 mins learning about geometry and parallel lines and all these famous math dudes. I mean… your videos are amazing. Just wanted to say that it’s appreciated.
This is insanely good. Explanations of the fundamentals of math, the interesting histories of the people behind them, what they teach us about the universe, all with really high production values. I simply love this video.
So many times I wished I paid more attention to math. It was difficult in high school. My cousin spent quite a few hours teaching me algebra. And I hated it until I started making a little progress. With a little more time it felt like a dam broke and finally, everything was making sense. Math is so beautiful. It's like a language that machines understand and humans who speak different languages do too. And if you feel that it's not your thing just remember that you just need a little more time. Of course, there are people who just get it, and most of us will never reach that level. How Newton came up with Calculus at 27 years of age is beyond me. Recently I watched a documentary about how Cruise Ships are made and operated. Some parts are so precise they can only be made in one country and in one special place that makes those parts. While watching it it occurred to me that there is someone who knows everything about this ship top to bottom and it blew my mind. Of course, some are more specific, like food preparation, doctors, security personnel, or how to find staff that is fluent in more than one language. It's almost like a small country on water. Amazing!
Isaac Newyon was a prodigy. He also was born into nobikity I think. It wasnt uncommon for peoppe to achieve landmarks before the age of thirty back then. Also the reason why math is difficult is because the way schools teach it is impractical.
Unless you're an unusual prodigy in it, I think you need at least one good math teacher to get into it at least to the level of formal logic and algebra, which sets everything else up for you. The first year I went to public school, I was lucky to actually have a good math teacher, and it really set me up for life as far as logic and math go.
Amazing video Derek. Sometimes you go too deep for my pea-size brain when you do maths or physics videos, but this time you really nailed it. Bravo and thank you.
Glad that people now can know more about Bólyai. His name is pronounced (sg like) bow-ya-ee, with the stress on the first syllable, not bully-eye, though. Awesome video!
As an EE and ham radio enthusiast, the Poincaré disk looked very familiar -- this transformation from 2D euclidian space to a finite-sized disk is exactly what we do to visualize complex impedances more easily. It's called a Smith diagram, it's an invaluable tool, and using it feels like doing black magic.
Derek, this was a fun journey. Thank you for taking us on this journey. Brilliantly produced. I was a pilot and flight instructor, now I am a high school teacher; from one educator to another, I would like to honor you with a compliment on how amazing of an educator you are. You are a phenomenal teacher. I consider myself a competent instructor and intelligent person dedicated to being a lifelong student, but it is my opinion that you are in a league of your own. I think educator is one role you can confidently say you are a master. Master educator, check. Professors could learn from you.
I've always had some kind of mental block when it comes to taking in mathematics, like a minor learning disability, but this video was made in a way where I could follow and understand what was being explained. Thank you for that. 😊
The brilliance of the content of this channel is well known. . But the efforts they put into visuals is very underrated. . 12:11 Observe the eyes of Carl F Gauss. . .when the side of the quote changes. . . Excellent attentions to detail man. . . you probably wont read this but Derik you have mastered the art of making Math interesting to all. . Keep up the good work. . .❤
Brilliant work this video. There is no way I could have understood these concepts from a text book. This approach opens up access to even to relativity and quantum physics imho. Thanks to Veritasium I have some hope of comprehending even modern terminologies without completely understanding the math.
Related note: if you’re interested in seeing more of and playing around with hyperbolic (and possibly others) geometry, I highly recommend the videogame HyperRogue. It’s a top-down (with poincare projection by default) roguelike, but also features many tools for building projections, tilings and pictures. It’s unique, offers an interesting point of view on a lot of these things and plays around with them in many different ways.
I love maths and I’ve always been intrigued by hyperbolic geometry, not to such a degree as to study it formally, but to look into it. This video, finally explained to me the motivation for hyperbolic, and spherical, geometry. Thanks for the insight. At some point I will certainly study non-Euclidean geometry formally.
I wish I could show this video to my younger self. This presentation makes so much sense, as someone who struggled with math throughout high school up until college. great video as always!
I remember about two years after leaving college I watched vsauces complete proof of all internal angles in a triangle adding to 180, I was struck by the fact that I knew every component part of it, the axioms, their reprocussions, the evidence, but no one ever explained to me how it fit together dispite being so beautifully simple It was so telling of what school had been for
Not going to lie, this video has me on the edge. One thing I believe can still remain true.... Just because what we see above our heads my have a certain shape doesn't mean that the ground below us has to have the same.
This is amazing. The reasoning line from euclid's basic geometry principles to the general relativity theory of einstein is amazing 🤓. I never thought of these principles these way. Also the way you explained non euclidean geometry opened my eyes. Hands down one of my favourite videos ever ❤
The way you make the audience connect with deep mathematical concepts as if they were intuitive and tangible speaks volumes to your skill as a communicator. Doing math viscerally hurts me, lol, but understanding the meaning of the math and how it applies to the nature of reality is endlessly fascinating. Your ability to translate the deep lore into a wondrous understanding is invaluable to me.
I truly enjoy watching your videos about math, geometry in particular. As a student in Belgium, I excelled in maths but was never motivated by the school or parents to pursue a degree in it. I switched from high maths to computer science before turning 17. Currently I work as an architect drawing in 3D and automating the software (Revit) with custom packages and dynamo scripts to assist collegues. I feel like ive wasted my potential in maths, especially since I was teaching my class at 13 in spherical geometry because the teacher himself didnt get his point across clearly. Seeing someonelike you, makes me realize what I wished I pursuit,even though I understand the chance I couldve gotten as far is slim. Keep making these videos please, thank you so much.
I resonate with you, I was so interested in maths but somewhere in class 11th I lost interest, it was covid Lockdown, I didn't have access to good teachers, I tried but I hated algebra, only until 12th when I found a youtube channel to learn calculus!! I eventually switched to engineering in computer science, now while learning the neural networks and AI, while watching veritasium videos, my love for maths is returning 🙂
This video was very refreshing to view. For many years I have ran into this subject. My initial 'solution' to the parallel lines was to use an extra dimension 'z'. This allowed for lines to be parallel at the same x,y coordinates, but not being the same lines, since they were apart in dimension z. The approach with spherical and heliospherical is new to my imagination and very fulfilling. Thank you 🙂 Henk Pietersma, Emmeloord, Holland
Let’s all appreciate Euclid’s effort he put into writing The Elements just so that Veritasium could make a video about it
credit to veritasium for supporting small authors like euclid
I
Yes
@@TheOneAndOnlyCumGuzzler yes 💯
As he said, it's exerted great influence, so
Imagine the greatness of the man who wrote 1 little paragraph and made mathematicians mad for 2000 years
Fr bros a menace
Haters pocket watching bro smh
The level of genius involved is unparalleled.
Greeks have been doing that for a long time
@@topherthe11th23 Greek architecture, sculpture, philosophy, democracy, science ( the atom ) etc. This is evidence of a high achieving population
The way this entire video beautifully transforms right from a single point in euclidean geometry to the shape of the entire observational universe itself is so fascinating
fascinating indeed
I’m convinced that math is the key to the secrets of the universe
@@matroxman11 bruhhhhhh obviously
a book call Quran (1400 years old ) talk beautifully about the shape of the universe and what will happen to it
the verse says : "" On the Day when We fold the heaven, like the folding of a book. Just as We began the first creation, We will repeat it-a promise binding on Us. We will act. ""
(Comment deleted due to comment crybabies; enjoy the contextless whining below!)
As a Mathematician that loves hyperbolic geometry, I'm grateful to you for making this video. I'm going to share it with all my students for sure!
I am a high school student rn , and I know nothing about geometry BUT i wanna study it from the very basics to the most advanced level there is , would it be possible for you to provide me with the roadmap and perhaps a guide book too if possible ? (please!)
@@abdussami8498 google is free goofy
I have a question that I have been wondering. If we were able to communicate, only using math, with another human civilization, would we be able to define the difference between a person's left hand vs right hand? Or would we first need to show them a picture of what we mean by these relative terms? Is there some fundamental difference that we could use as a beginning point?
i don't get the issue. euclid is obviously referring to a flat surface, where the 5th postulate self-evidently true
Veritasium's videos are generally great but the math ones are on another level
This is a fast-paced video. It doesn't give the opportunity to deepen and enjoy the beauty and the importance of these discoveries. Don't let yourself be derived by animations, a double-edged sword tool.
@@feynman_QED it's a perfectly paced video. It's not supposed to make you understand everything about the subject, just to introduce it in an interesting way and make people interested to learn more about it on their own. If it was longer and dived deeper, less people would care about it in the first place
@@n1ppe First flaw of your comment: I have never said that a video should let you understand EVERYTHING.
Second, the reason why people cannot catch this aspect is the same behind the many thumbs-ups received by an illogical comment: you don't want a more articulated video but you want "to dive deeper". Please, make a decision and select which one you wanna pursue because it's not possible to satisfy that requirement simultaneously.
I love this guy and how he produces videos. But videos are very often aimed at knowledgeable audiences who can keep up with a shortage of details and the fast pace.
And it is absolutely not true that one requires 3 hours to make a more articulated video. If you indeed are interested, you just find a few slots of time during your week and you watch it carefully.
Finally, I don't believe you're going to search a book and then study the topic in-depth. You're simply in the "infancy" stage when you are impressed easily by animation and hype, but you haven't developed an internal and sincere urge and interest for learning something more deeply. It's what happens with children: they are excited by toys, but after playing for a while they get annoyed.
Derek has good sources, and actually listens to them!
Yeah, I wholeheartedly agree. I took freshman Algeria 4 years in a row and graduated with a cumulative grade of a D- . So believe when I tell you, of everything that I think I know, there is only one thing that I know for certain and that is that I don't know anything. 🤣
This video combined 3 best kinds of videos you make:
1. History of science & math
2. Visualization of difficult concepts especially those of physics & mathematics
3. The current great curiousity of humanity
.
@@dinogt8477do you need a tampon?
So Flat Earth were way ahead of curve and Meant Flat Universe??? Also a side note... Euclid Book was one of the things demanded by Arabs ...after one of those Byzantine Arab wars...
I agree it is very Cosmos-esque and I think Carl Sagan would be proud.
And
4. An inspiring story about not listening to seniors about not pursuing your intuition, thinking from first principles
Veritasium’s math videos are so good. Just never gets bored watching them.
me too
Shortest 30 mins on RUclips
Man I used to think I hated math even though I was really good at it...every Veritasium video about math that I watch makes me feel more and more like they just trained me wrong as a joke
for real, learning has never been more exciting
yeah and you will always learn alot watching his videos.
I saw Professor Kontorovich this morning at the DMV and I couldn't remember where I had seen him. I even asked him if he was on TV because I recognized him. I found you professor, you are too humble, you are famous in my eyes!
Gauss never ceases to amaze me.
Wow lovely
Nice one
Vnvb
Sweet 🎉🎉🎉
Good jobs gauss never ceases to amaze me.
As an astrophysics major, I love how a video on ancient math turns into a cosmology lesson
Mayor , no less
That's how it all started.
Your Standard Model of Cosmology is a dead and stinking.
The BigBang-to-BlackHole sex-and-death cult has no scientific verification. It's all false assumptions for a foundation for a house of cards.
The god of gravity is dead.
Long live the Electric Universe Model.
Good luck in your search for a better understanding of reality.
Best wishes,
Charles A Campbell III
Checkout The Greatest Lie on Earth by Edward Hendrie. I can promise you are being fed a bunch of garbage
Sounds like a religious massive psyop. @@truthhub7395
the buildup from first principles to the payoff via einstein’s relativity is phenomenal. one of my favorite videos by you so far.
ti is
Yeah this was amazing
Agreed
Haven't seen the video yet, just the introduction (0:55 now). And I must say: it sounds extremely fishy for now.
Don't get me wrong, I very much like Veritasium and I appreciate is work. His means to get the public interested in sciences, even the fishy ones, I see them as a good ideas.
Doesn't change the fact that suggesting Euclide already knew about "Hidden Universes" (modern science ones) is, at best, sketchy. I know a bit of history of sciences and Euclide most certainly is one of this genius among geniuses. A mind like that would probably (hard to prove) make discoveries ahead of its time in any era. But still. It's very confusing to suggest that, since it leads to a very inaccurate understanding of what was the state of science (philosophy) back then.
It's a great way to introduce the concept. But I don't think you should repeat this idea at lunch time, you'll propagate a misunderstanding or pass for a fool. Well, maybe not, I have to watch the rest of the video to now ;-)
@@huyxiun2085 Watch the video.. I don't think you should repeat this idea at lunch time, you'll propagate a misunderstanding or pass for a fool.
it hurts to imagine that many great minds and their works were lost to arson in burning the libraries at Alexandria , Nalanda , Takshashila and Baghdad...what have we lost?
And incarceration in the Vatican Library.
I find it so wild that mathematicians can do crazy things like predicting one supernova appearing 5 times spaced 1 year apart, but do things like spending 2000 years arguing about 1 sentence
Edit - How did this start a war. I just exagerated some stuff to make a point
one is not possible without the other
Physicists were the ones predicting the supernova appearing one year later.... the pragmatic mathematicians.
Mathematicians in general@itzhexen0
I apologize for my actions
same thing 🤷♂@@capitano3483
To call Euclid just "Father of Geometry" is an understatement. The major branches of math are built from Axioms, and Euclid pioneered that. He might as well be called the Father of Pure Mathematics itself.
Euclid had a great merit in consolidating in the Elements most of the mathematical knowledge of his time. But he is by no means the "father of Geometry". At least 2 centuries before him, other pioneers like Thales of Miletus and Pytagoras of Samos had already devised the logic-deductive Method, on whitch rests all of Mathematics.
@@gilbertogarbi4479 yes he is by father of geometry by some means, saying "by no means father of geometry" is incorrect
He collected all the known math knowledge at that time, he didn’t create all of it by himself
@@Mayank-tm2km ok, so not Father of Geometry. More like Midwife of Modern Geometry?
@@gilbertogarbi4479Greeks are famous in history for just stealing all the other countries best ideas of cultures, inventions, math and making it seem like research was just like inventing. Greek alchemy is just middle eastern alchemy etc they've never come up with anything only debated other cultures creations they stole from and improved the original idea. Pythagore was a cult leader who stole sumerian math and has gone down in history as it's inventor.
I took a geometry course in college where we started from Euclid and went on to derive essentially everything that you covered in this video to end with the shape and dimensionality of the universe using relativity. It was the best class that I ever took and this video was an amazing refresher on it.
Whoa sounds great, what was it called?
@@happysailor315Probably differential geometry
What was it called, and please can you share resources that might help
Bump
iI loved my geometry course in uni and we did almost the same up to spherical and hyberbolic geometry, but your ending on the dimensionality of the universe sounds brilliant
Did anyone else notice how Gauss’s gaze followed the camera at 11:47 , I thought I was tripping. Veritassium your editing is a masterpiece
Wow. I did not notice that. How fun! Thank you.
I am a physicist, and this is one of the best explanations of curvature of spacetime I have seen on youtube, starting from absolute basics! Thank you so much, and keep up the good work. 🙂
ok
How does anybody know that postulates are true ?
😂@@Steve-si8hx
@@Steve-si8hx we all just assume that they are true, and develop from them
@@Steve-si8hx empirical observation of reality
This video surpasses your usual Veritasium content in a unique way. The layered storytelling, which included extra details beyond just non-Euclidean geometry, enriched my experience. It felt like a 3D exploration rather than a linear journey, giving me a deeper and more nuanced understanding.
I think this is one of the best ways to explain a topic yet.
Good job!
Great observation. In the 2nd episode of Cosmos, Sagan opens with a recounting of a 12th century Japanese battle only to segue into a discussion of selection/evolution: there's a magical quality to that scene that I've rarely felt elsewhere. This has a similar feeling, and "layered" captures it perfectly.
ok
Yeah, you are absolutely right:)
I really love the butchering of Greek and Arabic names, the misuse of the Latin Roman spelling for Greeks and those fantasy images of some material, where we actually have real historic content available. Stock Photos ... it's just a blessing ... Also getting Εὐκλείδης Axioms ignored and the purpose of Postulates confused is rather embarrassing. Well ... he had ONE JOB to do. I guess nobody's perfect?:) (Talking about "Journalists" here ... better consult a historian next time)
Being able to observe and predict a phenomenon as large scale as light bending around an entire galaxy to make a cosmic lense is insane. What a time to be alive.
Can't really do anything practical with it like funnel energy and hack into the quantum mainframe of reality, but it's cool.
The act of observing such a phenomena is practical in itself no? It's not a theory that we could observe gravitational lensing, we have done it.
wrong channel ;)
@@irg008 I was about to say this myself
People out here measuring galaxies while I’m struggling in trigonometry….
I think this is my favourite Veritasium episode ever! Especially well written and engaging.
Concur.
This is I think the 3rd or 4th time having professor Alex on the channel and I’ve loved it everytime. He seems so enthusiastic with his explanation to the point where it’s infectious.
I find his argument about definitions ridiculous back then that language most likely lead to a specific understanding.. otherwise, why does everybody else agree and well mathematics as well. Seems Alex was the only one who didn't understand.
@@Cameron-ls3qtNo. At first, I too wasn’t buying it. However, I heard him out (and digested his whole argument), and I can now see it. It’s actually pretty brilliant. If you write a definition, the definition is made up of things that also could be defined, of which all are composed of even more things to define, and so on. It’s either a cyclic (circular logic, flawed) or never-ending (no useful definition) problem. Instead of establishing definitions, the professor suggests to establish relationships. As in, given this thing (regardless of how it could be defined), here’s how it relates to other things (regardless of how they could be defined). It all of a sudden makes this never-ending definition problem into a finite relationship problem, and it has much more rigor this way (as the postulates now only need to establish relationships, which then could be used to demonstrate other relationships, proving theorems). Yes, one could certainly understand Euclid’s definitions (and they don’t invalidate his results). However, his definitions are hand-wavey and non-rigorous… and most importantly (as the professor explains), unnecessary.
@@Cameron-ls3qt it is language
You just summed up my entire university foundations of geometry course in 30 minutes. I admire your ability to educate so concisely immensely.
My question, was the hardship worth it, (the long nights to prove one theorem problem, while miscalculating several times)??
zzz
So you are saying that your university course was only superficial and just taught you some history and only explained concepts, but didn`t teach you how to calculate the stuff?
@@maythesciencebewithyou "Foundations of Geometry" sounds like your typical survey course for students aiming to one day teach high school mathematics/geometry. So, ironically enough, there's likely little in the way of teaching them how to actually "do" geometry.
As a Mathematician that loves hyperbolic geometry, I'm grateful to you for making this video. I'm going to share it with all my students for sure!
Psst... Euclid is describing parallax. Postulate 5 is a really stretched out triangle.
Take a look at the game Hyperbolica. It's set in a world with hyperbolic geometry. It takes a bit of adjusting to go back to moving around the real world after playing it for a while. Appropriately, the first tag to show up on Steam is "surreal".
Just call them your nerds, it's three less letters to type.
@@rocketscience4516he’s a mathematician, who loves hyperbolic geometry, why do you expect him to care about the length of words
Lmao
@@BisexualPlagueDoctor Aw, someone lacked the perspicacity to realise it must have been said in jest. Think a bit before you type.
For someone who barely understands mathematics and wants to learn more, this is articulated very well. Good job 👍
Learn basic math and algebra.
I love how some things went unsolved for millennia and then multiple people have the same idea at the same time. This has happened over and over in the history of science and mathematics.
its cause they all get new info to work with. Some day some new proof may come out that allows everyone to figure something else out at once
Often this also happen when and where institutions have been set up to publicize (or at least preserve) those findings in some way.
It's because individual geniuses are utterly meaningless to the history of progress. Humanity has always had plenty of smart people, what matters is the opportunity. If one famous historical person didn't discover something, someone else would've, and for the same reason that person did: Not specific individual intelligence, but individual intelligence applied to the sum of human knowledge at that point in time.
These are just the ones that have been on record, or at least have surviving records.
Makes you wonder if there was something about the time period of the 19th century (more mathematical geniuses?), or if older versions of the idea are lost to time. Possibly during 2000 years countless mathematicians came up with non-Euclidean geometry but never published it because they feared ridicule.
This is one of the greatest stories of human history. Thank you for explaining it for a large audience.
It really is. On a different note, flat earth confirmed
/s
Seriously: flat universe confirmed
@@cereal-killer4455 how
ahaha normie
@@cereal-killer4455, isn't that the bizarrest thing - he claims the universe to be essentially flat after just describing the reason why mathematically any sphere can be seen as essentially flat when zoomed in enough!
It's funny how quick people can be to misunderstand things though, Gauss never said anything negative about Bolyai in his letter
Gauss never ceases to amaze me. There isn't a single math or science class I've taken where his name hasn't come up. Someday I'd love to spend some time learning about all of his greatest discoveries and trying to connect all of the dots of the contributions he's made.
he was a monster, what a gigachad.
The German author Daniel Kehlmann wrote the superb novel "Measuring the World" on C.F. Gauss' and Alexander von Humboldt's (yes, THAT Humboldt) lives.
It was an sensation, depicting two crude geniuses in a absolutely entertaining, readable and intelligent way. The moment you open the book, you'll read it in one go, accompanying both Gauss and von Humboldt getting old, and even more strange.
Gauss did not publish all his findings. He published only if he decided that he treated a subject in it's entirety. E.g. he did not publish his vast and deep findings in mathematical knot theory for he just wanted to complete some details, as we learned from his duaries.. Decades after Gauss' death, other mathematicians began to devolop the very same ideas, that Gauss already had knew.
Don't sleep on my boy Euler. Lots of things are named after the person who discovered them after Euler, otherwise almost everything would be named after Euler
He was on the 10 DM bank note in Germany. Now we have soulless windows on our Euro notes. What a pity.
eulor is big, but his yxy still haunts my dreams@@XxZeldaxXXxLinkxX
Not a mathematician but the undefined terms explanation at 18:05 was cool and helpful !
Hey Derek, you probably won't read this but I just wanted to say that I've been watching your videos casually for many years when you first started. I just need to say that your production quality and ability to keep audiences engaged has evolved so beautifully. I watched this 30min video and it felt like only 5 minutes had gone by... and I'm not even that interested in mathematics let alone history. All I'm trying to say is well done. Thank you for all your years of educational content and thank you for continuing to impart the same level of passion in every project. I hope you continue for many years to come.
12:29 12:34 12:36
Your
Well said Monsieur.
Your right , he didn't read it😂
HAVE ERIC WEINSTEIN AND GIVE US GEOMETRIC UNITY
This has to be one of the better animated veritasium videos ever. A pleasure to watch as usual
Everybody says that after every history-based Veritasium video, lol. Which is saying something.
28:35 It's so mindblowing to me that Euclid's work was mostly based on the 2D plane. Then as the Earth was proven to be spherical, the math became more complex and humans had to adopt these new models of geometry to keep up. But apparently on a large enough (i.e. universal) scale, it's all apparently a 2D plane still. It's as if Euclid's genius came from some arcane, otherworldly knowledge.
I don't get that part. The universe is flat? Like it is wider than it is tall or something? Cuz theres definitely an up and down dimension with stuff scattered in every direction.
So how is it flat?
@@zwenkwiel816 I'm not gonna pretend to understand the math behind it, but yes, the data presented in the video points to the universe being flat. This next part is only my understanding, but yeah I think that that's what it boils down to - the universe is so unfathomably wide and expansive that the "up" and "down" (z axis) are nowhere near significant enough compared to it's length and width (x and y axes).
@@Grimlo9icFlat: as in that it doesn’t curve around in dimensions higher than 3 and meet itself on some other end like a hyper sphere or some other hyper shape. If you keep traveling in our 3D universe, you won’t come back to the same point. In this universe, parallel lines really are parallel.
@@thegreatreverendxor at the very least they were in the early universe, does it still hold for closer distances?/ more recent times ?
@@zwenkwiel816imagine a cone expanding from a point into everything
I am a physics and maths enthusiast and a game developer myself, and I generally love the explanations you provide also the small little details in the video, like moving the eyes of Gauss when the explanation texts goes from left to right of his picture. I mean ofcourse its not necessary but knowing that you guys put in the efforts into even the minor little things in video production makes me respect your efforts infinitely.
Learning new and often very complicated things is always so joyful and easy with your videos and passion. Thanks Veritasium team!
If someone had told me this when I was in highschool (I was fascinated with astronomy as a kid, so maybe even earlier), my relationship with math would be completely different.
This is fascinating
That’s what I’m saying. Now I wish I cared for it because it would make life easier. But no they wanted to torture us instead of nurture.
@@firstnamelastname9215they didn't necessarily want to torture you, there aren't many teachers as good as this channel but there are a lot of honest people trying their best
The system wanted to torture them is the point. And in a system like the best Finland lot of those honest people would be unable to qualify to be a teacher which is harder to do then get in med school. @@alecmartin8543
What change do you believe it caused you?
@@alecmartin8543 I love math and had a good teacher, but there are a lot of teachers who hate/mistreat children or aren't good at their job. I've definitely had more teachers that made me dread going to school than good ones
I find the quality of the content in this channel to be in a completely different league than most of the things you find in RUclips. Kudos Derek
good
True
Apart from all the misleading startup ads
@@MysticPing what startup ads?
@@MysticPing
.... and much more ... THE BLIND LEADING THE BLIND!
This video concretized my understanding of non-euclidean geometery in ways books couldn't.
Amazing work, Dr. Derek!
I love these history of science videos. It makes math and science feel like a lively art form rather than something mechanical and dead.
real
Rightly said
I feel like I finally understand a bunch of stuff that I've always heard, in relation to math and physics, but was never able to fully grasp and connect together, for example what people meant exactly by the curvature of space time caused by gravity and such. This video's narrative is absurdly good and really helps tie it all together in a very comprehensible way.
Just wow... this channel never ceases to amaze me.
If you want more checkout the ScienceClic English RUclips channel. It's the best for visualizing the math.
Finally understood what physics channels meant when they say that "the universe is flat."
@@joerionis5902 Unless you draw REALLY big triangles.
I had a math teacher with Elements sitting on his desk. I have dyscalculia, numbers are extremely confusing (if not downright nightmarish) and math was always my worst subject. Straight A's with a D- in algebra.
However, glancing through that book a little bit every class period, I found that the THEORY of math fascinated me. Sadly, schools only cared on if you could find answers to questions, and they didn't give a damn on if you knew WHY math worked.
In college, after struggling for 3 years with "self paced math" meant for people with learning disabilities, my campus came up with an experimental "Algebra for Liberal Arts Majors" class, where we had the option of doing 30 math problems, creating art projects to illustrate the math theory, or writing essays on the theorems, how mathematicians came about discovering and proving them, or how this particular type of math applies to the real world.
THAT I could do with ease, and it was my very first A in a math class.
Numbers are still a mystery, something I just cannot sort out with my weird brain, but I love the history of math and what went into the geniuses who came up with these ideas.
check out "fractals" that's probably how your brain is trying to operate. like mine, in reality, not fictional numbers. this thousand year old stuff is cool, but new thinkers might benefit more from realizing 3d math exists but is just way too complicated for most to even fathom. i figured it out on my own but then learned somebody already did in the 70s, thank god, cuz i wasn't trying to write that book myself.
the way i understand it is every atom is 3 parts. and reality is base 3 number system. everything in 3s, based on that simple postulate. expanding out in all directions, continuously. interesting rabbit hole, but that's the real infinite realm.
base 10 makes sense on paper, and counting on our fingers, but that's not how god designed the universe.
I've never heard of a course like that!
@@Sorrowdusk It was brand new when I took it back in 2004, a test program for students who don't need advanced math in their given major, especially folks like me with a learning disability that nearly prevented me from getting a degree. It was humiliating during matriculation when my counselor exclaimed, "How can you be in the top 1% in English and Logic but the bottom 1% in Mathematics?"
Dyscalculia. That's how. It's because my brain cannot process numbers, so it compensated by using logic. (Also part of being autistic.) Yet the California education system refused to give me a pass on the math requirement, even though it had NOTHING to do with my major.
Struggling with numbers doesn't mean that I can't have a successful career; in fact, the way my brain works is THE IDEAL for my job.... it just means I have to hire someone else to do my taxes, because my brain can't process numbers in the right order.
If this sort of program didn't catch on at other colleges, that's a real shame. We need an education style that evolves with our growing understanding of neurodiversity.
I've begun to work with Umbrella US, a NPO trying to change this sort of thing and get society to realize that not all brains work in "typical" ways. There are talented people out there being held back because they can't pass a course designed for neurotypical students.
Look at all the scientists over the generations who struggled in school, because their brain danced with numbers but struggled with language, or danced to the music of etymology but fell flat with numbers. Imagine if they lived today, where they had to pass all these frivolous classes mandated by the federal government, but have nothing to due with their interests, or else their ideas and theories are disregarded due to not graduating from the "right school."
One day, hopefully, programs like what I took become the norm. Give students the option to show the teacher that they truly understand a subject, even if the way they do that is not neurotypical.
Me too i hated math growing up but now that i am learning it's history and creative applications, I am really starting to appreciate it more and more. I'd say it's just a beautiful subject taught in an ugly manner
Brother/sister; math is just about seeing coherences and expressing these coherences with symbols we call numbers. Art and music are ALSO about seeing coherences and expressing these, but NOT in numeral symbols but having the coherences expressed in form and colour; or in the case of music: sound. You too are a mathematician, you just use a different language to describe the coherences you see.
This is the greatest video you've ever put out. WELL DONE!
Leaving aside the educational aspect, the production value of this was incredible. Congratulations Veritasium team!
My goodness, man, I think that quite often but I have to say this is one of your best videos to date. The level of storytelling and the way you managed to tie ancient knowledge all the way to the very edge of our current understanding of the universe was absolutely mesmerizing. And poetic, even, because just as in culture, arts, music and so forth, the new doesn't necessarily destroys the old, but rather builds higher grounds over earlier foundations. Chapeau!
because God made it that way
I am sad for Bolyai as he thought his hero Guass would appreciate his work. Still, when Guass replied that he didn't do anything except repredicting his work Bolyai would have been crushed deeply. I definitely see Bolyai as a legend doing such great work at the age of 23 in just 5 years while Guass had spent nearly decades finding out about it.
"Appreciation can make someone's day, even change lives. So even if the work is small or the best it is incomplete without a 'Good Job'."
- A Wise Man.
Nice 👌
What's even sadder is HE DID APPRECIATE IT VERY MUCH AND PRAISED BOLYAI TO ANOTHER MATHEMATICIAN but Bolyai never knew it!
If I were Gauss, I'd tell Bolyai why I couldn't publish the previous works, and would invite him to come and work with me
He didn't really say that the work was unimpressive or bad, the sentence is taken out of contex, we don't really know if he followed it up with praising
Ah yes, Guass, my favourite character from Code Guass.
Me pretending to understand:
For real lol😂
Yup. Deleted my comment after reading others. Lol. What's the point
summary: drawing lines on a sphere or a bendy shape follows different rules than on a flat surface. that's literally it. the spacetime stuff is pointless because we're inside whatever shape the visible universe is, it's the fishbowl problem, you can't be confined to a fishbowl and know the architecture of the house across the street
@ thanks, helped
I used to hate math class in school, but the topics that Veritasium covers are so interesting I always find myself going down a mathematics rabbit hole after i watch one of his videos.
because this isn't math, it's a history lesson and a story. You just hate making an effort which is what math requires and listening to a story does not.
yeah and I bet this guy didn't understand the last 10mins of the video lol@@zwan1886
Learning is fun, but its different when its out of your own curiosity, rather than being forced upon you.
I know. I'm realizing that my brain is no less inclined towards understanding complicated maths but at least I enjoy TRYING to understand it now.
No he hates the dry boring way that math is normally taught. A very valid point. And he actually states the story gets him interested in doing that effort you describe. Your opinion is why so few like math. @@zwan1886
Thanks so much! Great content very carefully done EVERY time!
Nice donation
Euclid: Makes 5th postulate bit long
Other mathematicians: * thinks intensly for 2000 years*
😅👍
they took it personal, lmao.
the greeks already knew the earth was round, and used spherical geometry as well (Eudoxus of Cnidus, Autolycus of Pitane, Hipparchus, Menelaus of Alexandria, Theodosius of Bithynia, Ptolemy...) they wrote books and theorems on spherical geometry, since the time of Euclid in fact. It's not true that it took 2000 years to figure out these things...
@@MARK-gp9hbdid you even watch the video?
@@izzylevi. yes all of it
I love the historical backgrounds upon which you base many of your videos; this greatly sets the stage for the upcoming knowledge that is so expertly and well delivered. Thank you.
Hyperbolic geometry is more than just a giant cosmological thing. You know how the outside edges of some types of lettuce and kale go all crinkly, just like with the crochet model? The cells in them are effectively living on a hyperbolic plane, and studying the shapes and sizes of the cells there - how they fit together and exchange resources and such - requires some of this geometry.
The crinkly bits on kale and lettuce, remind me of fractals'....they are everywhere....gotta love em
Are you a biologist or something? Where would i look to learn more about this stuff?
Ok
No. Geometry requires real life things to give it value. Geometry is the explanation, not the reality.
Wait. What? 😮
Leonard Mlodinow's Euclid's Window is a good book for those who want to dive deep into the history of geometry. Thank you, Veritasium, for animating the history and concepts. I am a math teacher and have always wanted to incorporate historical development of mathematics into math curriculum. I want to dilute the goal of math education from only problem solving to explaining math concepts. I want to tell stories like Galois' duel, Zeno's paradox, Newton & Leibniz's letters/rivalry, the centuries of proving Fermat's theorem (and Langland's program), al-Khwarizmi's completing the square, the discovery of the formula for cubic & higher (and the affairs) ....etc. Veritasiim and 3blue1brown are my favorite youtubers who have great influence to our online math community. Now we find THOUSANDS of math explainers on youtube who actually teach better than professors and grade school teachers (myself included).
Start a channel. Please
I read it all 2 years ago lol
More power to you!
The kind of mind you must have in order to actually want to teach math to the kids..... I commend you, and appreciate your drive to teach difficult things to difficult peoples.
I read his Drunkard's Walk book, and it is spectacular! I will look into Euclids Window...😂
It's always nice to see Professor Kontorovich in a Veritasium video. You can see that he really loves what he is talking about.
bro how many videos do u comment on for me to keep seeing you
@@Joe-sg9ll You'd be happy to know that mathematics proved that mathematics has true statements that cannot be proven
All of you liking bot comments 😂😂😂
wot
wat
THANK YOU !!!!
I wish I had been exposed to your video 58 years ago. The WORK they have put into ALL of this is incredible. The puzzle pieceS you've given me are overwhelming. Awesome.
Thanks !
15:57. That is devastating. Imagine if Bolyai and Gauss actually collaborated.
If only my teachers in high school had had this ability to present math in this way.... I'm grateful to finally be able to understand/grasp these concepts.
Unfortunately making a RUclips video is completely different from teaching a class, and teaching is not scripted
Teaching is live vs having an editing team for a content creator on social media w/millions of views. First relies on a fraction of the income and does their own prep. Not saying this channel didn’t take effort to build just not a fair comparison.
I have had this conversation with my class. About 5% of students are riveted-- having in every word. The other 95% are zoned out.
you didnt learn anything from this video its just an illusion
His father not only understood his scientific work, he was so proud and sent it to his peers.. What's more wholesome than that..!
Taking the literal five seconds to check how his name is pronounced. Nails on the chalk board, I tell you.
Isnt that like every stereotypical Asian parent?
@@zwojack7285 When Farakas cautioned his son Jonas Bolyai with a father's concern that he should come to nothing as he himself failed there being a teacher in the field. But when he later realized his son's originality and brilliance he accepted his mistake, when 1) he made his son's work as an addendum to his own and 2) he sent it to his old friend Gauss. So Farakas did the best thing and was not responsible for what happened next, viz. Bolyai's frustration due to Gauss's fear of "Bootier".
@@zwojack7285 The were Hungarians not asian....
@@rockjanohungarians are steppe people anyway
Vertasium just explained the craziest thing in the simplest way possible, props to him i love this channel
How terribly tragic it is that one lives, studies and discovers the incredible and never knew the greatness of their accomplishment in life.
How incredibly wonderful to live one’s life and celebrate each moment.
Likely he lived the exact life he preferred and would spit on your pity.
Are you talking about Bolyai?
I think we should not have that awareness.. u just keep doing it like animals procreate
Why tragic
@@-astrangerontheinternet6687might be true for him, definitily isn’t for others. People have been hanged or imprisonned for stuff they discovered. Or people like Kafka who has been depressed his whole life, thinking it amounted to nothing only to be successful after his death. It is tragic
The amount of work Veritasium puts in his videos is amazing
Literally doesn't know how to pronounce the MAIN guy's name. Did a 30 minute video and didn't bother to press play on Wikipedia next to the name.
he definitly has a production team working on the videos with him, but that doesnt take away from the passion he puts into explaining the topics he covers
He's good but he's been wrong on some things
@@kevinmahaley4916maybe because he's human?
@@kevinmahaley4916 wish I knew what being wrong was like, luckily I'm infallible
I honestly believe that learning to sew could have given insight for those mathematicians that spent 2000 years trying to understand the 5th postulate. All fabrics are essentially planes, but our body isn't and, depending on culture and time, it needs to closely follow our body's format - that is definitively non-euclidian.
You are my new hero for using sewing to describe math ❤
Thsi is why it's so important to make men way more feminine, toxic masculinity has stunted those great men of the past
@@noticing33 This has nothing to do with the comment. Maybe concern troll under a different bridge?
how dare you? @@Qay
You should do a video on the “flatness” of the universe to clear up misconceptions about what flat means in this context.
This concept is what confounded me the greatest. We know the universe must have thickness so it can't be a plane, much like a tabletop, which is flat but you can still measure its thickness. So how "flat" is the universe? Is it a sheet of paper or a tabletop or ...?
@@LeeNotSa the universe is not “flat” in the sense that it can have “thickness,” it is flat in that, if you move in one direction forever, you will move further and further from your starting point and never circle back around to your starting point, which is exactly what would happen on a spherical planet. Another way to think of it is: On Earth, you and another person start on two different locations on earth and head north. No matter where they start, they will always end up at the true North Pole, in the exact same spot. In space, that doesn’t happen, instead they just head straight in the same direction for eternity, like two parallel lines never crossing paths.
@@AaronSkone OK, but wouldn't the same thing happen if the universe were hyperbolic? Wouldn't a straight line still cause you to never return to your starting position?
@@LeeNotSa yes, however the difference is that in a hyperbolic universe, the parallel lines would grow infinitely further apart. There’s theories for either or and we’re not really sure! The universe is so massive that even measuring the small section of space-time we occupy would be inadequate (similar to someone looking at the open water and saying “looks flat to me”).
I know, I know... Hungarian is a pretty difficult language, but if you just tap listen in the Google translator, you will be amazed, how big the difference pronouncing Bolyai János in English and in Hungarian.
As a proud Hungarian, I thank you for this video!
Yes, it sounds like bow-yah-y yahn-noz (in Hungarian, like in East Asian languages, family name is said first).
The most impressive of all is how far ahead Euclid was that it took mathematicians thousands of years and forced them to invent a whole new field of mathematics and non-Euclidian geometry.
"The consequences of the fifth postulate are left as an exercise for the reader"
the entire math community: oh for fu-
😂
This is one of the best science/math videos - informative, well-organized, and produced - I've ever seen on RUclips. Thanks!
And sometimes not true at all
@@realdragon then in your opinion which one is?
@@devshankarnair6344 I don't watch that much pop science channels, I know Dr. Becky is astrophysicists delivering news on astrophysics. From math I know few, 3 blue 1 brown, mathologer and flammable maths
This is what videos on RUclips should look like but which, for the greater most part, they do not. Much appreciated.
Hi Derek!
I send you greetings from Göttingen. Right now, while I'm watching this, I am sitting at the Gauss Tower in the cities forest east of Göttingen and I am deeply touched by the emotional gravitas and the history behind the place and it's meaning for human society in conection with the 2000 years of history of the topic of your video. This is truly an intense moment for me it will probably stay in my mind for many, many years to come. Thank you very much ❤
As a Geismaraner I can see the tower every day but as far as I can remember the last time I visited the tower was over 15 years ago 😅
As soon as he started to talk about Gauss and Göttingen, I thought about going to the Gaussturm to admire the stars and get high on my curiosity about this universe we live in :)
Göttingers unite!!🚀
A new place to add to my bucket list! Enjoy your contemplations ☮️
ok
Your passion for what you do is contagious. It's evident that you genuinely love creating content, and that enthusiasm translates into an enjoyable viewing experience for your audience. Keep that passion alive!
Of course all youtoobers love creating content because of that sweet sweet ad revenue and sponsorships 😂
F
向导 不 佐 奥兹
Xiàngdǎo bù zuǒ ào zī
Oh well, Science GOES Hollywood !!!
@@tomaccino Go generalize massive numbers of people through your cynicism elsewhere
Thanks for the video! I love reviewing and scrutinizing the foundations of math. It is very exciting stuff! Is their any book like Euclid's for today's maths? Or is there any book that gives an exhaustive overview list of all the branches, fields, subfields, sub-subfields, sub-sub-subfields, and so on in maths?
Sword fights, geniuses, spurned admirations, secrets of the universe, and arguments about parallel lines. Only in Veritasium video could it coellese into something so crystal clear. It's shameful other educators leave out the history and context. It dymisyifies the subject and let's the mind feel safe to play with the ideas. It's brilliant you're teaching this way.
As usual, a wonderfully interesting and informative video!
I absolutely love how the story evolved from a simple, dry, millennia-old mathematics axiom we learn in high school, to an almost incomprehensible explanation of the structure of the entire universe.
ok
What is the difference between an axiom and a postulate
@@sumathipitchaimani same thing, different words
@@sumathipitchaimani actually, there is no difference between an axiom and a postulate in modern mathematics but euclid differentiated between them as such: Postulates were specific to geometry but axioms were general mathematical statements holding for all forms of maths
21:17 The man is falling from a skyscraper.
Everyone: "Call an ambulance!".
Einstein: *Is joyful*💀
Of course I know is just for the animation.
Mind continually blown. Thank you Dr. Muller (and cohorts) for your efforts to make this extraordinary topic accessible to aspiring minds like this one.
Fantastic video. Im shocked that i actually understood that. It helped that ive been watching videos on similar topics, but this one really made everything click for me.
It just blows my mind how everything has adds from the past body of work of mathematicians to the current body of work in different fields. During academics we just know mathematics is in the core of everything but this channel just initiates and finishes the stories we never knew they needed to be told. Thanks @Veritasium
How is this video available for free? the production quality, the storytelling and the animations are all perfect. Veritasium is truly levelling up every video.
Thank advertising
He’s a multimillionaire thanks to his patrons, advertising and YT views. That’s how it’s free (because it was also released earlier on Patreon)
No
He got the most valuable thing from you, time. Nothing is free
@@JuanWonOnewell, we got educated in return. so i think we got the better part of the deal ;)
Far out ! This blew my mind away and Math is not even my strongest suit.
So compelling, easy to understand, seamless narration and nicely presented. Thank you for this .
This is my third video I’ve watched from this channel (yes I subscribed) and it’s masterclass. The guy who had to cheat to pass math because it just doesn’t sink in spent 30 mins learning about geometry and parallel lines and all these famous math dudes. I mean… your videos are amazing. Just wanted to say that it’s appreciated.
This is insanely good. Explanations of the fundamentals of math, the interesting histories of the people behind them, what they teach us about the universe, all with really high production values. I simply love this video.
So many times I wished I paid more attention to math. It was difficult in high school. My cousin spent quite a few hours teaching me algebra. And I hated it until I started making a little progress. With a little more time it felt like a dam broke and finally, everything was making sense. Math is so beautiful. It's like a language that machines understand and humans who speak different languages do too. And if you feel that it's not your thing just remember that you just need a little more time. Of course, there are people who just get it, and most of us will never reach that level. How Newton came up with Calculus at 27 years of age is beyond me. Recently I watched a documentary about how Cruise Ships are made and operated. Some parts are so precise they can only be made in one country and in one special place that makes those parts. While watching it it occurred to me that there is someone who knows everything about this ship top to bottom and it blew my mind. Of course, some are more specific, like food preparation, doctors, security personnel, or how to find staff that is fluent in more than one language. It's almost like a small country on water. Amazing!
Could you please share the documentary? 🤔
Isaac Newyon was a prodigy. He also was born into nobikity I think.
It wasnt uncommon for peoppe to achieve landmarks before the age of thirty back then.
Also the reason why math is difficult is because the way schools teach it is impractical.
He was actually 24 when he invented Calculus. However, there's also proof that Leibniz made his own attributions to Calculus at the same time
Unless you're an unusual prodigy in it, I think you need at least one good math teacher to get into it at least to the level of formal logic and algebra, which sets everything else up for you. The first year I went to public school, I was lucky to actually have a good math teacher, and it really set me up for life as far as logic and math go.
Amazing video Derek. Sometimes you go too deep for my pea-size brain when you do maths or physics videos, but this time you really nailed it. Bravo and thank you.
Man! I truly believe that you are doing more for Physics and Science in general than most published author. Kudos!! Never stop.
Glad that people now can know more about Bólyai. His name is pronounced (sg like) bow-ya-ee, with the stress on the first syllable, not bully-eye, though. Awesome video!
16:00 The amount of human suffering that is born of misunderstanding, or assumptions that are in error is astonishing.
ambiguities are like microbes, the pathogenic ones steal the attention...
I believe they’ve all made a few.
As an EE and ham radio enthusiast, the Poincaré disk looked very familiar -- this transformation from 2D euclidian space to a finite-sized disk is exactly what we do to visualize complex impedances more easily. It's called a Smith diagram, it's an invaluable tool, and using it feels like doing black magic.
For anyone who came from TikTok, video starts at 6:42
I read this EXACTLY at 6:41 😂
thanks!
Derek, this was a fun journey. Thank you for taking us on this journey. Brilliantly produced. I was a pilot and flight instructor, now I am a high school teacher; from one educator to another, I would like to honor you with a compliment on how amazing of an educator you are. You are a phenomenal teacher. I consider myself a competent instructor and intelligent person dedicated to being a lifelong student, but it is my opinion that you are in a league of your own. I think educator is one role you can confidently say you are a master. Master educator, check. Professors could learn from you.
I've always had some kind of mental block when it comes to taking in mathematics, like a minor learning disability, but this video was made in a way where I could follow and understand what was being explained. Thank you for that. 😊
That's the magic of a professional science communicator
The brilliance of the content of this channel is well known. . But the efforts they put into visuals is very underrated. . 12:11 Observe the eyes of Carl F Gauss. . .when the side of the quote changes. . . Excellent attentions to detail man. . . you probably wont read this but Derik you have mastered the art of making Math interesting to all. . Keep up the good work. . .❤
That was one of the best explainations I have heard & I want to thank you for the time & effort put into this video!!
Brilliant work this video. There is no way I could have understood these concepts from a text book. This approach opens up access to even to relativity and quantum physics imho. Thanks to Veritasium I have some hope of comprehending even modern terminologies without completely understanding the math.
Related note: if you’re interested in seeing more of and playing around with hyperbolic (and possibly others) geometry, I highly recommend the videogame HyperRogue.
It’s a top-down (with poincare projection by default) roguelike, but also features many tools for building projections, tilings and pictures. It’s unique, offers an interesting point of view on a lot of these things and plays around with them in many different ways.
the game Hyperbolica brings it even into 3D/VR
@@silviodc1309 So does Hyperrogue!
@@silviodc1309 Side note: If you have motion sickness, that game will quite literally throw you into a coma.
I love maths and I’ve always been intrigued by hyperbolic geometry, not to such a degree as to study it formally, but to look into it. This video, finally explained to me the motivation for hyperbolic, and spherical, geometry. Thanks for the insight. At some point I will certainly study non-Euclidean geometry formally.
i prefer calmly delivered and measured geometry.
18:20 I would argue that the word defines the words in the definitions. The postulate tell us what a line is so we can infer what a part is.
I wish I could show this video to my younger self. This presentation makes so much sense, as someone who struggled with math throughout high school up until college. great video as always!
I remember about two years after leaving college I watched vsauces complete proof of all internal angles in a triangle adding to 180, I was struck by the fact that I knew every component part of it, the axioms, their reprocussions, the evidence, but no one ever explained to me how it fit together dispite being so beautifully simple
It was so telling of what school had been for
So what I've gathered from this video is that flat earthers just aren't thinking large enough. The earth may not be flat the universe is
Wait flat universe? We are in Petri dish? :D
Not going to lie, this video has me on the edge. One thing I believe can still remain true.... Just because what we see above our heads my have a certain shape doesn't mean that the ground below us has to have the same.
No no no, the flat earthers are right. The earth IS flat, it just exists as a large mass in a spherical universe
Problem is these guys deny the existence of the universe too.
@@WTfire10 Who are "these guys"?
this video is so informative, fun to watch, and comprehensive. congrats to everyone who worked on it
This honestly might be my favorite video ever. Reignited my passion for learning
This is amazing. The reasoning line from euclid's basic geometry principles to the general relativity theory of einstein is amazing 🤓. I never thought of these principles these way. Also the way you explained non euclidean geometry opened my eyes. Hands down one of my favourite videos ever ❤
@@RockBrentwood ok bro nobody is reading that unless you're a math major
@@bullshitdepartment I'm not a math major and I found it an interesting read
The way you make the audience connect with deep mathematical concepts as if they were intuitive and tangible speaks volumes to your skill as a communicator.
Doing math viscerally hurts me, lol, but understanding the meaning of the math and how it applies to the nature of reality is endlessly fascinating.
Your ability to translate the deep lore into a wondrous understanding is invaluable to me.
I truly enjoy watching your videos about math, geometry in particular.
As a student in Belgium, I excelled in maths but was never motivated by the school or parents to pursue a degree in it. I switched from high maths to computer science before turning 17.
Currently I work as an architect drawing in 3D and automating the software (Revit) with custom packages and dynamo scripts to assist collegues.
I feel like ive wasted my potential in maths, especially since I was teaching my class at 13 in spherical geometry because the teacher himself didnt get his point across clearly.
Seeing someonelike you, makes me realize what I wished I pursuit,even though I understand the chance I couldve gotten as far is slim.
Keep making these videos please, thank you so much.
I resonate with you, I was so interested in maths but somewhere in class 11th I lost interest, it was covid Lockdown, I didn't have access to good teachers, I tried but I hated algebra, only until 12th when I found a youtube channel to learn calculus!!
I eventually switched to engineering in computer science, now while learning the neural networks and AI, while watching veritasium videos, my love for maths is returning 🙂
It's never too late, friend! Think about how much you could get done in 20 years, and how old you'll be in 20 years.
This video was very refreshing to view. For many years I have ran into this subject. My initial 'solution' to the parallel lines was to use an extra dimension 'z'. This allowed for lines to be parallel at the same x,y coordinates, but not being the same lines, since they were apart in dimension z.
The approach with spherical and heliospherical is new to my imagination and very fulfilling. Thank you 🙂
Henk Pietersma, Emmeloord, Holland