How One Line in the Oldest Math Text Hinted at Hidden Universes 

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Discover strange new universes that turn up at the core of Einstein’s General Relativity. Head to brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
If you’re looking for a molecular modeling kit, try Snatoms - a kit I invented where the atoms snap together magnetically - ve42.co/SnatomsV
A massive thank you to Prof. Alex Kontorovich for all his help with this video.
A huge thank you to Prof. Geraint Lewis and Dr. Ashmeet Singh for helping us understand the applications of Non-Euclidean geometry in astronomy/cosmology.
Lastly, a big thank you to Dr. Henry Segerman and Dr. Rémi Coulon for helping us visualize what it’s like to be inside hyperbolic space and helping us understand hyperbolic geometry.
Euclid via Science Museum Group - ve42.co/Euclid
Geodesy survey via ams - ve42.co/Geodesy
John Wheeler via NAS Online - ve42.co/Wheeler
Dunham, W. (1991). Journey through Genius: Great Theorems of Mathematics. John Wiley & Sons.
Bonola, R. (1955). Non-Euclidean geometry: A critical and historical study of its development. Courier Corporation.
Library of Congress. (n.d.). The Library of Congress. - ve42.co/LibofCongress
Euclid’s Elements, Wikipedia - ve42.co/Elements
The History of Non-Euclidean Geometry, Extra History via TRvid - ve42.co/ExtraHistory
We (could) live on a 4D Pringle - Physics for the Birds via TRvid - ve42.co/4DPringle
Parallel Postulate, Wikipedia - ve42.co/Parallel
Prékopa, A., & Molnár, E. (Eds.). (2006). Non-euclidean geometries: János Bolyai memorial volume (Vol. 581). Springer Science & Business Media.
St Andrews, University of. (n.d.). Bolyai. MacTutor History of Mathematics. - ve42.co/Bolyai
Bolyai, J. (1896). The Science Absolute of Space.. (Vol. 3). The Neomon.
Gauss, Wikipedia - ve42.co/Gauss
Singh, U. (2022). Gauss-Bolyai-Lobachevsky: The dawn of non-euclidean geometry. Medium. - ve42.co/CPNonEuclidean
Landvermessung, D. Z. (1929). Abhandlungen ueber Gauss' wissenschaftliche Taetigkeit auf den Gebieten der Geodaesie, Physik und Astronomie Bd. 11, Abt. - ve42.co/Landvermessung
Nikolai Lobachevsky, Wikipedia - ve42.co/Lobachevsky
Lobachevskiĭ, N. I. (1891). Geometrical researches on the theory of parallels. University of Texas.
A Problem with the Parallel Postulate, Numberphile via TRvid - ve42.co/NumberphileParallel
Riemann, B. (2016). On the hypotheses which lie at the bases of geometry. Birkhäuser. - ve42.co/Riemann
Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891-921. - ve42.co/Einstein1905
ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. - ve42.co/Einstein1905
Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background. - ve42.co/NANOGrav
Secrets of the Cosmic Microwave Background, PBS Spacetime via TRvid - ve42.co/PBSCMB
Wood, C. (2020). How Ancient Light Reveals the Universe's Contents. Quanta Magazine. - ve42.co/AncientLight
Collaboration (2014). Planck 2013 results. XVI. Cosmological parameters. A&A, 571, A16. - ve42.co/Planck2013
WMAP Science Team, NASA. (2014). Matter in the Universe. WMAP, NASA. - ve42.co/WMAP2014
What Is The Shape of Space, minutephysics via TRvid - ve42.co/SpaceShape
Shape of the universe, Wikipedia - ve42.co/UniverseShape
Crocheting Hyperbolic Planes: Daina Taimina by Ted, via TRvid - ve42.co/Hyperbolic
Hyperbolic Crochet model - ve42.co/Crochet
Special thanks to our Patreon supporters:
Adam Foreman, Amadeo Bee, Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, Jesse Brandsoy, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Mario Bottion, Max Maladino, Meekay, meg noah, Michael Krugman, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures
Directed by Casper Mebius
Written by Casper Mebius, Petr Lebedev, Emily Zhang, Derek Muller, and Alex Kontorovich
Edited by Jack Saxon
Animated by Fabio Albertelli, Ivy Tello, and Mike Radjabov
Illustrations by Jakub Misiek and Celia Bode
Filmed by Derek Muller
Produced by Casper Mebius, Derek Muller, and Han Evans
Additional video/photos supplied by Getty Images, Pond5, and by courtesy of: NASA, NASA's Goddard Space Flight Center, NASA Goddard Flight Lab/ CI Lab, NASA’s WMAP science teams, ESO, and ESA/Hubble.
Music from Epidemic Sound
Thumbnail by Ren Hurley



20 Eki 2023




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@birindersingh4146 Aylar önce
Imagine the greatness of the man who wrote 1 little paragraph and made mathematicians mad for 2000 years
@Speedy9079 19 gün önce
Fr bros a menace
@sarc143 13 gün önce
Haters pocket watching bro smh
@m1k3vroom 11 gün önce
The level of genius involved is unparalleled.
@dwdelve 11 gün önce
Greeks have been doing that for a long time
@topherthe11th23 11 gün önce
@@dwdelve And so have many non-Greeks. There's nothing special about Greeks. There was something special about Euclid's achievement, and many special achievements of OTHER Greeks too, but that doesn't reflect glory on Greeks who DID NOT accomplish anything special with their lives. "Greekness" isn't some special trait that any Greek person should be allowed to feel good about.
@tomvesely4008 2 aylar önce
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.
@alecmartin8543 15 gün önce
​@@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
@milferdjones2573 15 gün önce
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
@LumaSloth 13 gün önce
What change do you believe it caused you?
@d_lta 12 gün önce
@@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
@vladbobe26 3 aylar önce
Leaving aside the educational aspect, the production value of this was incredible. Congratulations Veritasium team!
@kens1120 3 aylar önce
This video is so beautiful. All of your videos, spanning such a wide variety of topics, are wonderful in their own way, but this one is a special masterpiece to me. It starts so innocently, sets the scene perfectly, teaches about beatiful math fundamentals, evokes emotion, especially with the compelling story about János Bolyai, his father, and Gauß. Abstract theories are presented in a way in which the intuition behind them can be grasped easily. Each part of the video flows into the next one such that it just seems to make sense. Every step can be followed effortlessly, even though you are taking us on a magical journey. When watching, you suddenly wonder how you ended up here, with a new intuitional understanding and passion for Einstein's space-time fabric. The way past topics of the video are picked up again, to question the previous understanding or to explain a new concept with something we heard about just prior in a different context, connects all elements seamlessly into a cohesive whole. Thus, the lines between the different fields blur and the span of topics gets condensed in a way to be easily absorbed. All of your videos possess these qualities, maybe this one just hit the sweet spot for me, regarding prior knowledge, interest, and being intriguing in a way I want to learn more. You and your team once again crafted something truly inspriational - thank you.
@Kire1120 Aylar önce
This may be my favorite Veritasium video. I took non euclidean geometry in college and the whole course was like a slow trip through this video. I will share it with my family
Learning new and often very complicated things is always so joyful and easy with your videos and passion. Thanks Veritasium team!
@Gene-ns2wk 4 aylar önce
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
@Milana2006. 4 aylar önce
@mr.fhizzy 4 aylar önce
@PrabhasPatil 4 aylar önce
@@TheOneAndOnlyCumGuzzler yes 💯
@JohnDoe-qz1ql 4 aylar önce
As he said, it's exerted great influence, so
@shawnbibby2934 Aylar önce
Thinking the Universe is flat seems a lot like Gauss mapping the triangles of the three mountains, where the area of the information taken was too small. What we observe of the universe appears to also be too small. We also have the notion that flat, parabolic and sphere all exist simultaneously, which they will, so they are all true depending upon perspective. It is a fun game. Great video as always!
@orngjce223 23 gün önce
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.
@user-jd7qq2oc6p 2 aylar önce
MUCH easier to understand than other attempts, and helped greatly to understand the basic topics, while providing an amazing, and moving, historical perspective, that itself also demonstrates (rather poignantly) how similar discoveries can come about at similar times, often (but not always obviously) based on earlier work, while not at all discounting sheer genius. Just brilliant!
@suryamanibarad9750 2 aylar önce
The amount of research that Veritasium does into these topics is really appreciating. We are extremely grateful to have such a channel in youtube. Keep going Derek!!!
@roddlez Aylar önce
Brilliant coverage of Euclidean and non-Euclidean geometries, from the stories to the presentation and explanations and how they've shaped our modern understanding. Easily one of the best Veritasium pieces in recent memory.
@TimeBucks 4 aylar önce
Gauss never ceases to amaze me.
@walifortune-hc4fe 4 aylar önce
Wow lovely
@user-nj3dp5sj9n 4 aylar önce
Nice one
@IsmailMansir-qq4hl 4 aylar önce
@dsoli807 4 aylar önce
Sweet 🎉🎉🎉
@hdliubkrong6038 4 aylar önce
@curlyfries2956 13 gün önce
The fact that Euclid sorta instinctively knew this is incredible. Reminds me of how da Vinci instinctively knew that his designs for a perpetual motion machine wouldn’t work and the reasons as to why long before Newtonian laws or thermodynamics
@Pushups_press_play 3 aylar önce
Brother I was barely able to follow this, my mind is absolutely bent. But godamn I am glad we have people like you sharing your knowledge and furthering humanity's understanding of our relationship to this beautiful world and universe we live in
@almendratlilkouatl 5 gün önce
hav u converted to flat-universism already?
@_jp_0966 Aylar önce
this video is so informative, fun to watch, and comprehensive. congrats to everyone who worked on it
@jacobjames304 26 gün önce
I can't explain how grateful I am for your math videos. Always watch them multiple times even when they're extremely long. Your explanations are cleaver, clear and most importantly, interesting to watch and listen. Nobody does it better than you man. Hearing the stories of the math greats we all know from our math courses, is a different level education, that is never learnt in the university. Keep up the good work and make as many math videos as you can 😂
@TheDoc73 2 aylar önce
Brilliant video as always. Although, I swear there's a pattern that emerges when watching several over a short span. It feels like brief, guest cameos are used to bring up desired points in a pseudo-organic staging, rather than to enrich the conversation in a meaningful way. Take this video. I find myself constantly thinking back to the brief exchange about the 5th postulate and then the definitions in Euclid's geometry. While I appreciate his agreement with the 5th postulate, there was an important conversation that _should_ have been indulged. This being the fact that the purpose of the 5th postulate is to define his geometry as expressly flat. It means that he considered the existence of non-flat geometry, and implicitly stated that his geometry _only_ functions under the assumption that all planes are flat. But, honestly, this omitted conversation is equal in crime to the assertion that the definitions are superfluous or even harmful. They are not "infinitely recursive". They follow in logical order using language that is both clear and requiring of no outside reference beyond any of the previous definitions. From a linguistic standpoint, his definitions are absolutely brilliant and form just as important a foundation as the postulates. "A point is that which has no part." "A line is a breadthless length." These are such CLEAR and concise statements that make immediately obvious what these terms will mean going forward, such that there is no room for questions in the future. A point has no part? What does HE mean when he says what does that mean? What question could there possibly be? It means that a point is infinitely small, such that it can never be subdivided into anything less than its whole. A line is a breadthless length is equally clear, as it says even more precisely the exact nature of a line. _Especially_ when combined with the first definition. I have the privilege of being able to use language and terms that do not have to stand on their own without outside definition, unlike Euclid, so let's just say it once and for all. What he so brilliantly stated was that a point has zero dimensions, and a line has a single dimension. Without using such terminology, he was able to convey exactly what was necessary to understand everything which would follow without the need to ask for outside reference. It's a masterwork which must have taken ages to pin down so precisely, so that as he compiled this resource for all mathematicians, it could perform its function devoid of the need for any outside help.
@anneo8393 28 gün önce
I thought the exact same thing. When he said that the postulates should define the terms all I could think was, isn't that achieving the exact same goal but from a different perspective?
@jrow96 5 gün önce
@vaibhav3955 4 aylar önce
Veritasium's videos are generally great but the math ones are on another level
@feynman_QED 4 aylar önce
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.
@n1ppe 4 aylar önce
​​​@@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
@feynman_QED 4 aylar önce
​@@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.
@jonathantebo5459 4 aylar önce
That's why there's a pause button. I mean this to be helpful, not condescending.@@feynman_QED
@hattix6713 4 aylar önce
Derek has good sources, and actually listens to them!
@manticorenettleable 2 aylar önce
Amazing! Just had one moment where I needed to go do research: Why is the distance (r²) problematic in the gravity equation from the perspective of special relativity? The rabbit hole this took me down greatly improved my understanding of relativity - I didn't realise that was the key point between special and general relativity. Using a combination of ChatGPT and physics sites gave a good grounding of this issue. Thanks for this video, it's a real gem.
Your videos have ignited a passion for science and the mysteries of the universe within me. Thank you for being such an incredible source of inspiration.
@johngellare3507 2 aylar önce
Videos like these make me love our universe even more. There's so much to learn about!
I remember being stumped by postulate 5 when I was young. It is so simple and intuitive, that proving or disproving it got stupidly difficult. Was bad at math too but loved to understand concepts.
Original term is Axiom. Postulate is Latin word created by Romans centuries later.
@topherthe11th23 11 gün önce
16:35 - I.e., it might have been said, "On both a Euclidean plane and on a sphere, a straight line has no end". That simple statement is no less true of an endless line on a Euclidean plane and an endless Great Circle on a sphere.
@killmajaro1 4 aylar önce
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.
@tinobemellow 3 aylar önce
Can't really do anything practical with it like funnel energy and hack into the quantum mainframe of reality, but it's cool.
@yashsarda2263 3 aylar önce
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.
@irg008 3 aylar önce
wrong channel ;)
@TheEpicProOfMinecraf 3 aylar önce
​@@irg008 I was about to say this myself
@vattghern7592 3 aylar önce
People out here measuring galaxies while I’m struggling in trigonometry….
@raidtheferry 2 aylar önce
Easily your best video yet imo! Love this one
@JBNemeth 15 gün önce
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.
@hatersgotohell627 12 gün önce
THIS IS FASCINATING. Why didnt we learn these concepts in high school so more people would be interested.
@markobolo4465 Gün önce
i think we did learn euclid geometry
@Cranndaddy 2 aylar önce
echoing a lot of what people have said on here. I’m a biochemist so my lack of formal physics knowledge and study has been an insecurity of mine. I love space, I love the nature of time and reality. I can generally keep up with PBS space time now and get a lot of happiness from the deeper concepts, but this. This just walked me through to baby steps I never knew I needed to go through. This should be shown to every human being in the world, amazing video
@hariomtatsat8677 12 gün önce
A great talk. I am overwhelmed. Congratulations for bringing about such a wonderful talk.
@swarry3508 4 aylar önce
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
@atinkapruwan6780 4 aylar önce
fascinating indeed
@matroxman11 4 aylar önce
I’m convinced that math is the key to the secrets of the universe
@eddielally2045 4 aylar önce
​@@matroxman11 bruhhhhhh obviously
@3lilougps 4 aylar önce
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. ""
@daemongamingtv 4 aylar önce
(Comment deleted due to comment crybabies; enjoy the contextless whining below!)
@JamesToupin 3 aylar önce
An engrossing documentary with excellent presentation. Thank you.
@halfwayvinny9786 26 gün önce
As someone who struggles to learn about science and doesnt have the capabilities/skill to make it in a standard learning environment such as a standardly structured college course, even though im absolutely obssessed with it, i deeply value your contribution to teaching through your videos. Your sponsor brilliant has made it possible for me to continue to learn outside of a school environment which has done wonders for my brain and curiosity. I wish i could pick your brain on the day to day and passively learn as an 'apprentice' of sorts, but i know thats not a realistic wish as i am just a stranger in this online world, but thank you soooo much veritasium, it's people like you that feed my immense curiosity for the known and unknown. Watching this video made me giddy with excitement lol.
@jan-rw2qx Aylar önce
This Video was amazing, wasn't expecting to enjoy it that much, thank you :)
I’m only a minute into this video, and already the production feels like old school discovery or history channel and I’m here for it
@tbone9948 8 gün önce
youir channel is my new favorite. Great info, quality and delivery. Im a dumb person but your explanation of Brilliant convinced me to give it a try. I always wanted to be good at math. I'm hoping Brilliant will help. Thanks and keep up the good work.
@adityavardhanjain 4 aylar önce
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
@dinogt8477 4 aylar önce
@ryugo7713 4 aylar önce
@@dinogt8477do you need a tampon?
@aniket385 4 aylar önce
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.
@cherniaktamir612 4 aylar önce
And 4. An inspiring story about not listening to seniors about not pursuing your intuition, thinking from first principles
@dylanwolf 28 gün önce
I just love this channel. Thank you so much for loading your videos.
@vahid5355 3 aylar önce
Interesting, educational, enjoyable, and true! Thank you Derek!
@funkyfox7996 2 aylar önce
it's wild to think that looking up at the stars, there are potentially fewer than i see. not only because those distant stars could be dead by the time its light reaches my eyes, but also because some of them could be illusory copies.
@jaffasoft8976 Aylar önce
Entire Galaxies gravitationally lensing supernovas and time delays of a repeat for a year was mind blowing to me. What causes such long distances delays with light travelling so fast. How mathematicians work this out leaves me in complete awe!!
@cliffperry Aylar önce
I really appreciate all your video explanations even tho as a layman, i barely understand a hundredth. More than even beginning to grasp the concepts, my mind continually expands and for this I’m grateful. And your voice, clarity and enthusiasm make it easy to listen to.
@mosgon 3 aylar önce
As an astrophysics major, I love how a video on ancient math turns into a cosmology lesson
@TNT-km2eg 3 aylar önce
Mayor , no less
@Tomico. 3 aylar önce
That's how it all started.
@no36963 3 aylar önce
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
@truthhub7395 3 aylar önce
Checkout The Greatest Lie on Earth by Edward Hendrie. I can promise you are being fed a bunch of garbage
@Jakekelley-hs8bk 3 aylar önce
Sounds like a religious massive psyop. @@truthhub7395
@paulgrobar7098 Gün önce
Regarding circular/spherical geomitry: it is not possible to form a right angle with a curved line. Such an intersection will always be acute because the circle curves toward the line.
@Dominative 3 aylar önce
I always thought the universe was Sphere due to the big bang animations. This video was literally game changer and it has changed my perspective towards the cosmology.
@nillyk5671 2 gün önce
Does it have a form? I don't think it has a shape at all.
@Dominative Gün önce
I mean, I always thought that an explosion would go all direction and thus giving it a sphere like shape.@@nillyk5671
@boartank 3 aylar önce
We should think of historical figures as anime characters. I wouldn't remember Janos if I wasn't made invested in what he did and accomplished if it wasn't for your delivery. I now know he was 17 when he discovered he can have lines intersect and still be parallel while not realizing he's playing in a non-euclidian plane... and he 1v1'd people and played the violin on their corpses. Awesome people are awesome. Thank you, Veritasium for this beautiful video. You made me remember what it felt like when I was a kid looking at the stars and the cosmic horror that I felt when I realized I am looking at Infinity.
@nct948 4 gün önce
Stunning presentation sharing the excitement of mathematical challenges and their resolution relative to the actual reality of our universe. Thank you so much for guiding us through the thought processes leading to our present understanding of a flat universe. I am neither a physicist nor a mathematician and I can't help wondering why the cosmic background radiation is the same in any direction if the universe is flat!
@hebertaugust 9 gün önce
i can only understand veritasium videos while high was perfectly able to visualize how this worked in my head amazing work
@trunghungpham9414 4 aylar önce
Veritasium’s math videos are so good. Just never gets bored watching them.
@atinkapruwan6780 4 aylar önce
me too
@prerakmann1418 4 aylar önce
Shortest 30 mins on TRvid
@Ostinat0 4 aylar önce
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
@daddycationxx 4 aylar önce
for real, learning has never been more exciting
@TheNuke1111 4 aylar önce
yeah and you will always learn alot watching his videos.
Thousands of years later, his works are still read and applied as foundations in standard mathematics courses. Euclid and Cantor still blows my mind, esp with the latter's diagonal method of proof. Proof of contraction is earlier to grasp but proof of induction took sometime to get used to. My CS algorithm professor made us memorized all of the important proofs and I would think the diagonal proof was the cleverest I've remembered.
There's already so many comments, but this is really astounding work! From a pesky algebra postulate to space-time and the shape of the universe!
@CarryPotter007 9 gün önce
you are the greatest explorer/science enthusiasts/teacher to ever grace humanity my dad studied Physics and then Astrophysics and I was always fascinated about what he knows now I am almost certain for the first time in my life I finally understand the essential meaning and nature of relativity / space-time curvature thank you!
@onebadmoto5081 2 aylar önce
Your explanation was amazing🤙🏽
@jackbuff_I 7 gün önce
just wanna say a sincere thank you to the whole Veratisium team. I hope you know you're creating future geniuses, by the bucket load! If my generation (~90's) had these resources to educate ourselves, I might have fulfilled my potential!
@alex-nb3lh 4 aylar önce
the buildup from first principles to the payoff via einstein’s relativity is phenomenal. one of my favorite videos by you so far.
@opticalreticle 4 aylar önce
ti is
@user-fx5ii1kt8i 3 aylar önce
Yeah this was amazing
@0RbIt1000 3 aylar önce
@huyxiun2085 3 aylar önce
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 ;-)
@canderson9167 3 aylar önce
@@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.
@Twisted_Code 3 aylar önce
What's funny is that because the second postulate didn't hold before the change, spherical geometry would still be "non-Euclidean" in that one of the postulates doesn't hold, but not in the sense that specifically the fifth postulate doesn't hold (because the second one now does)!
@mr.mr.2318 2 aylar önce
These videos are so wild, great, and fun (for my brain) Thank you sir 😊
@lildragon0 2 aylar önce
An undefeated swordsman and a genius mathematician. A true gentleman.
@MissAynneK 16 gün önce
I dunno why the algorithm randomly brings me to these kinds of mathematics videos that take me way beyond my depth of understanding, but they sure are fascinating
@Efemral 9 gün önce
Brilliant quality video, the time it must take to publish these!
@myoky 4 aylar önce
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.
@mariemaier7393 4 aylar önce
Whoa sounds great, what was it called?
@black_crest 4 aylar önce
​@@mariemaier7393Probably differential geometry
@emmanuellawal2694 4 aylar önce
What was it called, and please can you share resources that might help
@AissamElkirafi 4 aylar önce
@matthewnoyce9089 4 aylar önce
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
@Joao-id4dn 2 aylar önce
the genius of the greeks in recognizing the 5th postulate as such in 300 BC is amazing. Incredible
@alexfido2935 2 aylar önce
Bold statement at the end about Euclid's book, I'd maintain Principia Mathematica is probably more famous
@lutzweb 2 aylar önce
one of the best video for general public. well done!
@johngeronimo8821 3 aylar önce
"... to discover a contradiction, an inconsistency, in this Non-Euclidean geometry..." in 13:06 This is like a poem to me, this is just beautiful.
@ChristopherCrimi 7 gün önce
Your coverage is fantastic!
@unvergebeneid 4 aylar önce
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
@culwin 4 aylar önce
Often this also happen when and where institutions have been set up to publicize (or at least preserve) those findings in some way.
@Tinil0 4 aylar önce
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.
@johnlucas6683 4 aylar önce
These are just the ones that have been on record, or at least have surviving records.
@patu8010 4 aylar önce
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.
@Rahooligan86 3 aylar önce
Brilliant! Thanks for creating such great content.
@ArthurGSiqueira 2 aylar önce
As a math fan, this is one of the best videos that I watched in the last time
@scottl8973 Aylar önce
This was amazing I feel like it was the first time I could visualize why the space station has micro gravity. Because it’s a straight line brilliant.
@res00xua 3 gün önce
Fascinating. Great job!!!
@federicomancini310 9 gün önce
One of the most Endearing explanation of Math ever heard
@RealGhoda 4 aylar önce
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
@itzhexen0 4 aylar önce
None of them spent 2000 years arguing over one sentence because they died.
@NNOTM 4 aylar önce
one is not possible without the other
@capitano3483 4 aylar önce
Physicists were the ones predicting the supernova appearing one year later.... the pragmatic mathematicians.
@RealGhoda 4 aylar önce
Mathematicians in general@@itzhexen0
@pickle380 4 aylar önce
I apologize for my actions
@puppetscorner5148 9 gün önce
This image of the triangles in this hyperbolic geometric representation looks familiar to the flower of life. Mathematic points intersecting to create a gorgeous image
@AbhishekKumar-gr7iz 2 aylar önce
One must not skip any veritasium video because a book worth of knowledge is crammed in a video of less than an hour.
@ramiljim55 18 gün önce
I can't believe that there was a time in my life that I understood complex math problems.
@nuvostef 18 gün önce
The 5th Postulate made perfect sense to me as soon as you illustrated it, and I flunked Math For Morons at university. It’s probably my abyssal inability to perform all but the simplest math problem, but what I DIDN’T understand through this entire viddy was why mathematicians - REAL mathematicians - had such a problem with #5. Either way, this was another excellent show. Thank you! 🤙🏼
@hawkatsea 9 gün önce
Kudos for the crochet maths reference!!! As an ecologist, I'm always dealing with non-Euclidean diststances and took up crochet after many of my forebearers had done to both conceptualize some multivariate spaces and also to just take the edge off, lol.
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. 🙂
@cheoa1473 3 aylar önce
@Steve-si8hx 3 aylar önce
How does anybody know that postulates are true ?
@archit1048 3 aylar önce
@ForkGenesis 3 aylar önce
@@Steve-si8hx we all just assume that they are true, and develop from them
@efhi 3 aylar önce
@@Steve-si8hx empirical observation of reality
@marshalbaek5580 2 aylar önce
Seeing the types of thoughts these brilliant people were pondering hundreds of years ago and even thousands of years ago, makes me feel small about pondering whether or not the light is actually off when the refrigerator door is closed.
@dennisolsen8945 3 aylar önce
Thank you for this great mind-bending video!!
@akachucknasty 3 aylar önce
Imagine parallels making you go crazy....and at the same time, the answer to the universe itself.
@jbot8530 Aylar önce
I loved your great work it's so inspiring, thank you. In additional to that, let's assume that our universe is an infinite sphere
@griffinbur1118 Aylar önce
For those who enjoyed this video, Roger Penrose's Road to Reality is a great book that starts with this very topic and builds slowly to some very cool stuff in physics.
@timothyshapka1309 4 aylar önce
You just summed up my entire university foundations of geometry course in 30 minutes. I admire your ability to educate so concisely immensely.
@briondalion3696 3 aylar önce
It was a very great explanation, and hopefully many get inspiration from! I am actually thinking about gravity again, time travel, entropy, antimatter, gravitational waves, and antigravity.
@grim_reaper977 3 aylar önce
My question, was the hardship worth it, (the long nights to prove one theorem problem, while miscalculating several times)??
@KhuongTuan-ef7hi 3 aylar önce
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?
@kyleshaw7966 12 gün önce
Still killin' it dude. Love all the videos.
@a-han9696 9 gün önce
Absolutely Amazing, good work maj
@erictaylor5462 15 gün önce
16:00 The amount of human suffering that is born of misunderstanding, or assumptions that are in error is astonishing.
@SamLyn 2 aylar önce
I remember learning these in high school geometry and struggling through proofs for the rest of the year 😅
@comic4relief 2 aylar önce
12:43 Do those angles that "go to zero" ever really become zero or just approach zero? I think it is about the infinte divisibility of area.
@caschque7242 4 aylar önce
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!
@em-agoo-481 4 aylar önce
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.
@minhvan1216 4 aylar önce
@dieSpinnt 4 aylar önce
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)
@timbo8366 3 aylar önce
Somebody finally explained weightlessness and curved space-time in a way I can understand, instead of just using the usual cone/conical shape with no explanation of what's going on.
@dangou-nchained5854 12 gün önce
This was absolutely amazing. Mind blown
@bomaniigloo 3 aylar önce
One of the best veratasium vid Edit: vids.
@SpataWorks 2 aylar önce
I wish i had this channel as an uninterested kid in highschool failing math. I took 6 math classes in college after finding out cool facts like this on youtube and getting into education
@topherthe11th23 11 gün önce
I have always wondered why so many textbooks on Geometry rephrase Euclid's Fifth Postulate to say "in a plane in which there is both a line and a point not on that line, there is never less than one and never more than one line passing through the point that does not intersect the line". (Some textbooks omit "never less than one" because (I've heard) you can prove the existence of one by the other Four Postulates, so it only needs to state that never MORE than one such line exists.) Or else it can be stated in terms of two lines crossed by a third which, if certain angles are equal, indicates that the first two lines are parallel (will never intersect). Why do different textbooks have different Fifth Postulates? All of the theorems you can prove with ANY of the alternative Fifth Postulates are the same as all those provable by any other. I'm not speaking here of the CONTRADICTORY alternatives that change Euclidean Geometry into Spherical or Hyperbolic Geometry. I'm speaking of alternative ways of writing a Fifth Postulate by which you can still do all of Euclidean Geometry but nothing non-Euclidean. Why do different versions exist?
@feliperiquelme8504 4 aylar önce
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!
@chaosopher23 4 aylar önce
Psst... Euclid is describing parallax. Postulate 5 is a really stretched out triangle.
@Roxor128 4 aylar önce
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".
@rocketscience4516 4 aylar önce
Just call them your nerds, it's three less letters to type.
@BisexualPlagueDoctor 4 aylar önce
@@rocketscience4516he’s a mathematician, who loves hyperbolic geometry, why do you expect him to care about the length of words Lmao
@rocketscience4516 4 aylar önce
@@BisexualPlagueDoctor Aw, someone lacked the perspicacity to realise it must have been said in jest. Think a bit before you type.
@TheMarman57 3 aylar önce
Wow. I was a complete math failure when in school. However, I don't get what it is in the simple 5th postulate that is so difficult to understand. So here's what I understand; if you have two horizontal lines, one above the other, and you add a vertical line going through both of them them, providing the two horizontal lines are level and parallel, and the vertical line is perfectly vertical, the angles of the intersecting lines will be 90° right-angles. If we make an observation that for instance, the angles on the intersections both upper and lower are less than 90° on one side then the two horizontal lines can no longer be said to be parallel, but can be said to actually meet each other at a distant point on the same side on which we have observed the intersecting angles are less than 90° - they uh slope toward one another. Did I miss it?
I don’t see what the big deal is either. It is pretty straightforward.
@topherthe11th23 11 gün önce
7:38 - As regards a flying in a straight line that doesn't appear to be straight on the map, I've heard that there is a point on the coast Great Britain and a point on the coast of New Zealand such that you can sail a ship these two points IN A STRAIGHT LINE (i.e. along a Great Circle of the Earth) while never hitting land. As you pass Dakar, Senegal, on the Continent of Africa, Dakar will be on your left. As you pass Natal, Brazil, on the Continent of South America, Natal will be on your right. You will have Tierra Del Fuego on the Continent of South America on your right as you keep going straight with Antarctica not far away from you on your left. Even though you adhere without deviation to this straight line (Great Circle of the globe), your compass will tell you that you are constantly changing directions vs. the compass's detection of north-south orientation. You will NOT be taking a route that will be a straight line on a Mercator Map (which is the map on which a straight line is a line of constant heading), but, rather, a route that will be a straight line on a globe. If after reaching New Zealand you were to extend this line all the way around a globe without deviating from it, you could use that line as a guide for cutting that globe into two equal and identical hemispheres (assuming the globe is a sphere, which we know the Earth ISN'T). This same route from Great Britain to New Zealand does not come close to appearing to be a straight line on most flat maps.
@BrokenChain195 2 aylar önce
I think I finally understand why I love mathematics and physics so much. I believe there’s a saying that goes “physicists are those who never stopped asking ‘why?’” Just as a child sees the world as magical and these magical things make them ask why, the mathematician and physicist see the magic of the universe through math and physics and continue to ask “why? their entire lives. Essentially, mathematics and physics, at least to me, bring back that magical view of the universe.