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

[@swarry3508]

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

[@atinkapruwan]

fascinating indeed

[@matroxman11]

I’m convinced that math is the key to the secrets of the universe

[@eddielally2045]

​@@matroxman11 bruhhhhhh obviously

[@ukleth]

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. ""

[@krakenmahboy]

(Comment deleted due to comment crybabies; enjoy the contextless whining below!)

[@Jeff_3007]

Let’s all appreciate Euclid’s effort he put into writing The Elements just so that Veritasium could make a video about it

[@TheOneAndOnlyCumGuzzler]

credit to veritasium for supporting small authors like euclid

[@Byzantia]

I

[@mr.fhizzy]

Yes

[@PrabhasPatil]

@@TheOneAndOnlyCumGuzzler yes 💯

[@JohnDoe-qz1ql]

As he said, it's exerted great influence, so

[@birindersingh4146]

Imagine the greatness of the man who wrote 1 little paragraph and made mathematicians mad for 2000 years

[@TarikSkubalEnjoyer457]

Fr bros a menace

[@sarc143]

Haters pocket watching bro smh

[@m1k3vroom]

The level of genius involved is unparalleled.

[@dwdelve]

Greeks have been doing that for a long time

[@pieteruys2032]

@@topherthe11th23 Greek architecture, sculpture, philosophy, democracy, science ( the atom ) etc. This is evidence of a high achieving population

[@Grimlo9ic]

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.

[@zwenkwiel816]

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?

[@Grimlo9ic]

@@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).

[@thegreatreverendx]

@@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.

[@LDVincenzo]

​@@thegreatreverendxor at the very least they were in the early universe, does it still hold for closer distances?/ more recent times ?

[@leonardosaboya55]

@@zwenkwiel816imagine a cone expanding from a point into everything

[@vaibhav3955]

Veritasium's videos are generally great but the math ones are on another level

[@feynman_QED]

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]

​​​@@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]

​@@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.

[@hattix6713]

Derek has good sources, and actually listens to them!

[@noway905]

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. 🤣

[@adityavardhanjain]

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]

.

[@ryugo7713]

@@dinogt8477do you need a tampon?

[@aniket385]

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...

[@jordanfrielingsdorf4761]

I agree it is very Cosmos-esque and I think Carl Sagan would be proud.

[@cherniaktamir612]

And 4. An inspiring story about not listening to seniors about not pursuing your intuition, thinking from first principles

[@mosgon]

As an astrophysics major, I love how a video on ancient math turns into a cosmology lesson

[@TNT-km2eg]

Mayor , no less

[@Tomico.]

That's how it all started.

[@no36963]

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]

Checkout The Greatest Lie on Earth by Edward Hendrie. I can promise you are being fed a bunch of garbage

[@Jakekelley-hs8bk]

Sounds like a religious massive psyop. @@truthhub7395

[@dailyknowledgeOG]

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!

[@abdussami8498]

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!)

[@clarencejohncabahug5466]

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.

[@gilbertogarbi4479]

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.

[@isaacpianos5208]

​@@gilbertogarbi4479 yes he is by father of geometry by some means, saying "by no means father of geometry" is incorrect

[@Mayank-tm2km]

He collected all the known math knowledge at that time, he didn’t create all of it by himself

[@patrikfloding7985]

@@Mayank-tm2km ok, so not Father of Geometry. More like Midwife of Modern Geometry?

[@linktv7979]

​@@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.

[@myoky]

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.

[@happysailor315]

Whoa sounds great, what was it called?

[@black_crest]

​@@happysailor315Probably differential geometry

[@emmanuellawal2694]

What was it called, and please can you share resources that might help

[@AissamElkirafi]

Bump

[@mustard1007]

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

[@killmajaro1]

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]

Can't really do anything practical with it like funnel energy and hack into the quantum mainframe of reality, but it's cool.

[@yashsarda2263]

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]

wrong channel ;)

[@TheEpicProOfMinecraf]

​@@irg008 I was about to say this myself

[@vattghern7592]

People out here measuring galaxies while I’m struggling in trigonometry….

[@samueldelatorre7752]

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!

[@RealGhoda]

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]

None of them spent 2000 years arguing over one sentence because they died.

[@NNOTM]

one is not possible without the other

[@capitano3483]

Physicists were the ones predicting the supernova appearing one year later.... the pragmatic mathematicians.

[@RealGhoda]

Mathematicians in general@@itzhexen0

[@pickle380]

I apologize for my actions

[@trunghungpham9414]

Veritasium’s math videos are so good. Just never gets bored watching them.

[@atinkapruwan]

me too

[@prerakmann1418]

Shortest 30 mins on KZbin

[@Ostinat0]

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]

for real, learning has never been more exciting

[@Micke240]

yeah and you will always learn alot watching his videos.

[@alex-nb3lh]

the buildup from first principles to the payoff via einstein’s relativity is phenomenal. one of my favorite videos by you so far.

[@opticalreticle]

ti is

[@JaiminPatel-t3r]

Yeah this was amazing

[@0RbIt1000]

Agreed

[@huyxiun2085]

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]

@@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.

[@deedsrae9323]

For someone who barely understands mathematics and wants to learn more, this is articulated very well. Good job 👍

[@nerobaal6655]

Learn basic math and algebra.

[@hirakbandyopadhyay699]

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]

ok

[@Steve-si8hx]

How does anybody know that postulates are true ?

[@archit1048]

😂@@Steve-si8hx

[@ForkGenesis]

@@Steve-si8hx we all just assume that they are true, and develop from them

[@efhi]

@@Steve-si8hx empirical observation of reality

[@unvergebeneid]

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.

[@catfishingfornitro3416]

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]

Often this also happen when and where institutions have been set up to publicize (or at least preserve) those findings in some way.

[@Tinil0]

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]

These are just the ones that have been on record, or at least have surviving records.

[@patu8010]

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.

[@TimeBucks]

Gauss never ceases to amaze me.

[@walifortune-hc4fe]

Wow lovely

[@AhmadDalhat-c6h]

Nice one

[@IsmailMansir-qq4hl]

Vnvb

[@dsoli807]

Sweet 🎉🎉🎉

[@dilshadjmati]

Good jobs gauss never ceases to amaze me.

[@iSherry]

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.

[@timothyshapka1309]

You just summed up my entire university foundations of geometry course in 30 minutes. I admire your ability to educate so concisely immensely.

[@grim_reaper977]

My question, was the hardship worth it, (the long nights to prove one theorem problem, while miscalculating several times)??

[@KhuongTuan-ef7hi]

zzz

[@maythesciencebewithyou]

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?

[@mrb5510]

​@@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.

[@caschque7242]

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]

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]

ok

[@dieSpinnt]

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)

[@rhov-anion]

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.

[@ATF2099]

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]

I've never heard of a course like that!

[@rhov-anion]

@@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.

[@suzuki8951]

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

[@aviilokinkshi]

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.

[@tshahin]

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

[@Skwertydogs]

Wow. I did not notice that. How fun! Thank you.

[@AT-27182]

This is one of the greatest stories of human history. Thank you for explaining it for a large audience.

[@cereal-killer4455]

It really is. On a different note, flat earth confirmed /s Seriously: flat universe confirmed

[@LeonEdwardsFitnessOfficial]

@@cereal-killer4455 how

[@ninebreaker274]

ahaha normie

[@fearlessjoebanzai]

​@@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!

[@PinguinKeks]

It's funny how quick people can be to misunderstand things though, Gauss never said anything negative about Bolyai in his letter

[@feliperiquelme8504]

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]

Psst... Euclid is describing parallax. Postulate 5 is a really stretched out triangle.

[@Roxor128]

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]

Just call them your nerds, it's three less letters to type.

[@BisexualPlagueDoctor]

@@rocketscience4516he’s a mathematician, who loves hyperbolic geometry, why do you expect him to care about the length of words Lmao

[@rocketscience4516]

@@BisexualPlagueDoctor Aw, someone lacked the perspicacity to realise it must have been said in jest. Think a bit before you type.

[@chanceroberson7517]

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.

[@Cameron-ls3qt]

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.

[@maxinator2002]

@@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.

[@opticalreticle]

@@Cameron-ls3qt it is language

[@nadiabairamis3854]

I think this is my favourite Veritasium episode ever! Especially well written and engaging.

[@ASDasdSDsadASD-nc7lf]

Concur.

[@tomvesely4008]

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

[@firstnamelastname9215]

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]

​@@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]

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]

What change do you believe it caused you?

[@ФдФ]

@@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

[@TheRealQuickSilver]

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.

[@ivanleon6164]

he was a monster, what a gigachad.

[@ImKinoNichtSabbeln]

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.

[@XxZeldaxXXxLinkxX]

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

[@SylveonSimp]

He was on the 10 DM bank note in Germany. Now we have soulless windows on our Euro notes. What a pity.

[@spiderspyy]

eulor is big, but his yxy still haunts my dreams@@XxZeldaxXXxLinkxX

[@mikehenson819]

How terribly tragic it is that one lives, studies and discovers the incredible and never knew the greatness of their accomplishment in life.

[@-astrangerontheinternet6687]

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.

[@justaspalabras]

Are you talking about Bolyai?

[@divyasasidharan2960]

I think we should not have that awareness.. u just keep doing it like animals procreate

[@jinfin221]

Why tragic

[@benjaminj883]

@@-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

[@TheSilentKid_yt]

Me pretending to understand:

[@heidis5188]

For real lol😂

[@eeccee11]

Yup. Deleted my comment after reading others. Lol. What's the point

[@benmastar]

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.

[@j_m3102]

12:29 12:34 12:36

[@WREFMAN]

Your

[@CaptainPeterRMiller]

Well said Monsieur.

[@karupt422]

Your right , he didn't read it😂

[@fearsomefoursome4]

HAVE ERIC WEINSTEIN AND GIVE US GEOMETRIC UNITY

[@18th_King]

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.

[@Sharkie1717]

Nice 👌

[@thewhitefalcon8539]

What's even sadder is HE DID APPRECIATE IT VERY MUCH AND PRAISED BOLYAI TO ANOTHER MATHEMATICIAN but Bolyai never knew it!

[@SamageetDutta]

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

[@kolyashinkarev7366]

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

[@apokalypthoapokalypsys9573]

Ah yes, Guass, my favourite character from Code Guass.

[@shininio]

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 KZbin. Kudos Derek

[@opticalreticle]

good

[@DishDelights170]

True

[@MysticPing]

Apart from all the misleading startup ads

[@opticalreticle]

@@MysticPing what startup ads?

[@ACuriousChild]

@@MysticPing .... and much more ... THE BLIND LEADING THE BLIND!

[@ubestbegood]

this was an awesome episode. seriously well done. the only note i have is somewhat of a big one. maybe it’ll fuel some curiosity on your part. that is… do not underestimate euclid by thinking he did not have very well thought out reasons for the language used in his definitions. the word “part” in particular is not a trivial word and harkens to one of the most important questions of metaphysics, especially at the time. that is, the question of one vs many. plato, parmenides, protagoras, proclus, aristotle, etc all weigh in on this. when he says “part” he is using a metaphysical notion. what is a part? well, mereology is an entire philosophy sub genre dedicated to this question and its origin is plato’s parmenides. the 2nd half of parmenides goes over this notion specifically. to understand what he means by part you likely need to understand plato’s metaphysics and notions like Ideas/Forms, One itself, the idea of a particular thing “partaking” in a form (in this case, the point partaking in the impartible One itself), etc. they’re talking about metaphysical stuff here. plato emphatically notes that the real aim of geometry is not to play with numbers but to use these objects which exist in a lower ontological reality (mathematical structures) to apprehend the highest reality which is One itself, Good itself, and the Ideas which these mathematical objects actually emanate from. so in this case, a point represents in space what One itself represents in itself. it is a unit. proclus covers this among others and i think rather than doing what the guy in the video did by presupposing these definitions can be substituted by any other definitions, favoring coherence over correspondence (something plato and surely euclid would absolutely not stand for based on his takes in cratylus) he might want to try and truly understand what proclus meant by each and every word of his definitions. it’s important.

[@MrAulic]

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.

[@usadefcon1]

If you want more checkout the ScienceClic English KZbin channel. It's the best for visualizing the math.

[@joerionis5902]

Finally understood what physics channels meant when they say that "the universe is flat."

[@Oscaragious]

@@joerionis5902 Unless you draw REALLY big triangles.

[@jacopolibera6974]

This has to be one of the better animated veritasium videos ever. A pleasure to watch as usual

[@jacobshirley3457]

Everybody says that after every history-based Veritasium video, lol. Which is saying something.

[@orngjce223]

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.

[@Guy-z6o]

The crinkly bits on kale and lettuce, remind me of fractals'....they are everywhere....gotta love em

[@Tdawg-b2b]

Are you a biologist or something? Where would i look to learn more about this stuff?

[@jevilsugoma1743]

Ok

[@niviamaeva]

Wait. What? 😮

[@localcragdirtbag8049]

Ya, fractals the Mandelbrot set is basically describing the pattern of life on earth. I mean yin and yang, right? Makes sense to me.

[@AaronSkone]

You should do a video on the “flatness” of the universe to clear up misconceptions about what flat means in this context.

[@LeeNotSa]

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 ...?

[@AaronSkone]

@@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.

[@LeeNotSa]

​@@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?

[@AaronSkone]

@@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”).

[@T_Dot94]

I love these history of science videos. It makes math and science feel like a lively art form rather than something mechanical and dead.

[@nineveh17]

real

[@storiesshubham4145]

Rightly said

[@UNr34]

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.

[@vidal9747]

"The consequences of the fifth postulate are left as an exercise for the reader"

[@AkiraDemi]

the entire math community: oh for fu-

[@TheSkystrider]

😂

[@omkarpawar2620]

Euclid: Makes 5th postulate bit long Other mathematicians: * thinks intensly for 2000 years*

[@adrian9098]

😅👍

[@ivanleon6164]

they took it personal, lmao.

[@MARK-gp9hb]

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...

[@izzylevi.]

@@MARK-gp9hbdid you even watch the video?

[@MARK-gp9hb]

@@izzylevi. yes all of it

[@urmotherivan]

For anyone who came from TikTok, video starts at 6:42

[@sundhar5229]

His father not only understood his scientific work, he was so proud and sent it to his peers.. What's more wholesome than that..!

[@XmarkedSpot]

Taking the literal five seconds to check how his name is pronounced. Nails on the chalk board, I tell you.

[@zwojack7285]

Isnt that like every stereotypical Asian parent?

[@GudiUTube]

@@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".

[@rockjano]

@@zwojack7285 The were Hungarians not asian....

[@sexmansex4776]

​@@rockjanohungarians are steppe people anyway

[@cbwavy]

15:57. That is devastating. Imagine if Bolyai and Gauss actually collaborated.

[@clionekimura9604]

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).

[@sharadsemilo]

Start a channel. Please

[@Albertandearthie]

I read it all 2 years ago lol

[@dlevi67]

More power to you!

[@Adroit1911]

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.

[@kwaherikwasasa]

I read his Drunkard's Walk book, and it is spectacular! I will look into Euclids Window...😂

[@claudetowery6227]

A vocabulary edit might help in videos about distance. “Farther” is correct for distance. “Further” is correct for time and metaphorical distance.

[@apolotorresart]

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!

[@opticalreticle]

because God made it that way

[@kolakoala6702]

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 ❤

[@moonman8450]

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 😅

[@tarmorboi5307]

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 :)

[@tarmorboi5307]

Göttingers unite!!🚀

[@sjsomething4936]

A new place to add to my bucket list! Enjoy your contemplations ☮️

[@thitran6105]

ok

[@JBNemeth]

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.

[@tannerman46]

Unfortunately making a KZbin video is completely different from teaching a class, and teaching is not scripted

[@jmc8076]

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.

[@tylerhaslam2083]

I have had this conversation with my class. About 5% of students are riveted-- having in every word. The other 95% are zoned out.

[@rev0live752]

you didnt learn anything from this video its just an illusion

[@luckytrinh333]

Bro summoned an entire community with this one 🥶

[@vladbobe26]

Leaving aside the educational aspect, the production value of this was incredible. Congratulations Veritasium team!

[@taisa8776]

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.

[@Grace-ms7un]

You are my new hero for using sewing to describe math ❤

[@noticing33]

Thsi is why it's so important to make men way more feminine, toxic masculinity has stunted those great men of the past

[@Qay]

@@noticing33 This has nothing to do with the comment. Maybe concern troll under a different bridge?

[@noticing33]

how dare you? @@Qay

[@3548374]

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!

[@xmystictitan6347]

Vertasium just explained the craziest thing in the simplest way possible, props to him i love this channel

[@meemdic8682]

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.

[@silviodc1309]

the game Hyperbolica brings it even into 3D/VR

[@meemdic8682]

@@silviodc1309 So does Hyperrogue!

[@themagicnerf]

@@silviodc1309 Side note: If you have motion sickness, that game will quite literally throw you into a coma.

[@flintsparks8406]

The amount of work Veritasium puts in his videos is amazing

[@barnabas.csermely]

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.

[@iateuranium-235forbreakfas7]

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

[@kevinmahaley4916]

He's good but he's been wrong on some things

[@Nyxyz999]

​@@kevinmahaley4916maybe because he's human?

[@ekksoku]

@@kevinmahaley4916 wish I knew what being wrong was like, luckily I'm infallible

[@marcoparco_9564]

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.

[@davidk676]

Thank advertising

[@SilentRacer911]

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)

[@MidwestFarmToys]

No

[@JuanWonOne]

He got the most valuable thing from you, time. Nothing is free

[@TheMaidenOnes]

​@@JuanWonOnewell, we got educated in return. so i think we got the better part of the deal ;)

[@GREGGRCO]

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 !

[@Sweet9964]

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.

[@zwan1886]

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.

[@IIT24Aspirant]

yeah and I bet this guy didn't understand the last 10mins of the video lol@@zwan1886

[@StarfireReborn]

​@@zwan1886 Funny Thing, I Hate Math But Love The Effort It Takes To Solve. 🤷🏽‍♀️

[@MsMiDC]

Learning is fun, but its different when its out of your own curiosity, rather than being forced upon you.

[@allrequiredfields]

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.

[@ClutchCps]

It's always nice to see Professor Kontorovich in a Veritasium video. You can see that he really loves what he is talking about.

[@ccost]

bro how many videos do u comment on for me to keep seeing you

[@ginalley]

@@Joe-sg9ll You'd be happy to know that mathematics proved that mathematics has true statements that cannot be proven

[@M2ProMBP]

All of you liking bot comments 😂😂😂

[@carnap355]

wot

[@carnap355]

wat

[@spunktasticjismmonkey8569]

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. 😊

[@tka3]

That's the magic of a professional science communicator

[@atanusingha2680]

Man! I truly believe that you are doing more for Physics and Science in general than most published author. Kudos!! Never stop.

[@valinhorn42]

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.

[@jozsefbodnar6177]

Just a small remark from a Hungarian mathematician: Bolyai is pronounced "Bo-yay" (with an extremely short "o" just like in "Mom") rather than "Bow-ley-eye"... It was very weird to hear this familiar name consistently pronounced that way :D For the content, I believe more details about the spherical geometry could have been useful: it might be a bit confusing first to say that "0 parallels is ruled out" and then coming up with a model with 0 parallels.

[@peterfireflylund]

He said it was disregarded by everybody because it was “obviously” nonsense. Turned out, it wasn’t nonsense.

[@adityakhanna113]

Now you know how indian mathematicians feel when people talk about Ramanujan

[@barnabas.csermely]

Amíg nem láttam a nevét kiírva full nem tudtam kiről beszél

[@VitezGonye]

@@barnabas.csermely same

[@adaliszk]

Until I saw it written I totally thought Bolyai was not Hungarian :D

[@CosmoTechChronicles]

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!

[@tomaccino]

Of course all youtoobers love creating content because of that sweet sweet ad revenue and sponsorships 😂

[@Tbwtas402]

F

[@IIllqpllll]

向导 不 佐 奥兹 Xiàngdǎo bù zuǒ ào zī

[@abnerasturias6380]

Oh well, Science GOES Hollywood !!!

[@nadarith1044]

@@tomaccino Go generalize massive numbers of people through your cynicism elsewhere

[@jbperez808]

This video concretized my understanding of non-euclidean geometery in ways books couldn't. Amazing work, Dr. Derek!

[@erictaylor5462]

16:00 The amount of human suffering that is born of misunderstanding, or assumptions that are in error is astonishing.

[@borisborcic]

ambiguities are like microbes, the pathogenic ones steal the attention...

[@nerobaal6655]

I believe they’ve all made a few.

[@Kyanzes]

Just a side note: Bolyai is pronounced as Boyai or Bo-ya-e. The "ly" is an old form of "j" in Hungarian which is pronounced similarly to the English "y". Cool video.

[@sujoms]

Haha I just wrote the same.

[@csokasg]

Yes, he should have asked/looked it up how to pronunciate his name :)

[@melybuvar]

It was really bugging me during the video. Not a hard task to check the pronouncing on google translate... On the other hand great video

[@majdnemkocka]

Yeah, the very first line in the Wikipedia article on Bolyai gives the pronunciation as [ˈjaːnoʃ ˈboːjɒi], it wouldn't have been that hard to look up.

[@akosbakonyi5749]

I am Hungarian I didn’t realise he was talking about Bolyai until the middle of the video when it was written on the screen 😅

[@alexandresofman3600]

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!

[@JorgMeyer-dr4eh]

Could you please share the documentary? 🤔

[@neonfroot]

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.

[@martiddy]

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

[@HateBear-real]

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.

[@GoodShepheardGames]

Isn't it wild how, the further history goes back the more people loved to learn anything and everything. And now that we have most information at our fingertips we hate learning things

[@voidmain9519]

Exactly right! I usually wonder the same. Because so much information, knowledge at my fingertips and I don't even even raise my finger to learn the things that have been here all along. I guess it's because of easy access and availability people take it for granted and postpone or ignore it. We're, most are intentionally ignorant and lazy.

[@prateekpanwar646]

​@@voidmain9519 The information we're given now a days is very very catered to our taste due to algorithms. Books allowed us to choose as library had every genre. While videos are selected by algorithms. It's one of the issues that how it's presented. We no longer get vegetables and make fresh dish. We can only buy ready to eat meal which is boring.

[@tachyeonine]

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

[@bob-pc9no]

To think that if Euclid had not included his 5th postulate in his text, Einstein might not have discovered general relativity. Amazing to think how past discoveries actively shape the discoveries we make today.

[@QueekHeadtaker]

Great confidence to include it, despite the seemingly insane implications that came with it.

[@sdbszz706]

Standing on the shoulders of giants

[@maolcogi]

Think about anything we take for granted nowadays. The screen you're looking at, who invented the materials, the manufacturing process, the coding to make it work, the electrical system powering it, everything ... There are so many ridiculously old inventions that made the device you're reading this on possible. And to think I'm impressed when I'm able to eat macaroni and cheese without getting cheese all over my moustache.

[@jasonrubik]

​@@maolcogimaolcogi doodle stuck a feather in his mustache and called it macaroni

[@EebstertheGreat]

If Euclid had not included his fifth postulate, his theory would have been too weak to prove most of the theorems he wanted to prove, and it never would have been an influential book in the first place. Then Archimedes or someone else would have come along and improved it by adding a similar postulate. There's really no way around it, and it wasn't a "choice" _per se._

[@billhollings6567]

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.

[@thoatran2718]

ok

[@sumathipitchaimani]

What is the difference between an axiom and a postulate

[@FPSIreland2]

@@sumathipitchaimani same thing, different words

[@mohammadahmednooruddin5990]

​@@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

[@BobIoNix]

A radial point line intersects only tangents to a circle at 90 degrees, not the curving circle itself, as the curving arc segments of a circle keep changing the angle itself.

[@Iluhajjot]

Great video, but a bit weird that Lobachevsky is mentioned so briefly - he developed non-euclidian geometry earlier than Bolyai and in more detail. Lobachevsky definitely deserves more than just 3 seconds in a video about non-euclidian geometry which he pioneered.

[@misslayer999]

I think he just really wanted to tell that fencing story

[@B.E.Z.nOtLayZ]

It's because Non-Euclidic. Check out Terrance Howard latest podcast with Eric Weinstein and you'll further understand why he only got a 3 seconds mention

[@axialagegamer]

He didn't duel enough dudes to make a fun video, tho. 😅

[@hardboo]

He's Russian, a russian genius.

[@benkamen]

@@B.E.Z.nOtLayZu gotta be kidding

[@cadekachelmeier7251]

Shout-out to the game Hyperbolica. The game world has Hyperbolic geometry and you can get a good sense of what it's like. It also has a level with spherical geometry which is actually pretty different from what you'd assume. The developer also has a bunch of interesting videos talking about the process building the game.

[@ZenoRogue]

Have you tried HyperRogue?

[@mkormos89]

Great video! As a Hungarian who attended a highschool named after Bolyai, the english pronounciation of his name was really strange to hear for the first time :) In hungarian it is pronounced Bo-ya-e, not Bo-li-ay. "Ly" is acutally a (double) letter in the hungarian abc, not two separate letters, and it sounds like the "y" in "yes".

[@akoskiss2065]

Hol jartal?

[@terrypussypower]

Boh-yah-ay? Is there an emphasis on either of the 3 syllables? Like *BOH* -yah-ay, or boh- *YAH* -ay, or boh-yah- *AY* ?

[@vincejeney]

@@akoskiss2065 szerintem a bolyaiba

[@andrasziegenham6766]

It's a great video and I bet it took them LOTS of hours to create, so I wonder why didn't they spend a minute to ask google translator to pronounce it for them and then a few more minutes to practice it... :(

[@andrasziegenham6766]

@@vincejeney van belőle pár az országban :D

[@MzeeMoja1]

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.

[@thomas6502]

Mind continually blown. Thank you Dr. Muller (and cohorts) for your efforts to make this extraordinary topic accessible to aspiring minds like this one.

[@ankokuraven]

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.

[@Matepp92]

Great video, thank you! Just a note: the 'Bolyai' name is pronounced nothing like in the video. 'Bo' is fine as you have used it, 'ly' in hungarian is pronounced as the 'y' in 'key'. 'a' and 'i' are pronounced separately with 'a' is something close to the 'a' in 'call' and 'i' being a shorter 'e' in 'we'. Actually I just typed into google now how to pronounce the name and the first couple of results all did a good job.

[@martonfejer6550]

Also the first name: [ˈjaːnoʃ]

[@kikicsoda]

Dzsánosz :D

[@vencdee]

Ya:nosh

[@agarsorchids7708]

You are all Hungarians! Only we care, but that is ok!😉

[@a1s2d3f4g5q1w2e3]

​@@agarsorchids7708I also care

[@athosgomesfonseca]

I discovered your channel whilst wrongfully incarcerated in the US and for roughly eight months, you helped me get through the insanity of it all. Now back home in South America, I still tune in. Thank you for great videos on science and math! 🙏🏼

[@bocicsoki]

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!

[@AndreasTriandafilidis]

Learning new and often very complicated things is always so joyful and easy with your videos and passion. Thanks Veritasium team!

[@Ad_Valorem]

This is one of the best science/math videos - informative, well-organized, and produced - I've ever seen on KZbin. Thanks!

[@realdragon]

And sometimes not true at all

[@devshankarnair6344]

@@realdragon then in your opinion which one is?

[@realdragon]

@@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

[@mayanktripathi8726]

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?

[@Explorinity]

It's amazing how Veritasium brings out such interesting content of Science. His element of suspense and the wide applications of that topic to other fields makes his videos no less than a film. Great to have creators like Derek. I can understand it takes a lot of time and effort to bring out such amazing content. I heartfully appreciate your work sir.

[@ChhandaDas-bl9oy]

True ... His videos are absolutely amazing...

[@barnabas.csermely]

Would have been a lot of time to say his name correctly.

[@petsandpaws8906]

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.

[@life-style6605]

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 🙂

[@AndreLobov]

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.

[@learninggodot]

I am a physics and astronomy student and next week I have exams, was getting really demotivated due to the difficulty, but this video re-ignited the candle of my interest. Thanks

[@lucaswalker6075]

Hypothetically if the universe is “flat” then its has to have and observable “height” almost like a rectangular prism from the side our things traveling through space could only follow one plane

[@LordGino]

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.

[@sabotagedgamerz]

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.

[@doyourownresearch7297]

i prefer calmly delivered and measured geometry.

[@Stoned_to_death_metal]

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.

[@WhatHappensIfIDoThis]

That was one of the best explainations I have heard & I want to thank you for the time & effort put into this video!!

[@ilikemoviesandmore]

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.

[@fikipilot]

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.

[@chrisn8349]

18:57 Geometry as a game with three different worlds is a really cool way to explain this.

[@matthewcarlton5693]

This video should win the Nobel Prize for the category of explaining really hard and interesting math for masses.