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

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

Discover strange new universes that turn up at the core of Einstein’s General Relativity. Head to 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 –

If you want to play around in hyperbolic space then check out:

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 –

Geodesy survey via ams –

John Wheeler via NAS Online –

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. –

Euclid’s Elements, Wikipedia –

The History of Non-Euclidean Geometry, Extra History via YouTube –

We (could) live on a 4D Pringle – Physics for the Birds via YouTube –

Parallel Postulate, Wikipedia –

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. –

Bolyai, J. (1896). The Science Absolute of Space.. (Vol. 3). The Neomon.

Gauss, Wikipedia –

Landvermessung, D. Z. (1929). Abhandlungen ueber Gauss’ wissenschaftliche Taetigkeit auf den Gebieten der Geodaesie, Physik und Astronomie Bd. 11, Abt. –

Nikolai Lobachevsky, Wikipedia –

Lobachevskiĭ, N. I. (1891). Geometrical researches on the theory of parallels. University of Texas.

A Problem with the Parallel Postulate, Numberphile via YouTube –

Riemann, B. (2016). On the hypotheses which lie at the bases of geometry. Birkhäuser. –

Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891-921. –

Why Gravity is NOT a Force, Veritasium via YouTube –

ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. –

Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background. –

Secrets of the Cosmic Microwave Background, PBS Spacetime via YouTube –

Wood, C. (2020). How Ancient Light Reveals the Universe’s Contents. Quanta Magazine. –

Collaboration (2014). Planck 2013 results. XVI. Cosmological parameters. A&A, 571, A16. –

WMAP Science Team, NASA. (2014). Matter in the Universe. WMAP, NASA. –

Shape of the universe, Wikipedia –

Crocheting Hyperbolic Planes: Daina Taimina by Ted, via YouTube –

Hyperbolic Crochet model –

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Directed by Casper Mebius
Written by Casper Mebius, Petr Lebedev, Emily Zhang and Derek Muller
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

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23 Responses

  1. bob1235 says:

    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 says:

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

    • sasmk says:

      Standing on the shoulders of giants

    • Colonel Corn says:

      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 says:

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

    • EebstertheGreat says:

      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._

  2. Jacopo Libera says:

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

  3. FetchDrierDoyle says:

    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.

  4. xi yi says:

    que bueno que finalmente alguien le da la importancia y grandeza que János Bolyai tiene. sus matematicas son verdades puras..🥰

  5. Thomas says:

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

  6. flintsparks says:

    The amount of work Veritasium puts in his videos is amazing

  7. Trung Hung Pham says:

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

  8. Brian Becher says:

    Thank you for everything you’ve published! I can only imagine what my academic career would have looked like if videos like this had been part of my education in middle and highschool some 20-30 years ago. Gives me hope for future generations.

    • Dana Mason says:

      i imagine i might have had one of those careers myself if so…

      still… i too am filled with excitement for our progeny

  9. Explorinity - Shubhajeet Das says:

    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.

  10. Penny Lane says:

    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.

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