Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015

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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Derek Muller, Adam Becker and Jonny Hyman
Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jonny Hyman
Math City Animation by Another Angle 3D Visuals (www.anotherangle.ee)
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music and SFX by Jonny Hyman Additional Music from Epidemic Sound
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett
Associate Producers: Petr Lebedev and Emily Zhang

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Mounting evidence suggests a lot of published research is false.
Check out Audible: http://bit.ly/AudibleVe
Support Veritasium on Patreon: http://bit.ly/VePatreon

Patreon supporters:
Bryan Baker, Donal Botkin, Tony Fadell, Jason Buster, Saeed Alghamdi

More information on this topic: http://wke.lt/w/s/z0wmO

The Preregistration Challenge: https://cos.io/prereg/

Resources used in the making of this video:

Why Most Published Research Findings Are False:
http://journals.plos.org/plosm....edicine/article?id=1

Trouble at the Lab:
http://www.economist.com/news/....briefing/21588057-sc

Science isn't broken:
http://fivethirtyeight.com/fea....tures/science-isnt-b

Visual effects by Gustavo Rosa

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Join me Thursday October 29th at 2:30PM Eastern time as I welcome to the Mbongi, Psychologist and Africologist, Wade Nobles, PhD. Dr. Nobles is a founding member of the Association of Black Psychologists and former national President (1994-95). He is Professor Emeritus of Africana Studies and Black Psychology at San Francisco State University and the author of over one hundred (100) articles, chapters, research reports and books; the co-author of the seminal article in Black Psychology, Voodoo or IQ: An Introduction to African Psychology. In this conversation we will discuss Black Psychology today, in what areas it has been most successful and other areas needed currently to further permeate, and current and future works in the making. This will be a powerful powerful show that you do not want to miss. So set your reminder, like, and share with friends and colleagues.

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This animation by Nucleus shows you the function of plant and animal cells for middle school and high school biology, including organelles like the nucleus, nucleolus, DNA (chromosomes), ribosomes, mitochondria, etc. Also included are ATP molecules, cytoskeleton, cytoplasm, microtubules, proteins, chloroplasts, chlorophyll, cell walls, cell membrane, cilia, flagellae, etc.

Watch another version of this video, narrated by biology teacher Joanne Jezequel here: https://youtu.be/cbiyKH9uPUw



#cell #nucleus #biology
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Watch other Nucleus Biology videos:
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- Active Transport: https://youtu.be/ufCiGz75DAk

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