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Veritasium ยท Published May 22, 2021
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 โQubitโ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video. โโโโโโโโโโโโโโโโโโโโโโโโโโ 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. โ https://ve42.co/Dunham2013 Conway, J. (1970). The game of life. Scientific American, 223(4), 4. โ https://ve42.co/Conway1970 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. โ 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. โ https://ve42.co/Gaifman2006 Lรฉnรกrt, I. (2010). Gauss, Bolyai, Lobachevskyโin 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. โ https://ve42.co/Lnrt2010 Attribution of Poincareโs quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. โ https://ve42.co/Poincare Irvine, A. D., & Deutsch, H. (1995). Russellโs paradox. โ https://ve42.co/Irvine1995 Gรถdel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. โ 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. โ https://ve42.co/Russel1910 Gรถdel, K. (1986). Kurt Gรถdel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. โ https://ve42.co/Godel1986 Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. โ https://ve42.co/Cubitt2015 โโโโโโโโโโโโโโโโโโโโโโโโโโ 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 โโโโโโโโโโโโโโโโโโโโโโโโโโ Executive Producer: Derek Muller Writers: Adam Becker, Jonny Hyman, Derek Muller Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman SFX & Music: Jonny Hyman Camerapeople: Derek Muller, Raquel Nuno Editors: Derek Muller Producers: Petr Lebedev, Emily Zhang Additional video supplied by Getty Images Thumbnail by Geoff Barrett โโโโโโโโโโโโโโโโโโโโโโโโโโ
