당신이 수학을 모르는 이유. (feat. 불완전성의 정리)

A video with 14 million views! Not everything can be proven false. This fact shed new light on infinity, shortened World War II, and led to the invention of modern computers. I remember questioning the usefulness of mathematics during my school days. Let's take a look at the long journey of mathematical endeavors, through various stories in the world of mathematics, that led to the computers and mobile phones you're watching in this video. Still confused after watching the video? That's normal. We don't! Supports 4K video. ** The part where it says B is a subset of A, because books fall like all other objects, is a mistake. Think of B as a piece of paper that fell together... Appearance: Hilbert, Gödel, Feynman, von Neumann, Henri Poincaré, and other legendary geniuses... #IfYouDon'tUnderstandEvenAfterWatchingTheVideo #CatchUp #StartWithMe Game of Life = 'The Game of Life' seems more natural. Corrected translation error 10:04 - "Therefore, the razor cannot shave himself, but he must shave because he is a man, which leads to a contradiction." (Corrected) "The razor in the village must shave 'all' men who do not shave themselves, but he cannot shave himself, which leads to a contradiction." You are correct. 10:17 - "Zermelo, a mathematician from the Hilbert School" (Corrected) Zermelo, a mathematician from the Hilbert School" 18:30 - "This axiom can be proven through the simplest proof, which states that 1 and 0 are not equal, by replacing x with 0." (Edit) This axiom completes the proof of the proposition that "1 and 0 are not equal" when 0 is substituted for x. Subtitle Edit 12:46 - (Edit) princi'p'ia Mathmatica 31:41 - (Edit) Laid the foundation. Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, to Prof. Toby 'Qubit' Cubitt for the help with the spectral gap, and to Henry Reich for the helpful feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Referenced Papers 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 Dubbed by Mingi Kwon Additional Edited by Jaehyuk Jung Translated by Yuna Lee ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Original video: Math's Fundamental Flaw Channel: @veritasium