Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war, and led to the creation of modern computers. SUBSCRIBE http://bit.ly/Subscribe_Veritasium_EN Special thanks to Professor Asaf Karagila for consultation on set theory and specific rewrites, Professor Alex Kontorovich for reviews of earlier drafts, Professor Toby 'Qubit' Cubitt for help with the spectral gap, and Henry Reich for help with feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 Quote attribution from Poincare, The Mathematical Intelligencer, Vol. 13, No. 1, Winter 1991. - https://ve42.co/Poincare Irvine, AD, and 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 and III, 1927, paperback edition a* 56. Cambridge UP. - https://ve42.co/Russel1910 Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, United States. - https://ve42.co/Godel1986 Cubitt, TS, Perez-Garcia, D., & Wolf, MM (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 by Epidemic Sound Additional video supplied by Getty Images Thumbnail by Geoff Barrett Associate Producers: Petr Lebedev and Emily Zhang Maths Has a Terrible Flaw You can't prove everything that is true Video in English from the @veritasium Channel: • Math's Fundamental Flaw Math Has a Fatal Flaw ------------------------------------------------------------------------ ???? This Youtube channel is managed by: https://www.unilingo.tv/ ❓Comments or translation suggestions: [email protected] ------------------------------------------------------------------------ #veritasiumenespañol