Math's Fundamental Flaw
27,016,963
Published 2021-05-22
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. — ve42.co/Dunham2013
Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — ve42.co/Conway1970
Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — ve42.co/Churchill2019
Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — 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. — ve42.co/Lnrt2010
Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — ve42.co/Poincare
Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — ve42.co/Irvine1995
Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — 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. — ve42.co/Russel1910
Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — ve42.co/Godel1986
Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — 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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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
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All Comments (21)
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Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die
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I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another
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Everytime people get into the weeds with math like this i feel like im just listening to philosophy with a different label.
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Why didn't they just have three people stand beside John Conway after he died?
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So basically... Can math prove itself? No. But math can prove that math can't prove itself.
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Godel's friends: "No one's trying to kill you Godel" Godel: "You can't prove that!"
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So this is how these things are connected to each other. In my CS degree we had to study about almost every one of these topics (at least a very little of every topic) and they seemed very disconnected and apart of each other. Discrete mathematics, Automata, Set theory, proofs... etc. This video connects dots. An actual tear fell from my eye at the end of video. Thanks for making these amazing videos.
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Truly one of the greatest mathematics-related video out there on YouTube. I often find myself returning back to this video, and thanks to you, I was inspired to major in engineering. I started loving math; it's such a great language!
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I love how the set theorists answer to self reference was "I changed the definition so that doesnt count."
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Ah yes, the iconic half way point of the video where I stop comprehending a single thing said
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I love how tightly intertwined mathematics and philosophy are
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I learn about the Veritasium by watching this video about 2 years ago, and it turned out to be the most valuable 30 minutes that I spent on the internet. Maths became almost religious to me after watching it, for it is capable of proving its own limitations within its limited system, although my father kinda disagrees with me on the religious part as a professional in maths. But there's a reason for me. It actually reminds me of the philosophical question of "what we are" and "what we are made for" since they are also related to the self-reference paradox. I have been suffering from depression and anxiety at the time when I first saw this video. I was about to graduate but had no idea of what I am going to do nor what is the meaning of my life. But this video somehow saved me. For no reason, I suddenly feel relaxed after learning about Godel number and the answer and proof to the three questions. I realized that, just like maths, life is not about meaningful or desidablility either, but we may find what we have done meaningful years later. And this is a proven truth. Just like one of the most famous Chinese poems said, "everyone was made with some talent that must be useful". Anyway. I finally found my own belief after watching this video. And now, after 2 years, I am back to the college for postgraduate degree and for working out my own value of life. Many thanks to Veritasium for the great work. Wish everyone a great life.
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mom: why did you get a B in math! me: math has a fatal flaw
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If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.
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This is actually the MOST interesting video I have EVER seen. Every minute was amazingly clear and intriguing.
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I've known these topics for years and also watched many videos, I have to say this one is so beautifully done, all those thoughtful illustrations
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"1+1=2" "The above proposition is occasionally useful."
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"How about you just hire another barber?" Said the engineer
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I truly believe that this was the most spectular video I've ever seen on this channel! Congratulations to you and your team, Derek!
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This is top 10 videos of all time. Literally the best explanation ever of one of the most interesting scientific (and existential) concepts.