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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 🤍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. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 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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HeQX2HjkcNo&t=20m09s 20:09 No. If you prove it is false, you have proved that there is a proof to it.
I swear this is my favourite video on the internet. I've watched it easily 20 times
I swear this is my favourite video on the internet. I've watched it easily 20 times
Great video!
Turing's legacy lives on in everyday parlance among software engineers. When talking about a new novel programming language we always ask "Is it Turing complete?" Which asks if any system of logic can be expressed in it. HTML and XML for example are not Turing complete, where as JavaScript and c++ is.
HeQX2HjkcNo&t=1m13s 1:13 re: John Conway, "sadly, he passed away in 2020 from Covid 19" – the existence of which also happens to be impossible to prove.
the real question is: are there true unprovable statements that are not self referencing?
HeQX2HjkcNo&t=15m15s 15:15 - The fact that it was Neumann who paid attention doesn't surprise me. The guy was genius among geniuses. In fact upon hearing Gödel he quickly realized and proved inconsistency by himself. Only when he took it to Gödel, he was informed Gödel already submitted work on that also.
simple. Infinity does not exist as everything is finite. fixed. Fields Medal please
The first law of the heavens above is order. The one who gave the first law of that order is God. To know God is the beginning of wisdom in understanding the law of order in the heavens.
HeQX2HjkcNo&t=25m00s 25:00 I love this. It explains the dimensions of thought processing patterns
HeQX2HjkcNo&t=20m00s 20:00
“Statements that are true but have no proof”
HeQX2HjkcNo&t=9m30s 9:30 - HeQX2HjkcNo&t=10m10s 10:10
Very humorous. Especially If you take the “h” out of shave..
HeQX2HjkcNo&t=6m20s 6:20 - HeQX2HjkcNo&t=6m45s 6:45
The Reals list can never be created because its infinite which means you can never finish the diagonal which means the diagonal is in a superstate of existing and not existing
It’s like saying that something can live longer than eternity.😂
Apparently, your definition of infinity and mine are different.😂
I can not live long enough to figure out the results of most every arrangement, so I can't solve all of them. BUT, that doesn't mean every single one of them is not fully predictable.
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