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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 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.
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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. —
Conway, J. (1970). The game of life. Scientific American, 223(4), 4. —
Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. —
Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. —
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. —
Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. —
Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. —
Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. —
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. —
Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. —
Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. —
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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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From Pop Star to Slimmer Self: Unveiling Kelly Clarkson's Weight Loss Secrets
Kelly Clarkson, a renowned American singer and TV personality, has been open about her weight struggles in the past. However, with dedication and perseverance, she managed to achieve significant weight loss that has transformed both her physical appearance and mental well-being.
Breaking Down Weight Loss Myths: What Really Works
When it comes to shedding unwanted pounds, there are numerous fad diets and quick fixes advertised on social media or touted by celebrities. Clarkson's approach is refreshingly different from these gimmicks; she emphasizes the importance of understanding how our bodies work in conjunction with a balanced diet and regular exercise.
Clarkson attributes her weight loss success to maintaining a healthy lifestyle that includes portion control, choosing whole foods over processed ones, and staying hydrated throughout the day. She has often shared on social media about incorporating physical activities into her daily routine such as running or simply taking longer walks around town during breaks from filming.
The Role of Mindful Eating in Achieving Weight Loss Goals
While maintaining a healthy weight can be challenging for many people due to emotional eating habits, mindful eating practices have proven beneficial for both Clarkson and millions worldwide who strive towards their wellness goals. This approach focuses on savoring each meal without distractions like TV or smartphones which allow us more time with food that ultimately lead better consumption choices.
For Kelly, practicing mindfulness not only helps her make healthier choices but also reduces anxiety levels allowing her focus entirely one goal staying happy fit and balanced life balance she strives for daily routine now serves as foundation successful journey.
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