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 https://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. — 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

▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
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

▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
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

▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

This edition of #JournalistsHangout discusses the abduction of students in Kebbi state and other security challenges.

SUBSCRIBE to our YouTube channel for more great videos: http://www.youtube.com/tvcnewsnigeria

Follow us on Twitter: https://twitter.com/tvcnewsng

Like us on Facebook: https://www.facebook.com/tvcnewsng

For more great content go to https://tvcnews.tv

Download our mobile app for iPad, iPhone and Android at http://mobile.tvcnews.tv or go to the store

The rich in Germany been never been as well-off as they are today and assets have never been so unevenly distributed. But who are they? How do they live? And what do they think of their country? A journey into the discreet world of the super-rich.

One percent of Germans own over a quarter of the country's assets, whilst half of the country’s citizens have no assets at all. But while the German media report on the growing poverty in the country on a daily basis, little is known about the super-rich. They keep a very low profile and can walk the streets unrecognized. "Manager Magazin” says there were around 200 billionaires living in Germany in 2018, and their numbers are increasing. The documentary "Top of the World" asks why rich Germans are so unwilling to talk about their wealth. Its author immerses himself in the discreet world of big money and meets financial advisors with 800 years of family tradition behind them and billionaires such as drugstore king Dirk Rossmann and mail-order company heir Michael Otto - as well as a self-made businessmen such as Rainer Schaller. They talk about their notions of money and justice, the origins of their wealth and their fear of social envy.


--------------------------------------------------------------------

DW Documentary gives you knowledge beyond the headlines. Watch high-class documentaries from German broadcasters and international production companies. Meet intriguing people, travel to distant lands, get a look behind the complexities of daily life and build a deeper understanding of current affairs and global events. Subscribe and explore the world around you with DW Documentary.

Subscribe to DW Documentary:
https://www.youtube.com/channe....l/UCW39zufHfsuGgpLvi

Our other YouTube channels:
DW Documental (in spanish): https://www.youtube.com/dwdocumental
DW Documentary وثائقية دي دبليو: (in arabic): https://www.youtube.com/dwdocarabia

For more documentaries visit also:
http://www.dw.com/en/tv/docfilm/s-3610
Instagram
https://www.instagram.com/dwdocumentary/
Facebook:
https://www.facebook.com/dw.stories

DW netiquette policy: https://p.dw.com/p/MF1G

⁣When the Soviet Union collapsed in 1990, Cuba's economy went into a tailspin. With imports of oil cut by more than half – and food by 80 percent – people were desperate. This film tells of the hardships and struggles as well as the community and creativity of the Cuban people during this difficult time. Cubans share how they transitioned from a highly mechanized, industrial agricultural system to one using organic methods of farming and local, urban gardens. It is an unusual look into the Cuban culture during this economic crisis, which they call "The Special Period." The film opens with a short history of Peak Oil, a term for the time in our history when world oil production will reach its all-time peak and begin to decline forever. Cuba, the only country that has faced such a crisis – the massive reduction of fossil fuels – is an example of options and hope.


www.powerofcommunity.org

Many hand dug wells dry up at the end of the dry season, because more water is taken out than is coming in by the natural recharge. Reasons of limited groundwater recharge are heavy rainfall in short time, (climate change) compact topsoil layers, erosion because of loss of vegetation, etc. Options to increase the recharge of ground water are above or underground dams, the planting of trees and plants such as vetivar grass, making contour canals etc. An other option is the so called “Tube recharge”. This low-cost option combines a manually drilled hole with a drainage tube, a filter and a small pond. Rainwater, that otherwise would run off to rivers or evaporate, thus penetrates into the ground and reaches the first aquifer.
Download the free manual from MetaMeta at:
- www.metameta.nl/publications
Also visit:
- https://justdiggit.org
- www.gaia-movement.org