The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

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Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Connect With Us ---------------------------------------------- Sign up for our newsletter: http://bit.ly/TEDEdNewsletter Follow us on Facebook: http://bit.ly/TEDEdFacebook Find us on Twitter: http://bit.ly/TEDEdTwitter Peep us on Instagram: http://bit.ly/TEDEdInstagram ---------------------------------------------- Keep Learning ---------------------------------------------- View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper Animator's website: https://basaestudio.com ---------------------------------------------- Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.

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The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

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,Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Connect With Us ---------------------------------------------- Sign up for our newsletter: http://bit.ly/TEDEdNewsletter Follow us on Facebook: http://bit.ly/TEDEdFacebook Find us on Twitter: http://bit.ly/TEDEdTwitter Peep us on Instagram: http://bit.ly/TEDEdInstagram ---------------------------------------------- Keep Learning ---------------------------------------------- View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper Animator's website: https://basaestudio.com ---------------------------------------------- Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.