-
Mathematics - Russell's Paradox
In this video, I show you the basics around Russell's Paradox and how to overcome it. Enjoy:)
published: 25 Mar 2013
-
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.
Thank you to Professor Joel David Hamkins for your help with this video.
Hi! I'm Jade. Subscribe to Up and Atom for physics, math and computer science videos!
*SUBSCRIBE TO UP AND ATOM* https://www.youtube.com/c/upandatom
Visit the Up and Atom Store
https://store.nebula.app/collections/up-and-atom
*Follow me* @upndatom
Up and Atom on Instagram: https://www.instagram.com/upndatom/
Up and Atom on Twitter: https://twitter.com/upndatom?lang=en
A big thank you to my AMAZING PATRONS!
Purple Penguin, Pierre-Yves Gatouillat, Ofer Mustigman, Daeil Kim, Harsh Tank, Alan McNea, Daniel Tan-Holmes, Simon Mackenzie, Lynn Shackelford, Richard Far...
published: 25 Mar 2019
-
Russell's Paradox - a simple explanation of a profound problem
I am writing a book! If you want to know when it is ready (and maybe win a free copy), submit your email on my website: https://www.jeffreykaplan.org/
I won’t spam you or share your email address with anyone.
This is a video lecture explaining Russell's Paradox. At the very heart of logic and mathematics, there is a paradox that has yet to be resolved. It was discovered by the mathematician and philosopher, Bertrand Russell, in 1901. In this talk, Professor Jeffrey Kaplan teaches you the basics of set theory (a foundational branch of mathematics dating back to the 1870s) in 20 minutes. Then he explains Russell’s Paradox, which is quite a thrilling thing if you are learning it for the first time. Finally, Kaplan argues that the paradox goes even deeper than Russell himself realized.
Also...
published: 08 Sep 2022
-
Definition: Russell's paradox
Russell's paradox is a standard way to show naïve set theory is flawed.
Naïve set theory uses the comprehension principle. This states that 'given any property there exists a set containing all objects that have that property'.
Russell's paradox demonstrates the looseness of this definition leads to a contradiction.
Consider the set defined by the property:
'The set of all sets which don't contain themselves.'
You will see in the video that this leads to a contradiction.
published: 13 Jun 2012
-
What is Bertrand Russels Barber Paradox?
Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we naturally assume that an answer must exist. In the case of Bertrand Russell's Barber Paradox, a solution does exist, but it becomes even less obvious than other statements like it.
Proposed by Bertrand Russell in the early 1900s, the barber paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves. These statements may seem simple at first, but a paradoxical proposition arises: who shaves the barber?
Let's take a look and see just what's going on in this puzzling paradox...
All images courtesy of Creative Commons or protected under...
published: 29 Aug 2022
-
Russell's Paradox Unraveled: A Journey with Bertrand Russell
Join Bertrand Russell, one of the 20th century's greatest minds, as he takes you on a fascinating journey through logic and paradoxes. In this video, Russell himself unveils the paradox that bears his name and revolutionized set theory. You'll uncover the twists and turns of the barber paradox, grapple with complex mathematical ideas, and discover the profound impact Russell's work has had on mathematics and philosophy. Suitable for all ages, this video is a must-watch for anyone curious about the captivating world of mathematical paradoxes.
Keywords: Bertrand Russell, Russell's paradox, set theory, logic, philosophy, mathematics, mathematical logic, paradoxes, history of mathematics, philosophy of mathematics, foundational crisis, type theory
Also be sure to check out these amazing STEM...
published: 17 May 2023
-
Set Theory - Russell's Paradox: Oxford Mathematics 3rd Year Student Lecture
This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes:
"Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Modern mathematics can be built on set theory. These lectures begin to explore how".
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):
https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year l...
published: 12 Sep 2021
-
Bertrand Russell, Set Theory and Russell's Paradox - Professor Tony Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes. Bertrand Russell is a towering figure in Mathematics and Philosophy for his paradox, which is wonderfully explained here. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/
published: 22 Feb 2015
-
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
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
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Support us on Patreon: http://bit.ly/TEDEdPatreon
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Conn...
published: 20 Jul 2021
-
Math's Fundamental Flaw
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.
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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 Pres...
published: 22 May 2021
3:03
Mathematics - Russell's Paradox
In this video, I show you the basics around Russell's Paradox and how to overcome it. Enjoy:)
In this video, I show you the basics around Russell's Paradox and how to overcome it. Enjoy:)
https://wn.com/Mathematics_Russell's_Paradox
In this video, I show you the basics around Russell's Paradox and how to overcome it. Enjoy:)
- published: 25 Mar 2013
- views: 231543
14:15
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.
Thank you...
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.
Thank you to Professor Joel David Hamkins for your help with this video.
Hi! I'm Jade. Subscribe to Up and Atom for physics, math and computer science videos!
*SUBSCRIBE TO UP AND ATOM* https://www.youtube.com/c/upandatom
Visit the Up and Atom Store
https://store.nebula.app/collections/up-and-atom
*Follow me* @upndatom
Up and Atom on Instagram: https://www.instagram.com/upndatom/
Up and Atom on Twitter: https://twitter.com/upndatom?lang=en
A big thank you to my AMAZING PATRONS!
Purple Penguin, Pierre-Yves Gatouillat, Ofer Mustigman, Daeil Kim, Harsh Tank, Alan McNea, Daniel Tan-Holmes, Simon Mackenzie, Lynn Shackelford, Richard Farrer, Adam Thornton, Dag-Erling Smørgrav, Chris Flynn, Andrew Pann, Anne Tan, Joe Court, Bob Wolford, Matt G, Bookmobile, Robert Maxon, Timur Kiyui, Ayan Doss, Broos Nemanic, John Satchell, John Shioli, Sung-Ho Lee, Todd Loreman, Susan Jones, Marc Watkins, Atila Pires dos Santos, Adam J, Roger Johnson, Hervé Dago, Tim Sorbera, Michael McCloskey, Philip Freeman, Bogdan Morosanu, khAnubis, Jareth Arnold, Simon Barker, Shawn Patrick James Kirby, Simon Tobar, Dennis Haupt, Ammaar Esmailjee, Renato Pereira, Simon Dargaville, Noah McCann and Magesh.
If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
https://www.patreon.com/upandatom
For a one time donation, head over to my PayPal :)
https://www.paypal.me/upandatomshows
*Other Videos You Might Like*
Lagrangian Mechanics - A beautiful way to look at the world
https://youtu.be/dPxhTiiq-1A
Complex Numbers - Rotating The Number Line
https://youtu.be/sZrOxm5Gszk
Cantor's Infinity Paradox | Set Theory
https://youtu.be/X56zst79Xjg
*Sources*
https://plato.stanford.edu/entries/russell-paradox/
https://plato.stanford.edu/entries/frege-theorem/
https://plato.stanford.edu/entries/frege/
https://youtu.be/bqGXdh6zb2k
https://youtu.be/xXD57a5BEO0
*Music*
https://www.epidemicsound.com/
https://wn.com/Russell's_Paradox_A_Ripple_In_The_Foundations_Of_Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.
Thank you to Professor Joel David Hamkins for your help with this video.
Hi! I'm Jade. Subscribe to Up and Atom for physics, math and computer science videos!
*SUBSCRIBE TO UP AND ATOM* https://www.youtube.com/c/upandatom
Visit the Up and Atom Store
https://store.nebula.app/collections/up-and-atom
*Follow me* @upndatom
Up and Atom on Instagram: https://www.instagram.com/upndatom/
Up and Atom on Twitter: https://twitter.com/upndatom?lang=en
A big thank you to my AMAZING PATRONS!
Purple Penguin, Pierre-Yves Gatouillat, Ofer Mustigman, Daeil Kim, Harsh Tank, Alan McNea, Daniel Tan-Holmes, Simon Mackenzie, Lynn Shackelford, Richard Farrer, Adam Thornton, Dag-Erling Smørgrav, Chris Flynn, Andrew Pann, Anne Tan, Joe Court, Bob Wolford, Matt G, Bookmobile, Robert Maxon, Timur Kiyui, Ayan Doss, Broos Nemanic, John Satchell, John Shioli, Sung-Ho Lee, Todd Loreman, Susan Jones, Marc Watkins, Atila Pires dos Santos, Adam J, Roger Johnson, Hervé Dago, Tim Sorbera, Michael McCloskey, Philip Freeman, Bogdan Morosanu, khAnubis, Jareth Arnold, Simon Barker, Shawn Patrick James Kirby, Simon Tobar, Dennis Haupt, Ammaar Esmailjee, Renato Pereira, Simon Dargaville, Noah McCann and Magesh.
If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
https://www.patreon.com/upandatom
For a one time donation, head over to my PayPal :)
https://www.paypal.me/upandatomshows
*Other Videos You Might Like*
Lagrangian Mechanics - A beautiful way to look at the world
https://youtu.be/dPxhTiiq-1A
Complex Numbers - Rotating The Number Line
https://youtu.be/sZrOxm5Gszk
Cantor's Infinity Paradox | Set Theory
https://youtu.be/X56zst79Xjg
*Sources*
https://plato.stanford.edu/entries/russell-paradox/
https://plato.stanford.edu/entries/frege-theorem/
https://plato.stanford.edu/entries/frege/
https://youtu.be/bqGXdh6zb2k
https://youtu.be/xXD57a5BEO0
*Music*
https://www.epidemicsound.com/
- published: 25 Mar 2019
- views: 1409045
28:28
Russell's Paradox - a simple explanation of a profound problem
I am writing a book! If you want to know when it is ready (and maybe win a free copy), submit your email on my website: https://www.jeffreykaplan.org/
I won’t ...
I am writing a book! If you want to know when it is ready (and maybe win a free copy), submit your email on my website: https://www.jeffreykaplan.org/
I won’t spam you or share your email address with anyone.
This is a video lecture explaining Russell's Paradox. At the very heart of logic and mathematics, there is a paradox that has yet to be resolved. It was discovered by the mathematician and philosopher, Bertrand Russell, in 1901. In this talk, Professor Jeffrey Kaplan teaches you the basics of set theory (a foundational branch of mathematics dating back to the 1870s) in 20 minutes. Then he explains Russell’s Paradox, which is quite a thrilling thing if you are learning it for the first time. Finally, Kaplan argues that the paradox goes even deeper than Russell himself realized.
Also, I should mention Georg Cantor, Gotlob Frege, Logicism, and Zermelo–Fraenkel set theory in this description for keyword search reasons.
https://wn.com/Russell's_Paradox_A_Simple_Explanation_Of_A_Profound_Problem
I am writing a book! If you want to know when it is ready (and maybe win a free copy), submit your email on my website: https://www.jeffreykaplan.org/
I won’t spam you or share your email address with anyone.
This is a video lecture explaining Russell's Paradox. At the very heart of logic and mathematics, there is a paradox that has yet to be resolved. It was discovered by the mathematician and philosopher, Bertrand Russell, in 1901. In this talk, Professor Jeffrey Kaplan teaches you the basics of set theory (a foundational branch of mathematics dating back to the 1870s) in 20 minutes. Then he explains Russell’s Paradox, which is quite a thrilling thing if you are learning it for the first time. Finally, Kaplan argues that the paradox goes even deeper than Russell himself realized.
Also, I should mention Georg Cantor, Gotlob Frege, Logicism, and Zermelo–Fraenkel set theory in this description for keyword search reasons.
- published: 08 Sep 2022
- views: 8105746
1:53
Definition: Russell's paradox
Russell's paradox is a standard way to show naïve set theory is flawed.
Naïve set theory uses the comprehension principle. This states that 'given any property ...
Russell's paradox is a standard way to show naïve set theory is flawed.
Naïve set theory uses the comprehension principle. This states that 'given any property there exists a set containing all objects that have that property'.
Russell's paradox demonstrates the looseness of this definition leads to a contradiction.
Consider the set defined by the property:
'The set of all sets which don't contain themselves.'
You will see in the video that this leads to a contradiction.
https://wn.com/Definition_Russell's_Paradox
Russell's paradox is a standard way to show naïve set theory is flawed.
Naïve set theory uses the comprehension principle. This states that 'given any property there exists a set containing all objects that have that property'.
Russell's paradox demonstrates the looseness of this definition leads to a contradiction.
Consider the set defined by the property:
'The set of all sets which don't contain themselves.'
You will see in the video that this leads to a contradiction.
- published: 13 Jun 2012
- views: 45573
2:15
What is Bertrand Russels Barber Paradox?
Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we natural...
Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we naturally assume that an answer must exist. In the case of Bertrand Russell's Barber Paradox, a solution does exist, but it becomes even less obvious than other statements like it.
Proposed by Bertrand Russell in the early 1900s, the barber paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves. These statements may seem simple at first, but a paradoxical proposition arises: who shaves the barber?
Let's take a look and see just what's going on in this puzzling paradox...
All images courtesy of Creative Commons or protected under Fair Use. For questions or concerns about the use of any media, please contact the page directly.
https://wn.com/What_Is_Bertrand_Russels_Barber_Paradox
Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we naturally assume that an answer must exist. In the case of Bertrand Russell's Barber Paradox, a solution does exist, but it becomes even less obvious than other statements like it.
Proposed by Bertrand Russell in the early 1900s, the barber paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves. These statements may seem simple at first, but a paradoxical proposition arises: who shaves the barber?
Let's take a look and see just what's going on in this puzzling paradox...
All images courtesy of Creative Commons or protected under Fair Use. For questions or concerns about the use of any media, please contact the page directly.
- published: 29 Aug 2022
- views: 30107
3:27
Russell's Paradox Unraveled: A Journey with Bertrand Russell
Join Bertrand Russell, one of the 20th century's greatest minds, as he takes you on a fascinating journey through logic and paradoxes. In this video, Russell hi...
Join Bertrand Russell, one of the 20th century's greatest minds, as he takes you on a fascinating journey through logic and paradoxes. In this video, Russell himself unveils the paradox that bears his name and revolutionized set theory. You'll uncover the twists and turns of the barber paradox, grapple with complex mathematical ideas, and discover the profound impact Russell's work has had on mathematics and philosophy. Suitable for all ages, this video is a must-watch for anyone curious about the captivating world of mathematical paradoxes.
Keywords: Bertrand Russell, Russell's paradox, set theory, logic, philosophy, mathematics, mathematical logic, paradoxes, history of mathematics, philosophy of mathematics, foundational crisis, type theory
Also be sure to check out these amazing STEM-related creators on Bertrand Russel and his paradox!
Up and Atom: https://www.youtube.com/watch?v=xauCQpnbNAM
Jeffrey Kaplan: https://www.youtube.com/watch?v=ymGt7I4Yn3k
Numberphile: https://www.youtube.com/watch?v=mZBwsm6B280
https://wn.com/Russell's_Paradox_Unraveled_A_Journey_With_Bertrand_Russell
Join Bertrand Russell, one of the 20th century's greatest minds, as he takes you on a fascinating journey through logic and paradoxes. In this video, Russell himself unveils the paradox that bears his name and revolutionized set theory. You'll uncover the twists and turns of the barber paradox, grapple with complex mathematical ideas, and discover the profound impact Russell's work has had on mathematics and philosophy. Suitable for all ages, this video is a must-watch for anyone curious about the captivating world of mathematical paradoxes.
Keywords: Bertrand Russell, Russell's paradox, set theory, logic, philosophy, mathematics, mathematical logic, paradoxes, history of mathematics, philosophy of mathematics, foundational crisis, type theory
Also be sure to check out these amazing STEM-related creators on Bertrand Russel and his paradox!
Up and Atom: https://www.youtube.com/watch?v=xauCQpnbNAM
Jeffrey Kaplan: https://www.youtube.com/watch?v=ymGt7I4Yn3k
Numberphile: https://www.youtube.com/watch?v=mZBwsm6B280
- published: 17 May 2023
- views: 19066
6:47
Set Theory - Russell's Paradox: Oxford Mathematics 3rd Year Student Lecture
This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes:
"Infinity baffled mathematicians, and everyone else, for thou...
This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes:
"Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Modern mathematics can be built on set theory. These lectures begin to explore how".
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):
https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
https://wn.com/Set_Theory_Russell's_Paradox_Oxford_Mathematics_3Rd_Year_Student_Lecture
This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes:
"Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. Modern mathematics can be built on set theory. These lectures begin to explore how".
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):
https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
- published: 12 Sep 2021
- views: 10176
5:20
Bertrand Russell, Set Theory and Russell's Paradox - Professor Tony Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes. Bertrand Russell is a towering figure in Mathematics and Philosophy for his par...
A short mind-bending trip through the wonderful world of Mathematical Paradoxes. Bertrand Russell is a towering figure in Mathematics and Philosophy for his paradox, which is wonderfully explained here. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/
https://wn.com/Bertrand_Russell,_Set_Theory_And_Russell's_Paradox_Professor_Tony_Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes. Bertrand Russell is a towering figure in Mathematics and Philosophy for his paradox, which is wonderfully explained here. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/
- published: 22 Feb 2015
- views: 50296
5:20
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements.
--
Consider the following sentence: “...
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
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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.
https://wn.com/The_Paradox_At_The_Heart_Of_Mathematics_Gödel's_Incompleteness_Theorem_Marcus_Du_Sautoy
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
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Support us on Patreon: http://bit.ly/TEDEdPatreon
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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.
- published: 20 Jul 2021
- views: 3814072
34:00
Math's Fundamental Flaw
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 ...
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.
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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. — 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
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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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https://wn.com/Math's_Fundamental_Flaw
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
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
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
▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
- published: 22 May 2021
- views: 27915597