For once, I'm doing something different: in this video, you'll discover not the fate of a person, but of an idea! More precisely, an unproven mathematical theory. A CONJECTURE, as they say. And not just any conjecture, but Fermat's Last Theorem, which is regularly cited as the most important enigma in the history of mathematics.
Fermat, Euler, Germain... many others have tried and failed to solve this conjecture... until... until... well, until you see the end of the video!
This video took me (again) quite a bit of time and research, so thank you for your ever-growing support. Please know that I am truly grateful.
► TO SUPPORT THE CHANNEL:
• Subscribe: @mathadorlachaine
• A small tip?
https://utip.io/mathadorlachaine/
https://fr.tipeee.com/mathador
• Share this video with your friends
• Give it a thumbs up and leave comments
► SOURCES
• My main source for this video is the excellent book: "Fermat's Last Theorem" by Simon Singh, published by Lattès and Hachette Littératures. This book is full of examples and anecdotes that I couldn't include in my video due to space or time constraints. I highly recommend reading it if you enjoyed the video.
Furthermore, I also consulted the following links:
• https://www.maths-et-tiques.fr/index.....
• https://fr.wikipedia.org/wiki/Dernier...
• https://www.echosciences-sud.fr/commu...
• https://www.lemonde.fr/sciences/artic...
• https://www.bibmath.net/dico/index.ph...
• http://serge.mehl.free.fr/chrono/wile...
►ERRATUM
• The video states that Ribet's work, proving that Fermat's theory derives from Taniyama-Shimura dates from the 1960s. This is an error. Ribet's article dates from 1986;
• At 3:00, when I say that the infinite number of right triangles implies an infinite number of integer triplets: This reasoning is flawed. The infinity of right triangles does indeed imply an infinite number of triplets, okay... but not necessarily integers.
• Sophie Germain only proved PART of Germain's conjecture for prime numbers.
• At 11:23, there is an anachronism in the illustrations. "At the beginning of the 20th century." The construction of the Eiffel Tower was completed in 1889.
• When I say "He begins his presentation by...", this is incorrect. The verb "débuter" is intransitive; I should have said "he begins his intervention by..."
► SOCIAL MEDIA
• Facebook: Facebook: Mathador-960047670809006
• Twitter: Twitter: mathador5
• Instagram: Instagram: franckdunas
► The Mathador channel is a member of Café des Sciences: https://www.cafe-sciences.org/
For once, I'm doing something different: in this video, you'll discover not the fate of a person, but of an idea! More precisely, an unproven mathematical theory. A CONJECTURE, as they say. And not just any conjecture, but Fermat's Last Theorem, which is regularly cited as the most important enigma in the history of mathematics.
Fermat, Euler, Germain... many others have tried and failed to solve this conjecture... until... until... well, until you see the end of the video!
This video took me (again) quite a bit of time and research, so thank you for your ever-growing support. Please know that I am truly grateful.
► TO SUPPORT THE CHANNEL:
• Subscribe: @mathadorlachaine
• A small tip?
https://utip.io/mathadorlachaine/
https://fr.tipeee.com/mathador
• Share this video with your friends
• Give it a thumbs up and leave comments
► SOURCES
• My main source for this video is the excellent book: "Fermat's Last Theorem" by Simon Singh, published by Lattès and Hachette Littératures. This book is full of examples and anecdotes that I couldn't include in my video due to space or time constraints. I highly recommend reading it if you enjoyed the video.
Furthermore, I also consulted the following links:
• https://www.maths-et-tiques.fr/index.....
• https://fr.wikipedia.org/wiki/Dernier...
• https://www.echosciences-sud.fr/commu...
• https://www.lemonde.fr/sciences/artic...
• https://www.bibmath.net/dico/index.ph...
• http://serge.mehl.free.fr/chrono/wile...
►ERRATUM
• The video states that Ribet's work, proving that Fermat's theory derives from Taniyama-Shimura dates from the 1960s. This is an error. Ribet's article dates from 1986;
• At 3:00, when I say that the infinite number of right triangles implies an infinite number of integer triplets: This reasoning is flawed. The infinity of right triangles does indeed imply an infinite number of triplets, okay... but not necessarily integers.
• Sophie Germain only proved PART of Germain's conjecture for prime numbers.
• At 11:23, there is an anachronism in the illustrations. "At the beginning of the 20th century." The construction of the Eiffel Tower was completed in 1889.
• When I say "He begins his presentation by...", this is incorrect. The verb "débuter" is intransitive; I should have said "he begins his intervention by..."
► SOCIAL MEDIA
• Facebook: Facebook: Mathador-960047670809006
• Twitter: Twitter: mathador5
• Instagram: Instagram: franckdunas
► The Mathador channel is a member of Café des Sciences: https://www.cafe-sciences.org/
Par contre, il y a quelques imprécisions mathématiques, même si l'essentiel du contenu est très bon ! J'imagine que cela a été du par la volonté de simplifier et de vulgariser des sujets aussi pointus, avec énormement de nuances et de subtilités.
- Le fait que les triplets pythagoriciens soient nombreux ne peut pas s'expliquer par le fait que les triangles rectangles soient nombreux. Car la plupart des triangles rectangles ne correspondent pas à des triplets pythagoriciens. Pour qu'ils le soient, il faut que leurs longueurs soient commensurables, ce qui filtre les solutions. Sinon, avec ce raisonnement, des solutions réelles de a³ + b³ = c³, il y en a une infinité, et c'est le fait de chercher des solutions rationnelles ou entières qui filtre beaucoup.
- L'unicité de la factorisation en nombres premiers est valable dans les entiers "classiques", mais elle est aussi vraie dans certains anneaux de nombres imaginaires, et elle est fausse dans certains anneaux de nombres réels. Le fait qu'ils soient réels ou imaginaire n'est pas ce qui détermine si un anneau est factoriel. Déterminer avec précision les anneaux de nombres qui sont factoriels est encore un problème ouvert aujourd'hui.
- Les fonctions elliptiques n'étaient pas connues au temps des grecs anciens, car leur découverte se fondait sur les nombres complexes. Leur découverte a été par Guilio Fagnano vers 1730 sur l'étude de la lemniscate. Les formes modulaires ont été introduites précisément pour classifier les fonctions elliptiques : ces deux sujets sont donc liées naturellement. Mais le théorème de modularité (celui conjecturé par Taniyama et Shimura, puis démontré par Wiles) révèle une seconde connexion entre les deux sujets, qui était elle totalement innatendue.
En tout cas, j'ai passé un très bon moment avec cette vidéo qui m'a permis de me plonger dans l'histoire de ce théorème, qui doit être l'un des plus épiques des mathématiques.