L'Ultimo Teorema di FERMAT: Una Storia durata 350 anni! Come prendere una mosca sulla LUNA!

It all started with a sentence written in the margin of a 17th-century book, in which Pierre de Fermat claimed to have a "wonderful proof" of a theorem... but it was too large to fit in the available space. That note would launch one of the longest adventures in mathematics. The problem seems simple: for the exponent 2, we obtain the Pythagorean theorem, but what happens if the exponent is larger? Fermat maintains that there are no solutions, but leaves no proof. In the following centuries, mathematicians such as Euler, Gauss, Sophie Germain, Legendre, and Dirichlet tackled the mystery, each making important contributions. In the 19th century, Ernst Kummer even invented new mathematical tools—ideals—to advance the proof. Meanwhile, other discoveries transformed research: elliptic integrals, elliptic curves, the first ideas of algebraic geometry, and the Taniyama–Shimura conjecture, which surprisingly linked geometry and number theory. In the 1980s, Frey and Ribet showed that, if a solution to Fermat's equation truly existed, an "impossible" elliptic curve would arise, contradicting that famous conjecture. And then Andrew Wiles entered the scene: an English mathematician who, as a child, had dreamed of solving that problem. Working in secret for years, he built new theories and announced the proof in 1993. After an initial error, he managed to correct it together with Richard Taylor. After 350 years, the puzzle was finally solved. Fermat's theorem, which began as a footnote, became one of the most extraordinary triumphs of modern mathematics. #Fermat #Fermat'sLastTheorem #AndrewWiles #HistoryOfMathematics #Mathematics #MathHistory #NumberTheory #EllipticCurves #TaniyamaShimura #Kummer #SophieGermain #Gauss #Euler #Ribet #Frey #Faltings #EllipticIntegrals #FreyCurve #Pythagoras #PythagorasTheorem #PopularMathematics #MathExplained #Science #ScienceChannel #Mathematicians #MathematicalPuzzles #historyofscience ⭐️Subscribe and board the science spaceship ⭐️:    / @yousciences   Where Find me 💎: ➤YOUSCIENCES: https://www.yousciences.it/ ➤OFFICIAL WEBSITE: https://www.giuseppesottile.it/ ➤INSTAGRAM: @yousciences @___giux___ ➤FACEBOOK:   / giuseppe.sottile.56   ➤LINKEDIN:   / giuseppe-sottile-3a8599b0   ➤TELEGRAM: https://t.me/joinchat/abNZYJqE7MVlODA0 ➤TIKTOK: https://www.tiktok.com/@yousciences?l... Other videos by: Various ⚛️:    • Various   📽️ VIDEO STREAM ALL: https://www.yousciences.it/videostream/ https://www.giuseppesottile.it/video.php Chapter Summary 00:00 Overture: A Fly on the Moon! 1:16 Fermat's Last Theorem 1:50 Pythagorean Triples 3:11 Pierre De Fermat 5:00 Infinite Descent 6:25 The Race to Prove 7:20 An Army of Amateurs 8:24 Kummer's Ideals 11:10 New Ideas 12:30 Elliptic Integrals 15:46 Gender 17:50 A Prize 19:15 The End of History 22:30 Taniyama-Shimura-Weil 23:25 Frey and Ribet 24:05 Andrew Wiles Executive Production by GIUX