Podcast appearances and mentions of Andrew Wiles

Janna Levin is a theoretical physicist and cosmologist specializing in black holes, cosmology of extra dimensions, topology of the universe, and gravitational waves. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep468-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https://lexfridman.com/janna-levin-transcript CONTACT LEX: Feedback - give feedback to Lex: https://lexfridman.com/survey AMA - submit questions, videos or call-in: https://lexfridman.com/ama Hiring - join our team: https://lexfridman.com/hiring Other - other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Janna's X: https://x.com/JannaLevin Janna's Website: https://jannalevin.com Janna's Instagram: https://instagram.com/jannalevin Janna's Substack: https://substack.com/@jannalevin Black Hole Survival Guide (book): https://amzn.to/3YkJzT5 Black Hole Blues (book): https://amzn.to/42Nw7IE How the Universe Got Its Spots (book): https://amzn.to/4m5De8k A Madman Dreams of Turing Machines (book): https://amzn.to/3GGakvd SPONSORS: To support this podcast, check out our sponsors & get discounts: Brain.fm: Music for focus. Go to https://brain.fm/lex BetterHelp: Online therapy and counseling. Go to https://betterhelp.com/lex NetSuite: Business management software. Go to http://netsuite.com/lex Shopify: Sell stuff online. Go to https://shopify.com/lex AG1: All-in-one daily nutrition drink. Go to https://drinkag1.com/lex OUTLINE: (00:00) - Introduction (00:51) - Sponsors, Comments, and Reflections (09:21) - Black holes (16:55) - Formation of black holes (27:45) - Oppenheimer and the Atomic Bomb (34:08) - Inside the black hole (47:10) - Supermassive black holes (50:39) - Physics of spacetime (53:42) - General relativity (59:13) - Gravity (1:15:47) - Information paradox (1:24:17) - Fuzzballs & soft hair (1:27:28) - ER = EPR (1:34:07) - Firewall (1:42:59) - Extra dimensions (1:45:24) - Aliens (2:01:00) - Wormholes (2:11:57) - Dark matter and dark energy (2:22:00) - Gravitational waves (2:34:08) - Alan Turing and Kurt Godel (2:46:23) - Grigori Perelman, Andrew Wiles, and Terence Tao (2:52:58) - Art and science (3:02:37) - The biggest mystery PODCAST LINKS: - Podcast Website: https://lexfridman.com/podcast - Apple Podcasts: https://apple.co/2lwqZIr - Spotify: https://spoti.fi/2nEwCF8 - RSS: https://lexfridman.com/feed/podcast/ - Podcast Playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 - Clips Channel: https://www.youtube.com/lexclips

Imaginez un théorème si simple à énoncer qu'un collégien pourrait le comprendre… et pourtant, il a défié les plus grands esprits pendant 358 ans !Dans ce hors-série, nous plongeons avec Aurélien et Sébastien dans l'histoire du dernier théorème de Fermat, du "post-it" griffonné par Pierre de Fermat jusqu'à sa démonstration par Andrew Wiles en 1994.En chemin, on parle de cryptographie, d'intelligence artificielle et d'un projet fou : faire comprendre cette preuve à un ordinateur !Un épisode qui lie histoire, science et mathématiques modernes, le tout avec une touche de bonne humeur.

Imaginez un théorème si simple à énoncer qu'un collégien pourrait le comprendre… et pourtant, il a défié les plus grands esprits pendant 358 ans !Dans ce hors-série, nous plongeons avec Aurélien et Sébastien dans l'histoire du dernier théorème de Fermat, du "post-it" griffonné par Pierre de Fermat jusqu'à sa démonstration par Andrew Wiles en 1994.En chemin, on parle de cryptographie, d'intelligence artificielle et d'un projet fou : faire comprendre cette preuve à un ordinateur !Un épisode qui lie histoire, science et mathématiques modernes, le tout avec une touche de bonne humeur.

Episode: 1971 In which Lame, Cauchy, and Kummer race to prove Fermat's last theorem.  Today, guest scientist Andrew Boyd relives a race.

Andrew Wiles. He's credited with having solved the most difficult Math theorem in modern history. And when he announced it, he might as well have been talking about the weather. What a man. God, give us the grace to be so humble.

If you'd like to buy me a coffee or donate you can do so over at ⁠⁠https://ko-fi.com/theunadulteratedintellect⁠⁠. I would seriously appreciate it! __________________________________________________ Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal by the Royal Society. He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018, was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow. Audio source ⁠here⁠⁠ Full Wikipedia entry ⁠here⁠ --- Support this podcast: https://podcasters.spotify.com/pod/show/theunadulteratedintellect/support

"I think I'll stop here." This is how, on 23rd June 1993, Andrew Wiles ended his series of lectures at the Isaac Newton Institute (INI), our neighbour here at the Centre for Mathematical Sciences. The applause, so witnesses report, was thunderous. Wiles had just announced a proof that had eluded mathematicians for over 350 years: the proof of Fermat's Last Theorem. Wiles' announcement, 30 years ago today, was a thrilling moment in mathematical history. But Fermat's Last Theorem is not just the story of one person. Jack Thorne, who works on new mathematics that builds on Wiles' proof, told us that it is actually a story of people talking to each other over a period of centuries. To celebrate 30 years since that exciting moment, we were lucky enough to speak with Andrew Wiles and Jack Thorne, and also to Tom Körner, who was there the day Wiles announced the proof.   This is a special joint episode with the INI's Living Proof podcast, made in collaboration with our friend Dan Aspel, from the INI. You can find out more about Fermat's Last Theorem in the article that accompanies this podcast, and in this collection of further reading.   This podcast was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

The 23rd of June 2023 marks exactly thirty years since Sir Andrew Wiles announced his historic first proof of Fermat's Last Theorem. He did so at the Isaac Newton Institute, during the culmination of three days of special lectures, delivered as part of the June 1993 L-functions and arithmetic programme - one of the first research meetings to take place at the recently founded INI. To mark this happy occasion, we - together with our colleagues at Plus magazine and the Maths on the move! podcast - present this short documentary. In it we speak not only to Wiles himself, but to others who were a part of this historic moment or whose work the proof continues to inspire.Find more, including a video interview with Andrew Wiles and accompanying article, right here: https://www.newton.ac.uk/news/ini-news/wiles-flt-30/ 

Este programa supone la tercera entrega del Quilo de mi profe, Miguel Pocoví Mieras. En el episodio de hoy, Miguel nos introduce por el fascinante mundo del teorema de Fermat, que aparece incluso en varios episodios de los Simpsons, y relata alguno de los terribles avatares sufridos por Andrew Wiles el genial matemático que lo demostró. En 1637 Pierre de Fermat formuló un teorema de la siguiente forma: Si “n” es un número entero mayor que 2, entonces no existen números enteros no nulos “a”,  “b” y “c” tales que se cumpla la igualdad: a&sup n; + b&supn; = c&supn; Es decir, esta igualdad sólo es posible si n=2.

Este programa supone la tercera entrega del Quilo de mi profe, Miguel Pocoví Mieras. En el episodio de hoy, Miguel nos introduce por el fascinante mundo del teorema de Fermat, que aparece incluso en varios episodios de los Simpsons, y relata alguno de los terribles avatares sufridos por Andrew Wiles el genial matemático que lo demostró. En 1637 Pierre de Fermat formuló un teorema de la siguiente forma: Si “n” es un número entero mayor que 2, entonces no existen números enteros no nulos “a”,  “b” y “c” tales que se cumpla la igualdad: a&sup n; + b&supn; = c&supn; Es decir, esta igualdad sólo es posible si n=2.

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Productive Mistakes, Not Perfect Answers, published by Adam Shimi on April 7, 2022 on The AI Alignment Forum. I wouldn't bet on any current alignment proposal. Yet I think that the field is making progress and abounds with interesting opportunities to do even more, giving us a shot. Isn't there a contradiction? No, because research progress so rarely looks like having a clearly correct insight that clarifies everything; instead it often looks like building on apparently unpromising ideas, or studying the structure of the problem. Copernican heliocentrism didn't initially predict observations as well as Ptolemaic astronomy; both ionic theory and the determination of basic molecular formula came from combining multiple approaches in chemistry, each getting some bits but not capturing the whole picture; Computer Science emerged from the arid debate over the foundations of mathematics; and Computational Complexity Theory has made more progress by looking at why some of its problems are hard than by waiting for clean solutions. In the end you do want to solve the problem, obviously. But the road from here to there goes through many seemingly weird and insufficient ideas that are corrected, adapted, refined, often discarded except for a small bit. Alignment is no different, including “strong” alignment. Research advances through productive mistakes, not perfect answers. I'm taking this terminology from Goro Shimura's characterization of his friend Yutaka Taniyama, with whom he formulated the Taniyama-Shimura Conjecture that Andrew Wiles proved in order to prove Fermat's last theorem. (Yutaka Taniyama and his time. Very personal recollections, Goro Shimura, 1989) Though he was by no means a sloppy type, he was gifted with the special capability of making many mistakes, mostly in the right direction. I envied him for this, and tried in vain to imitate him, but found it quite difficult to make good mistakes. So much of scientific progress takes the form of many people proposing different ideas that end up being partially right, where we can look back later and be like “damn, that was capturing a chunk of the solution.” It's very rare that people arrive at the solution of any big scientific problem in one nice sweep of a clearly adequate idea. Even when it looks like it (Einstein is an example people like to bring up), they so often build on many of the weird and contradictory takes that came before, as well as the understanding of how the problem works at all (in Einstein's case, this includes the many, many unconvincing attempts to unify mechanics and electromagnetism, the shape of Maxwell's equations, the ether drag hypothesis, and Galileo's relativity principle; he also made a lot of productive mistakes of his own). Paul Graham actually says the same thing about startups that end up becoming great successes. (What Microsoft Is This The Basic Altair Of?, Paul Graham, 2015) One of the most valuable exercises you can try if you want to understand startups is to look at the most successful companies and explain why they were not as lame as they seemed when they first launched. Because they practically all seemed lame at first. Not just small, lame. Not just the first step up a big mountain. More like the first step into a swamp. Graham proposes a change of polarity in considering lame ideas: instead of looking for flaws, he encourages us to steelman not the idea itself, but how it could lead to greatness. (What Microsoft Is This The Basic Altair Of?, Paul Graham, 2015) Most people's first impulse when they hear about a lame-sounding new startup idea is to make fun of it. Even a lot of people who should know better. When I encounter a startup with a lame-sounding idea, I ask "What Microsoft is this the Altair Basic of?" Now it's a puzzle, and the burden is on me to solve it. So...

El Premio Abel es lo más parecido que tienen las matemáticas a un Premio Nobel. Por prestigio las Medallas Fields tienen probablemente más, pero son un tipo de premio distinto: se entregan cada cuatro años, y se conceden sólo a matemáticos de menos de 40 años. Sea como sea, este año el Premio Abel ha galardonado a Dennis Sullivan, matemático estadounidense experto en topología, y en particular en sus aspectos algebraicos y en su aplicación a sistemas dinámicos. Como el trabajo de Sullivan es realmente amplio y ha servido para conectar áreas muy distantes de las matemáticas, hoy no hemos intentado resumirlo en la sección: lo que hemos hecho es tomar un ejemplo de problema matemático que se ha podido resolver gracias a las técnicas de Sullivan, y lo hemos convertido en una especie de juego. Os animamos a hacer el siguiente ejercicio: tomad una función matemática, la que queráis, y aplicádsela a un número; después aplicadla otra vez al resultado; luego otra vez, y otra más, así por lo menos siete u ocho veces. Y entonces preguntaos cuál es el resultado de este proceso: ¿obtenemos números cada vez más grandes? ¿Nos acercamos cada vez más a una cantidad fija? ¿Vamos pasando de un valor a otro cada vez que aplicamos la función? Este procedimiento se llama iteración de funciones, y parte del trabajo de Sullivan ha sido elucidar qué ocurre cuando iteramos una función muchísimas veces. En el programa de hoy hacemos el ejercicio con una función muy sencilla: x^2 - 1. Nos encontraremos números a los que esta función lleva al infinito, y otros a los que deja "encerrados" en un bucle eterno. Os animamos a que vosotros, en casa, tratéis de averiguar qué pasa con otras funciones :) Si queréis conocer a otros ganadores del Premio Abel, en 2015 os contamos que se lo otorgaron a John Nash por sus contribuciones en geometría; lo podéis escuchar en el capítulo s04e29. En 2016 premiaron a Andrew Wiles, por demostrar el Último Teorema de Fermat, del que os hablamos en el episodio s03e16. Y en 2019 la agraciada fue Karen Uhlenbeck, que fusionó el mundo de la geometría con las ecuaciones diferenciales (os lo contamos en el capítulo s08e25). También podéis aprender más sobre las Medallas Fields, las "rivales" del Premio Abel, en los episodios s04e07 y s07e50. Este programa se emitió originalmente el 25 de marzo de 2022. Podéis escuchar el resto de audios de La Brújula en la app de Onda Cero y en su web, ondacero.es

In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Since then he's explored mathematics, computer science, and even gotten a mathematical constant named after him. Robert J. Marks leads the discussion with Professor Gregory Chaitin on… Source

This interview was recorded for the GOTO Book Club at CodeNode in London.http://gotopia.tech/bookclubSimon Singh - Author of "Fermat's Last Theorem" & "The Simpsons and Their Mathematical Secrets" and many more booksKevlin Henney - Author of "97 Things Every Programmer Should Know" & Co-Editor of "97 Things Every Java Programmer Should Know" and many more booksDESCRIPTIONMath is all around us, you just need to look for it. And look he did. In this GOTO Book Club episode, Simon Singh, author of the best-sellers "Fermat's Last Theorem," "The Code Book," and "Big Bang" gives fascinating insights into the mathematical secrets embedded in the celebrated TV series The Simpsons. You'll learn how Simon started on the path to writing this story, and why he thinks it will be his last book.The interview is based on Simon's book "The Simpsons and Their Mathematical Secrets": https://amzn.to/3w9WcRsRead the full transcription of the interview here:https://gotopia.tech/bookclub/episodes/from-fermats-last-theorem-to-the-simpsons-and-their-mathematical-secretsRECOMMENDED BOOKSSimon Singh • The Simpsons and Their Mathematical Secrets • https://amzn.to/3w9WcRsSimon Singh • Fermat's Last Theorem • https://amzn.to/3wekpG9Simon Singh • The Code Book • https://amzn.to/3k4RYFVSimon Singh • Big Bang • https://amzn.to/3bHsZnmSimon Singh & Edzard Ernst • Trick or Treatment • https://amzn.to/2ZThR4IKevlin Henney & Trisha Gee • 97 Things Every Java Programmer Should Know • https://amzn.to/3kiTwJJKevlin Henney • 97 Things Every Programmer Should Know • https://amzn.to/2Yahf9UHenney & Monson-Haefel • 97 Things Every Software Architect Should Know • https://amzn.to/3pZuHsQHenney, Buschmann & Schmidt • Pattern-Oriented Software Architecture Volume 4 • https://amzn.to/3k4SMurhttps://twitter.com/GOTOconhttps://www.linkedin.com/company/goto-https://www.facebook.com/GOTOConferencesLooking for a unique learning experience?Attend the next GOTO conference near you! Get your ticket at https://gotopia.techSUBSCRIBE TO OUR YOUTUBE CHANNEL - new videos posted almost daily.https://www.youtube.com/user/GotoConferences/?sub_confirmation=1

Dr Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford. She is also a Supernumerary Fellow at Balliol and the author of two great books aimed at general audiences, namely ‘Closing the Gap' and ‘Why Study Mathematics?'. Vicky Neale is a great communicator of Mathematics. She was given an MPLS Teaching Award in 2016 and she also won an award for being the Most Acclaimed Lecturer in MPLS in the student-led Oxford University Student Union Teaching Awards 2015.Follow her on Twitter: @VickyMaths1729 For some clear proofs of a selection of mathematical theorems, check out her YouTube channel: https://www.youtube.com/channel/UCBGhXXBCAzbzQV65JZoGhjw and her blog https://theoremoftheweek.wordpress.com/ Conversation Outline: 00:00 Guest Introduction01:05 Vicky's mathematical background04:13 Motivations for writing a book on reasons to study mathematics07:11 Are good reasons for studying Mathematics timeless? Would this book have more or less the same contents, had it been written many years ago? 10:10 Is the job of pure mathematicians safe from AI developments?12:13 What are the benefits (for the non-mathematician) of knowing about mathematical notions such as integrals, derivatives, matrices and so on? 15:39 Are some people more mathematically talented than others? 18:45 Does the discussion of talent change when we are talking about research-level Mathematics? Douglas Hofstadter's experience.22:45 Aesthetics of Mathematics25:00 Is Number Theory more beautiful than other mathematical subfields? 25:52 A mathematician's view of the metaphysics of numbers27:58 Fermat's Last Theorem, Andrew Wiles and finding meaning in Mathematics29:26 FLT and the Twin Prime Conjecture32:27 Should graduate students tackle famous open problems?33:41 Closing the Gap: significant progress towards solving the Twin Prime Conjecture35:10 Polymath: an example of collaborative Mathematics39:40 Do we have reasons to believe that the Twin Prime Conjecture is actually true?Enjoy!Apple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Bit of a personal episode this one is! Ben learns how to be a twitter warrior while Vaden has a full-on breakdown during quarantine. Who knew work addiction was actually a real thing? And that there are 12 step programs for people who identify as being "powerless over compulsive work, worry, or activity"? And that mathematics can create compulsive behavior indistinguishable from drug addiction? Vaden does, now.People mentioned in this episode:- Andrew Wiles (look at his face! the face of an addict!)- Grigori Perelman - Terry Tao's blog post ("There is a particularly dangerous occupational hazard in this subject: one can become focused, to the exclusion of other mathematical activity (and in extreme cases, on non-mathematical activity also)" - italics added) Work slavishly without sleeping or eating to send email over to incrementspodcast@gmail.com.

L'ultimo teorema di Fermat, così facile da enunciare, ma così difficile da dimostrare, è stato per più di tre secoli il problema simbolo della matematica fino a che Andrew Wiles non riuscì a dimostrarlo. Ma non vi racconterei questa storia se non ci fosse ancora un piccolo segreto sotto...

In today's episode, Amy Winder tells us about Andrew Wiles and how he solved the centuries old mathematical puzzle of Fermat's Last Theorem.    To find out more about Wakefield Litfest, find us on twitter @wakeylitfest or on Instagram @wakefieldlitfest or search for us on Facebook.

Il 24 giugno 1993 il New York Times riportava in prima pagina la notizia della dimostrazione del teorema di Fermat: un'osservazione estemporanea (scritta 350 anni prima sul margine di un libro) con una dimostrazione troppo lunga per l'esiguo spazio del margine. Tra le carte di Fermat si era trovato un primo abbozzo, che lasciava immaginare che la sua osservazione non fosse soltanto millanteria. Alla fine del 900 il teorema era stato verificato in milioni di casi,ma non in generale. L'annuncio del New York Times poneva fine alla saga, rendendo noto che dopo un lavoro solitario di 7 anni il matematico Andrew Wiles aveva finalmente risolto il mistero. Il nuovo ciclo di puntate è dedicato a questa serie di conversazioni, andate in onda su Radio 2 tra il 18 novembre e il 13 dicembre 2002 per il ciclo Alle otto della sera. Nelle venti puntate di “Chi ha ucciso Fermat?”, Odifreddi oltre a raccontarci la storia della soluzione di un problema, della dimostrazione del famoso teorema di Fermat, ci introduce in maniera informale nel mondo dei numeri in particolare, e della matematica in generale. In questo primo episodio potrete ascoltare le seguenti puntate: 1. L'annuncio sul New York Times 2. Nascita, vita e morte di un teorema 3. Tutto è numero 4. Il giardino dei numeri --- Send in a voice message: https://podcasters.spotify.com/pod/show/vito-rodolfo-albano7/message

On today's show, I talk with Andreas Elpidorou, the author of Propelled: How Boredom, Frustration and Anticipation Lead us to the Good Life.Andreas leads us on a fascinating discussion that covers a lot of ground related to happiness and the role emotions play in our pursuit of a meaningful life. IN THIS EPISODE, YOU'LL LEARN:What makes life difficult is also what makes life worth livingThe surprising role boredom can play as a warning system and a guideWhy there is more to the Good Life than happiness…a lot moreWhy authenticity and ownership of our life is so importantHow frustration energizes and informs usWhat we can learn from Andrew Wiles' pursuit of Fermat's Last TheoremThe surprising result of the Ikea Effect and what that tells us about happinessWhy “movement toward goals” may be the ultimate state of happiness BOOKS AND RESOURCESPropelled: How Boredom, Frustration and Anticipation Lead Us to the Good Life by Andreas ElpidorouCapital One. This is Banking Reimagined. What's in your wallet?Browse through all our episodes (complete with transcripts) here.Support our free podcast by supporting our sponsors.HELP US OUT!Help us reach new listeners by leaving us a rating and review! It takes less than 30 seconds and really helps our show grow, which allows us to bring on even better guests for you all! Thank you – we really appreciate it!See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.

Subscribe to the podcast and notes: https://qurantalk.podbean.com/ Quran translation on iOS: https://apple.co/2C1YGXj Additional Resources: http://www.masjidtucson.org Contact: qurantalk (at) gmail (dot) com   Theorem: a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.   In mathematics, the Pythagorean theorem, relation of the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. a^2+b^2=c^2 There are over 350 proofs to how to prove that this is true for all conditions Fermat's last theorem   Pierre de Fermat, (born August 17, 1601, Beaumont-de-Lomagne, France—died January 12, 1665, Castres), French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Andrew Wiles spent 7 years in secrecy working on the theorem  First heard about the theorem when he was 10 years old In 1986, when he was 33 years old he was a professor at Princeton and spent the next 7 years of his life working in secret trying to prove this theorem In June 1993, he presented his proof to the public for the first time at a conference in Cambridge. He gave a lecture a day on Monday, Tuesday and Wednesday with the title "Modular Forms, Elliptic Curves and Galois Representations". There was no hint in the title that Fermat's last theorem would be discussed, Dr. Ribet said. ... Finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general case of the Taniyama conjecture. Then, seemingly as an afterthought, he noted that that meant that Fermat's last theorem was true. Q.E.D.[17] In August 1993, it was discovered that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing, rather than closing, this area came to him on 19 September 1994, when he was on the verge of giving up. Together with his former student Richard Taylor, he published a second paper which circumvented the problem and thus completed the proof. Both papers were published in May 1995 in a dedicated issue of the Annals of Mathematics.[18][19] https://en.wikipedia.org/wiki/Andrew_Wiles   [9:109] Is one who establishes his building on the basis of reverencing GOD and to gain His approval better, or one who establishes his building on the brink of a crumbling cliff, that falls down with him into the fire of Hell? GOD does not guide the transgressing people. [59:29] If we revealed this Quran to a mountain, you would see it trembling, crumbling, out of reverence for GOD. We cite these examples for the people, that they may reflect. [4:82] Why do they not study the Quran carefully? If it were from other than GOD, they would have found in it numerous contradictions.   Treat the Quran like a theorem If there is a contradiction then it is our understanding that needs to be redefined Quran is consistent no contradiction  [39:23] GOD has revealed herein the best Hadith; a book that is consistent, and points out both ways (to Heaven and Hell). The skins of those who reverence their Lord cringe therefrom, then their skins and their hearts soften up for GOD's message. Such is GOD's guidance; He bestows it upon whoever wills (to be guided). As for those sent astray by GOD, nothing can guide them. [39:27] We have cited for the people every kind of example in this Quran, that they may take heed. [39:28] An Arabic Quran, without any ambiguity, that they may be righteous. [39:29] GOD cites the example of a man who deals with disputing partners (Hadith), compared to a man who deals with only one consistent source (Quran). Are they the same? Praise be to GOD; most of them do not know. [3:7] He sent down to you this scripture, containing straightforward verses—which constitute the essence of the scripture—as well as multiple-meaning (ambiguous) or allegorical verses. Those who harbor doubts in their hearts will pursue the multiple-meaning verses to create confusion, and to extricate a certain meaning. None knows the true meaning thereof except GOD and those well founded in knowledge. They say, "We believe in this—all of it comes from our Lord." Only those who possess intelligence will take heed. Abrogation indicate that there is a contradiction [2:106] When we abrogate any miracle, or cause it to be forgotten, we produce a better miracle, or at least an equal one. Do you not recognize the fact that GOD is Omnipotent? [10:20] They say, "How come no miracle came down to him from his Lord?" Say, "The future belongs to GOD; so wait, and I am waiting along with you." [6:115] The word of your Lord is complete, in truth and justice. Nothing shall abrogate (change/substitute) His words. He is the Hearer, the Omniscient. [18:27] You shall recite what is revealed to you of your Lord's scripture. Nothing shall abrogate (change/substitute) His words, and you shall not find any other source beside it. [78:37] Lord of the heavens and the earth, and everything between them. The Most Gracious. No one can abrogate (object) His decisions. [67:3] He created seven universes in layers. You do not see any imperfection in the creation by the Most Gracious. Keep looking; do you see any flaw? [67:4] Look again and again; your eyes will come back stumped and conquered. Intoxicants [4:43] O you who believe, do not observe the Contact Prayers (Salat) while intoxicated, so that you know what you are saying. Nor after sexual orgasm without bathing, unless you are on the road, traveling; if you are ill or traveling, or you had urinary or fecal-related excretion (such as gas), or contacted the women (sexually), and you cannot find water, you shall observe Tayammum (dry ablution) by touching clean dry soil, then wiping your faces and hands therewith. GOD is Pardoner, Forgiver. [5:90] O you who believe, intoxicants, and gambling, and the altars of idols, and the games of chance are abominations of the devil; you shall avoid them, that you may succeed. Violence towards others [33:61] They have incurred condemnation wherever they go; (unless they stop attacking you,) they may be taken and killed. [2:190] You may fight in the cause of GOD against those who attack you, but do not aggress. GOD does not love the aggressors. [2:191] You may kill those who wage war against you, and you may evict them whence they evicted you. Oppression is worse than murder. Do not fight them at the Sacred Mosque (Masjid), unless they attack you therein. If they attack you, you may kill them. This is the just retribution for those disbelievers. [2:192] If they refrain, then GOD is Forgiver, Most Merciful. [2:193] You may also fight them to eliminate oppression, and to worship GOD freely. If they refrain, you shall not aggress; aggression is permitted only against the aggressors. Inheritance laws  One of the worst offenses is to attribute lies to God [29:68] Who is more evil than one who fabricates lies and attributes them to GOD, or rejects the truth when it comes to him? Is Hell not a just retribution for the disbelievers? [39:32] Who is more evil than one who attributes lies to GOD, while disbelieving in the truth that has come to him? Is Hell not a just requital for the disbelievers? [6:144] Regarding the two kinds of camels, and the two kinds of cattle, say, "Is it the two males that He prohibited, or the two females, or the contents of the wombs of the two females? Were you witnesses when GOD decreed such prohibitions for you? Who is more evil than those who invent such lies and attribute them to GOD? They thus mislead the people without knowledge. GOD does not guide such evil people.” [5:101] O you who believe, do not ask about matters which, if revealed to you prematurely, would hurt you. If you ask about them in light of the Quran, they will become obvious to you. GOD has deliberately overlooked them. GOD is Forgiver, Clement. [5:102] Others before you have asked the same questions, then became disbelievers therein. [20:114] Most Exalted is GOD, the only true King. Do not rush into uttering the Quran before it is revealed to you, and say, "My Lord, increase my knowledge."

Pythagoras! Pierre Fermat! Sophie Germain! Andrew Wiles! One of these people created a math problem which challenged great thinkers for hundreds of years! One of these people had the greatest sex in the entire history of humanity! One of these people was an old Greek dude you've probably already heard about! Who did what? How long did it take them? How are they all related? It won't take a lifetime to figure out, just 48 minutes of quality podcasting for you to enjoy!

In the first Oxford Mathematics London Public Lecture, in partnership with the Science Museum, world-renowned mathematician Andrew Wiles lectured on his current work around Elliptic Curves followed by conversation with Hannah Fry. In a fascinating interview Andrew talked about his own motivations, his belief in the importance of struggle and resilience and his recipe for the better teaching of his subject, a subject he clearly loves deeply.

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Å være gift med en matematiker kan noen ganger være som å være gift med en vegg. Etter sju års ensomt arbeide hadde Wiles lagt fram sitt store matematiske bevis. Men så fant noen en feil! Reporter: Torkild Jemterud.

Han var ti år gammal då han sat på biblioteket og kom over ei gammal matematisk gåte: Fermats problem. Andrew Wiles let problemet bestemme retninga livet hans tok som matematikar. Så langt gjekk det at han nærmast isolerte seg i sju år for å finne løysinga på gåta som mange før han hadde prøvd seg på, til inga nytte. Men Wiles greidde det. Og den mediesky mottakaren av Abelprisen har takka nei til intervju med BBC og andre store mediehus, men gjorde eit unnatak for Ekko. Reporter: Torkild Jemterud

NyhetssakerAbelprisen 2016 til Andrew Wiles for beviset av Fermats siste sats. Les også denne populærvitenskapelige forklaringen.Rakettoppskytning: ESAs ExoMars!IntervjuJørgen og Leisha fikk huket tak i Edzard Ernst, som var gjest hos Skeptikere på puben fredag 11. mars, og resultatet var et lite intervju. Edzard Ernsts kronikk i Aftenposten 11.3. // Svar på kronikken fra leder for Norske homeopaters landsforbund 15.3.AnbefalingerBBC Horizon: Fermat's Last Theorem, regi Simon SinghPodcastanbefaling: Det finnes ingen dumme spørsmål m/Ingeborg Senneset. I tillegg til iTunes finner du denne også på Aftenpostens Soundcloud-side.

Andrew Wiles var bare ti år gammel da han på det lokale biblioteket i Cambrige fant et eksemplar av en bok om Fermats siste teorem. Han ble fengslet av problemet – at det ikke finnes noen heltallig løsning for ligningen xn + yn = zn der n er større enn 2 – noe som var enkelt å forstå, men som hadde vært uløst i tre hundre år. Forrige uke vant han Abel-prisen og i denne spesialutgaven av Abels tårn fra Litteraturhuset i Oslo, får du både møte Wiles selv og høre om hvorfor dette teoremet var så vanskelig å løse. Programleder: Torkild Jemterud

En este capítulo os hablamos un verdadero mito de las matemáticas: el Último Teorema de Fermat. Se trata de una afirmación aparentemente sencilla sobre relaciones entre números: dice que si cogemos tres números enteros y los elevamos todos a la misma potencia nunca podremos, sumando dos de las potencias, encontrar la tercera, salvo si la potencia que hemos elegido es un cuadrado. Dicho más formalmente, el teorema afirma que x^n + y^n = z^n sólo puede ser cierto si n=1 o n=2. Esta afirmación fue planteada en primer lugar por Pierre de Fermat en 1637, quien afirmó que sabía demostrarla, pero no nos legó la demostración. A partir de ahí generaciones enteras de matemáticos trataron de averiguar si Fermat estaba en lo cierto, y durante 358 años todos fallaron. En este capítulo os explicamos el final de esta larga epopeya matemática, que encontró su final a manos del británico Andrew Wiles allá por mediados de la década de 1990. Si os interesan los números y las matemáticas, otros capítulos de La Brújula de la Ciencia en los que hablamos sobre ellos son el s05e12 y s04e41. También podéis buscar los especiales "Alberto Aparici en la Lotería de Navidad", en los que contamos curiosidades sobre los números. Este programa se emitió originalmente el 17 de enero de 2014. Podéis escuchar el resto de audios de La Brújula en su canal de iVoox y en la web de Onda Cero, ondacero.es

Eine alte Fragestellung lautet, was die Summe der Kehrwerte aller natürlicher Zahlen ist. Mit anderen Worten: existiert der Grenzwert der Harmonischen Reihe ? Die Antwort, die man im ersten Semester kennenlernen ist: Diese Reihe ist divergiert, der Wert ist nicht endlich. Über die spannenden Entwicklungen in der Zahlentheorie, die sich daraus ergaben, berichtet Fabian Januszewski im Gespräch mit Gudrun Thäter. Eine verwandte Fragestellung zur harmonischen Reihe lautet: Wie steht es um den Wert von ? Diese Frage wurde im 17. Jahrhundert aufgeworfen und man wußte, daß der Wert dieser Reihe endlich ist. Allerdings kannte man den exakten Wert nicht. Diese Frage war als das sogannte Basel-Problem bekannt. Eine ähnliche Reihe ist Ihr Wert läßt sich elementar bestimmen. Dies war lange bekannt, und das Basel-Problem war ungleich schwieriger: Es blieb fast einhundert Jahre lang ungelöst. Erst Leonhard Euler löste es 1741: Die Riemann'sche -Funktion Die Geschichte der L-Reihen beginnt bereits bei Leonhard Euler, welcher im 18. Jahrhundert im Kontext des Basel-Problems die Riemann'sche -Funktion' entdeckte und zeigte, dass sie der Produktformel genügt, wobei die Menge der Primzahlen durchläuft und eine reelle Variable ist. Diese Tatsache ist äquivalent zum Fundamentalsatz der Arithmetik: jede natürliche Zahl besitzt eine eindeutige Primfaktorzerlegung. Eulers Lösung des Basel-Problems besagt, daß und diese Formel läßt sich auf alle geraden positiven Argumente verallgemeinern: , wobei die -te Bernoulli-Zahl bezeichnet. Im 19. Jahrhundert zeigte Bernhard Riemann, dass die a priori nur für konvergente Reihe eine holomorphe Fortsetzung auf besitzt, einer Funktionalgleichung der Form genügt und einen einfachen Pol mit Residuum bei aufweist. Letztere Aussage spiegelt die Tatsache wieder, dass in jedes Ideal ein Hauptideal ist und die einzigen multiplikativ invertierbaren Elemente sind. Weiterhin weiß viel über die Verteilung von Primzahlen. Setzen wir dann zeigte Riemann, daß die so definierte vervollständigte Riemann'sche -Funktion auf ganz holomorph ist und der Funktionalgleichung genügt. Da die -Funktion Pole bei nicht-positiven ganzzahligen Argumenten besitzt, ergibt sich hieraus die Existenz und Lage der sogenannten "trivialen Nullstellen" von : für . Konzeptionell sollte man sich den Faktor als Eulerfaktor bei vorstellen. John Tate zeigte in seiner berühmten Dissertation, daß dies tatsächlich sinnvoll ist: Die endlichen Eulerfaktoren werden von Tate als Integrale über interpretiert, und der "unendliche" Eulerfaktor ist ebenfalls durch ein entsprechendes Integral über gegeben. Er legte damit den Grundstein für weitreichende Verallgemeinerungen. Die Riemann'sche -Funktion ist der Prototyp einer -Funktion, einem Begriff, der langsam Schritt für Schritt verallgemeinert wurde, zunächst von Richard Dedekind, Lejeune Dirichlet und Erich Hecke und weiter von Emil Artin, Helmut Hasse, André Weil, Alexander Grothendieck, Pierre Deligne, Jean-Pierre Serre und Robert Langlands et al. -Funktionen spielen in der modernen Zahlentheorie eine zentrale Rolle, und bis heute ranken sich fundamentale Vermutungen um diesen Begriff. Selbst die Mysterien der Riemann'schen -Funktion sind auch heute bei weitem nicht vollständig ergründet. Die berühmteste Vermutung in diesem Kontext ist die Riemann'sche Vermutung. Riemann zeigte 1859 nicht nur, daß die Riemann'sche -Funktion eine holomorphe Fortsetzung auf besitzt, sondern stellte auch einen engen Zusammenhang zwischen der Verteilung der Primzahlen und den Nullstellen von her. Eulers Produktenwicklung von für zeigt, dass stets für . Aus der Funktionalgleichung von ergibt sich, dass für natürliche Zahlen . Die sind die sogenannten trivialen Nullstellen der -Funktion. Riemann vermutete, dass sämtliche nicht-trivialen Nullstellen auf der Geraden liegen. Euler bestimmte im wesentlichen die Werte für positives . Bis heute wissen wir sehr wenig über die Werte an positiven ungeraden Argumenten. Ein Satz von Apéry besagt, daß irrational ist. Wir haben allerdings keine einfache Formel für diesen Funktionswert. Konzeptionell unterscheiden sich die ungeraden von den geraden positiven Argumenten darin, daß der in auftretende Faktor der -Funktion für ungerades positives dort einen Pol besitzt, was ebenfalls das Verschwinden von zur Folge hat. Über die Werte an negativen ungeraden Argumenten wissen wir aus der Funktionalgleichung, daß . Insbesondere gilt . Dieser Wert kann in gewissen Kontexten als Grenzwert (der divergierenden!) Reihe interpretiert werden (formal ergeben diese Identitäten natürlich keinen Sinn). In gewissen Situationen ist der Funktionswert ein sinnvoller endlicher Ersatz für den nicht existierenden Grenzwert der Reihe . Derartige Phänomene treten in Zahlentheorie an vielen Stellen auf. Literatur und Zusatzinformationen Haruzo Hida, Elementary theory of -functions and Eisenstein series, Cambridge University Press, 1993. Jean-Pierre Serre, "Cours d'arithmétique", Presses Universitaires de France, 1970. Goro Shimura, "Introduction to the arithmetic theory of automorphic functions." Princeton University Press, 1971. Jürgen Neukirch, Algebraische Zahlentheorie, Springer Verlag, 1992. André Weil, Basic Number Theory, Springer Verlag, 1973. Podcast Modellansatz 036: Analysis und die Abschnittskontrolle Bernhard Riemann, Über die Anzahl der Primzahlen unter einer gegebenen Grösse, Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 1859 John T. Tate, "Fourier analysis in number fields, and Hecke's zeta-functions", Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, 1950, S. 305–347. Andrew Wiles, "Modular Elliptic Curves and Fermat’s Last Theorem." Annals of Mathematics 142, 1995, S. 443–551. Richard Taylor, Andrew Wiles, "Ring-theoretic properties of certain Hecke algebras." Annals of Mathematics 142, 1995, S. 553–572. Brian Conrad, Fred Diamond, Richard Taylor, "Modularity of certain potentially Barsotti-Tate Galois representations", Journal of the American Mathematical Society 12, 1999, S. 521–567. Christophe Breuil, Brian Conrad, Fred Diamond, Richard Taylor, "On the modularity of elliptic curves over Q: wild 3-adic exercises", Journal of the American Mathematical Society 14, 2001, S. 843–939. Frobeniushomomorphismus Galois-Darstellungen Weil-Vermutungen Standard-Vermutungen Automorphe Formen Das Langlands-Programm Wikipedia: Automorphe L-Funktionen Emil Artin, Über eine neue Art von -Reihen, Abh. Math. Seminar Hamburg, 1923. Armand Borel, "Automorphic L-functions", in A. Borel, W. Casselman, "Automorphic forms, representations and L-functions" (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Oregon, 1977), Teil 2, Proc. Sympos. Pure Math., XXXIII, American Mathematical Society, 1979, S. 27–61. Robert P. Langlands, "Problems in the theory of automorphic forms", in "Lectures in modern analysis and applications III," Lecture Notes in Math 170, 1970, S. 18–61. Robert P. Langlands, '"'Euler products", Yale University Press, 1971. Wikipedia: Spezielle Werte von L-Funktionen Pierre Deligne; "Valeurs de fonctions L et périodes d’intégrales." , in A. Borel, W. Casselman, "Automorphic forms, representations and L-functions" (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Oregon, 1977)'', Teil 2, Proc. Sympos. Pure Math., XXXIII, American Mathematical Society, 1979, S. 313–346.

Gresham Professor of Geometry, Raymond Flood, begins his series 'Great Mathematicians, Great Mathematics' with Pierre de Fermat:http://www.gresham.ac.uk/lectures-and-events/fermats-theoremsThe seventeenth century mathematician Pierre de Fermat is mainly remembered for contributions to number theory even though he often stated his results without proof and published very little. He is particularly remembered for his 'last theorem' which was only proved in the mid-1990s by Andrew Wiles. He also stated other influential results, in particular Fermat's 'Little Theorem' about certain large numbers which can be divided by primes. His 'Little Theorem' is the basis of important recent work in cryptography and internet security.The transcript and downloadable versions of the lecture are available from the Gresham College Website: http://www.gresham.ac.uk/lectures-and-events/fermats-theoremsGresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,500 lectures free to access or download from the website.Website: http://www.gresham.ac.ukTwitter: http://twitter.com/GreshamCollegeFacebook: https://www.facebook.com/greshamcollege

Melvyn Bragg and his guests discuss Fermat's Last Theorem. In 1637 the French mathematician Pierre de Fermat scribbled a note in the margin of one of his books. He claimed to have proved a remarkable property of numbers, but gave no clue as to how he'd gone about it. "I have found a wonderful demonstration of this proposition," he wrote, "which this margin is too narrow to contain". Fermat's theorem became one of the most iconic problems in mathematics and for centuries mathematicians struggled in vain to work out what his proof had been. In the 19th century the French Academy of Sciences twice offered prize money and a gold medal to the person who could discover Fermat's proof; but it was not until 1995 that the puzzle was finally solved by the British mathematician Andrew Wiles. With:Marcus du Sautoy Professor of Mathematics & Simonyi Professor for the Public Understanding of Science at the University of OxfordVicky Neale Fellow and Director of Studies in Mathematics at Murray Edwards College at the University of CambridgeSamir Siksek Professor at the Mathematics Institute at the University of Warwick.Producer: Natalia Fernandez.

Melvyn Bragg and his guests discuss Fermat's Last Theorem. In 1637 the French mathematician Pierre de Fermat scribbled a note in the margin of one of his books. He claimed to have proved a remarkable property of numbers, but gave no clue as to how he'd gone about it. "I have found a wonderful demonstration of this proposition," he wrote, "which this margin is too narrow to contain". Fermat's theorem became one of the most iconic problems in mathematics and for centuries mathematicians struggled in vain to work out what his proof had been. In the 19th century the French Academy of Sciences twice offered prize money and a gold medal to the person who could discover Fermat's proof; but it was not until 1995 that the puzzle was finally solved by the British mathematician Andrew Wiles. With: Marcus du Sautoy Professor of Mathematics & Simonyi Professor for the Public Understanding of Science at the University of Oxford Vicky Neale Fellow and Director of Studies in Mathematics at Murray Edwards College at the University of Cambridge Samir Siksek Professor at the Mathematics Institute at the University of Warwick. Producer: Natalia Fernandez.

Solving Fermat's Last Theorem had intrigued mathematicians for centuries. In June 1993 a British academic, Andrew Wiles, thought he'd cracked it. But then someone pointed out a flaw in his calculations and it took him another year to correct it.