The Abel Prize Award Ceremony May 24, 2016 The University Aula, Oslo Procession accompanied by the “Abel Fanfare” (Klaus Sandvik) Performed by musicians from The Staff Band of the Norwegian Armed Forces H.R.H. Crown Prince Haakon enters the University Aula Come Again John Dowland (1563–1626) Opening speech by Professor Ole M. Sejersted President of The Norwegian Academy of Science and Letters From Winterreise: Gute Nacht Franz Schubert (1797–1828) The Abel Committee’s citation by Professor John Rognes Chair of the Abel Committee H.R.H. Crown Prince Haakon presents the Abel Prize to Sir Andrew Wiles Acceptance speech by the Abel Laureate Youkali Kurt Weill (1900–1950) / Roger Fernay (1905–1983) H.R.H. Crown Prince Haakon leaves the University Aula Procession leaves The Prize Ceremony will be followed by a reception at Midtgolvet in Det Norske Teatret. During the reception, the Laureate will be interviewed by Nadia Hasnaoui. More info on page 11. science and scholarship, and in its strategy it attaches importance to contributing to good research Professor Ole M. Sejersted policy, disseminating knowledge as a basis for decisions and strengthening the best research. The President of The Norwegian Academy of Science and Letters award ceremony and the various activities during the Abel week, especially those aimed at young people, thus provide the Academy with an excellent opportunity to showcase its work and goals. Your Royal Highness, Minister, Excellencies, Dear Abel Prize Laureate To achieve the intention behind the Abel Prize, the Academy has appointed an Abel Board, Sir Andrew Wiles, Dear friends of mathematics and basic science, which has been charged with stimulating an interest in mathematics among children and young Ladies and Gentlemen people by supporting projects in kindergartens, schools and science centres, etc. The initiatives supported include the Norwegian Mathematical Olympiad for upper secondary pupils and the On behalf of The Norwegian Academy of Science and Letters, I am very UngeAbel contest for teams of pupils in year 9. This year's young winners are here with us in the pleased and honored to welcome you to this year's Abel Prize Award Cermony. audience today. You are important ambassadors for mathematics. The Abel Prize was established in 2002, 200 years after Niels Henrik Abel's birth. The Abel Prize Fostering an interest in mathematics in young people also requires good teachers. Niels Henrik is administered by The Norwegian Academy of Science and Letters on behalf of the Norwegian Abel's teacher, Bernt Michael Holmboe, was pivotal to Abel's career. To emphasize the important Ministry of Education and Research and is awarded for outstanding work in the field of math- role teachers play, a teacher is honored each year with the Holmboe Memorial Prize through the ematics. The main purpose of the Abel Prize is to recognize pioneering scientific achievements in Norwegian Mathematical Council. This year's Holmboe Prize winner is Ingunn Valbekmo from mathematics. Byåsen School in Trondheim. Another great Norwegian mathematician, Sophus Lie, proposed the establishment of an Abel I would like to thank Petroleum Geo-Services (PGS) for their support in Norway and internation- Prize more than a century ago, but as Fridtjof Nansen put it: "The Abel Prize promised by blessed ally to stimulate interest in mathematics, especially among children and young people, in develop- King Oscar disappeared into thin air along with the union". It was only in 2001 that the Norwegian ing countries, specifically Ghana. This is a prime example of long-term public–private collaboration. Government announced the establishment of an Abel Fund, the purpose of which was to award a Sir Andrew Wiles and all the previous Abel Prize laureates are important role models for young prize in Abel's honor. researchers. The Heidelberg Laureate Forum is an annual event where former winners of prizes In addition to recognizing the contribution made by the prize winner, the Abel Prize is intended in mathematics and computer science meet talented young researchers from around the world to help enhance the status of mathematics in society and encourage children and young people for mutual inspiration. I would like to thank the Heidelberg Laureate Forum Foundation for having to become interested in mathematics. The Abel Prize highlights the fundamental importance of taken the initiative to arrange these annual forums. basic research in finding solutions to the major challenges faced by society. In mathematics, we Today is the fourteenth time the Abel Prize is awarded. Over the years the Abel Prize has often find clear examples that advanced solutions that were initially the result of a desire to solve achieved a very high status in the mathematical research community all over the world. The Abel a theoretical problem have subsequently been of unintentional and unexpectedly great practical Committee, with members nominated by the International Mathematical Union and the European importance. Mathematical Society, deserves much of the honor for the recognition that the Prize has attained This year's prize winner, Sir Andrew Wiles, receives the prize "for his stunning proof of Fermat's internationally. I would like to take this opportunity to thank the Abel Committee, headed by Profes- Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new sor John Rognes, for their excellent work. era in number theory". Mathematicians have tried to prove Fermat's Last Theorem for 350 years, The Norwegian Academy of Science and Letters would also like to thank the Norwegian math- without success, indicating that mathematicians regard this as one of the great mathematical ematics community in general and everyone who helps underscore the importance of mathematics puzzles. The Abel Committee says that Sir Andrew's work has heralded a new era in number in society. The knowledge society is dependent on the kind of outstanding basic research that the theory. To me, this indicates that the work on the theorem required the development of an entirely Abel Prize seeks to recognize. The Award Ceremony provides an excellent opportunity to draw new mathematical foundation, the significance of which goes far beyond the actual proving of the attention to this. Last but not least, the Abel Board works tirelessly to showcase mathematics and theorem. Sir Andrew and Niels Henrik Abel had one thing in common – they both worked on elliptic the importance of mathematics. I would especially like to thank the chair of the Abel Board, Profes- functions. sor Kristian Ranestad, for his dedication and hard work. The Norwegian Academy of Science and Letters is pleased and honored to have responsibility Distinguished guests and most honored prize winner, Sir Andrew Wiles: This is a great day, not for awarding of the Abel Prize. The Academy's main purpose is to support the advancement of only for you, but for the field of mathematics, for all of us who are here today, and for society at large. Once again, I welcome you to this year's award ceremony. 4 5 forms of a specific type, we now also know that there are no solutions to Fermat's Professor John Rognes equation. Chair of the Abel Committee How did Wiles come to solve this problem? He read about the equation at an early age. Your Royal Highness, Minister, Your Excellencies, honoured Laureate, When he heard, in 1986, that Ken Ribet had connected the modularity conjecture to dear colleagues and guests! Fermat's last theorem, Wiles realised that he had an exceptional opportunity to try to prove these two results. His earlier work on elliptic curves and Iwasawa theory could How did Fermat's last theorem come to be important? The story give him exactly the expertise needed to attack the problem. He was already a tenured starts well over three thousand years ago. A Babylonian clay tablet professor at Princeton University, and was free to judge, by himself, how he should best lists integer solutions to the equation x2 + y2 = z2. The first row reads use his research time. The project he decided to grapple with was unusually daring. 1192 + 1202 = 1692. Over a thousand years later this equation became known as the Hardly anyone else thought that the modularity conjecture could be proven. Therefore Pythagorean theorem about the sides of a right triangle. Pythagoras also discovered the mathematical world was overwhelmed when he seven years later announced that he a connection between music and mathematics. The ratio of the frequencies of two had found the elusive proof. But this was not the end of the story. By the end of the year, notes that sound good together is a fraction with small numerator and denominator. For it had become clear that the most recent part of the proof was incomplete. A calculation an octave, the ratio is two to one. For a major third, the ratio is five to four. That three was not fully justified. The joy turned into dread. major thirds sound like one octave corresponds to 53 being almost twice 43, that is, 125 is close to 128. This coincidence is special enough that human hearing recognises How did he manage to keep working, after the mistake was found? Wiles knew that the it, perhaps already from birth. Multiplying by eight we find that 102 = 1024 is close to conceptual part of his proof already gave deep new insights, but to prove the modularity 1000, which we recognise in the confusion about what a kilobyte really is. That such conjecture and Fermat's last theorem he needed the calculation. Only when he could coincidences exist, but that they are rare enough to be audible to us, expresses a subtle understand why the calculation failed was he able to see the way ahead.