The Abel Prize Award Ceremony May 19, 2015 The University Aula, Oslo Procession accompanied by the “Abel Fanfare” (Klaus Sandvik) Performed by musicians from The Staff Band of the Norwegian Armed Forces His Majesty King Harald enters the University Aula Fanteguten Trad/ Arr: Sverre Indris Joner Opening speech by Professor Kirsti Strøm Bull President of the Norwegian Academy of Science and Letters Skjøre (Fragile) Music: Sting/ Norwegian lyrics: Kjell Inge Torgersen/ Arr: Pitsj The Abel Committee’s Citation by Professor John Rognes Chair of the Abel Committee His Majesty King Harald presents the Abel Prize to John F. Nash, Jr. and Louis Nirenberg Acceptance speech by the Abel Laureates Tanta til Beate Music: Lillebjørn Nilsen/ Arr: Børre Dalhaug His Majesty King Harald 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 laureates will be interviewed by Vivienne Parry. More info on page 11. John F. Nash Jr., aged 86, spent his career at Princeton University and the Massachusetts Professor John F. Nash, Jr. Institute of Technology. Louis Nirenberg, aged 90, worked at New York University’s Courant Princeton University Institute of Mathematical Sciences. Even though they did not formally collaborate on any papers, they influenced each other greatly during the 1950s. The results of their work are felt Professor Louis Nirenberg more strongly today than ever before. Courant Institute, New York University Nash and Nirenberg are two mathematical giants of the twentieth century. They are being Abel Laureates 2015 recognized for their contributions to the field of partial differential equations (PDEs), which are equations involving rates of change that originally arose to describe physical phenomena but, “for striking and seminal contributions to the theory of nonlinear partial as they showed, are also helpful in analysing abstract geometrical objects. The Abel commit- differential equations and its applications to geometric analysis.” tee writes: “Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory.” In the 1950s Nash proved important theorems about PDEs, which are considered by his peers to be his deepest work. Outside mathematics, however, Nash is best known for a paper he wrote about game theory, the mathematics of decision-making, which ultimately won him the 1994 Nobel Prize for economics, and which features strongly in the 2001 film about him,A Beautiful Mind. Nirenberg, who was born in Canada, has had one of the longest and most feted careers in mathematics, having produced important results right up until his 70s. Unlike Nash, who wrote papers alone, Nirenberg preferred to work in collaboration with others, with more than 90 per cent of his papers written jointly. Many results in the world of elliptic PDEs are named after him and his collaborators, such as the Gagliardo–Nirenberg inequalities, the John–Nirenberg inequality and the Kohn–Nirenberg theory of pseudo-differential operators. Photo: Princeton University/Department of mathematics “Far from being confined to the solutions of the problems for which they were devised, the results proven by Nash and Nirenberg have become very useful tools and have found tremen- dous applications in further contexts,” the Abel committee says. Both men have received many distinguished awards. As well as winning the prize in economic sciences in memory of Alfred Nobel, Nash has won the John von Neumann Theory Prize (1978) and the American Mathematical Society’s Steele Prize for a Seminal Contribution to Research (1999). Nirenberg has won the American Mathematical Society’s Bôcher Memorial Prize (1959) the inaugural Crafoord Prize awarded by the Royal Swedish Academy of Science Photo: Peter Badge Photo: NYU Photo Bureau: Hollenshead (1982), the Steele Prize for Lifetime Achievement from the American Mathematical Society (1994) and the first Chern Medal for lifetime achievement from the International Mathematical Union and the Chern Medal Foundation (2010). 4 5 These are areas in which this year's Abel Prize winners have submitted some of their Professor Kirsti Strøm Bull most important contributions. President of The Norwegian Academy of Science and Letters The connection back to former mathematicians illustrates a characteristic feature of mathematics as a science. Mathematics is timeless and universal. A mathematical proof transcends different cultures and ideologies as well as elapsed time. Mathematics links the past to the present. Even though mathematical research is in a period of rapid development, old ideas are not rejected as so often occurs in other branches of science. One of the Abel Prize's important objectives is to stimulate children and youth to become Your Majesty, Excellencies, dear prize winners John Forbes Nash Jr. and Louis interested in mathematics. Good, inspiring mathematics teachers play a very important Nirenberg, ladies and gentlemen, role in this endeavour. Niels Henrik Abel's mathematics teacher played a crucial role in his development. To emphasise the importance of the teacher's role, a teacher prize On behalf of the Norwegian Academy of Science and Letters, I have the pleasure and has been established in connection with the Abel Prize. This Prize is named after Abel's honour of welcoming you all to the Abel Prize Award Ceremony for 2015. The Abel Prize teacher, Bernt Michael Holmboe. This year's prize was awarded yesterday at Abel's old was established by the Norwegian Government in 2002, 200 years after Niels Henrik school, Oslo Cathedral School. This year's prize winners are a staff of ten mathematics Abel's birth. However, the idea of creating a major international prize in mathematics that teachers at Hellerud Upper Secondary School in Oslo. would bear Niels Henrik Abel's name had already been aired in 1898 by our other great Norwegian mathematician, Sophus Lie. Lie's idea was to establish a major international The Abel Board also supports other important measures among children and youth. prize for outstanding work in the field of pure mathematics on the 100th anniversary celebration of Niels Henrik Abel's birth. This idea gained considerable support among In just a short period of time, the Abel Prize has become one of the great international his European mathematics colleagues who all wished to contribute financial support to prizes in mathematics. With members from many different countries, who are nominated a prize of this sort. A year later, however, Sophus Lie passed away, and his dream of an by the key international mathematics organisations, the Abel Committee deserves much Abel Prize was not realised until the 200th anniversary of Abel's birth. of the honour for the status that the Prize has attained. I would like to thank the Abel Committee, chaired by Professor John Rognes, for this important and demanding work. The Abel Prize is a prize for outstanding scientific work in mathematics. The Prize is a recognition of scientific contributions of exceptional depth and significance for the The Norwegian Academy of Science and Letters would also like to thank the other discipline of mathematics. key participants involved in the Prize and its associated events - the Abel Board, the Norwegian Government and the Norwegian Ministry of Education and Research, the John Forbes Nash, Jr. and Louis Nirenberg are receiving the prize “for striking and semi- Norwegian Mathematical Council and the Norwegian mathematics community. nal contributions to the theory of nonlinear partial differential equations and its applica- tions to geometric analysis.” Honoured guests, Abel Prize Winners John Forbes Nash and Louis Nirenberg, once again I wish you welcome to this year's Abel Prize Award Ceremony. There is a connection between this year's prize winners and Sophus Lie. In the period 1870-1890, Sophus Lie developed the theory of continuous groups of symmetries, now better known as Lie groups. At present, the study of these groups constitutes an independent field in mathematics, but Sophus Lie was originally motivated to develop this theory in order to answer questions about geometry and differential equations. 6 7 differential equations, to which Nash and Nirenberg have made some of their most Professor John Rognes cited contributions. Chair of the Abel Committee Irregularity can arise from the accumulation of many small contributions. In mathematical terms this leads to infinite sums called series, about which Abel wrote to Holmboe: “Divergent Series are the Work of the Devil and it's a Shame that one dares base any Demonstration upon them. You can get whatever result you want when you use them, and they have given rise to so many Disasters and so many Paradoxes. [...] [T]he most Your Majesty, Minister, Your Excellencies, honoured Laureates, dear colleagues and important features of Mathematics stand without Substantiation. Most of them are guests! correct; that is a fact, and it is exceedingly surprising. I am striving to find a Basis for these. An extremely interesting task.” [Translation: Stubhaug, Daly (2000).] The theory of differential equations began with the calculus for rates of change. Newton's first study concerned planetary motion around the Sun, and involved two This task led Abel to his summation formula, a discrete analogue of integration by quantities: the position and the velocity of the planet. Both vary with time, and these parts, which is at the heart of the modern notion of a weak solution to a differential variations are linked: the planet's velocity determines the change in position, and the equation. At first, a weak solution only exists in a virtual sense, through its interaction planet's position determines the change in velocity. A key premise in this framework with other quantities. To become useful for applications, and to be accessible through is that “velocity” means “instantaneous velocity”.