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Although not as publicly well-known as the Nobel Prizes, the Fields Medal shares the same intellectual standing and is the equivalent award in the field of mathematics. This volume presents a selected list of 22 Fields Medallists and their contributions to give a highly interesting and varied bird's eye view of mathematics over the past 60 years. The contributions relate directly to the work for which the Medals were awarded or to the medallists' more current interests. In most cases, they are preceded by the introductory speech given by another leading mathematician during the prize ceremony, a photograph and up-to-date biographical notice.
This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these “systems” may serve as prototypes for design of universal learning computer programs. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.
Mathematics is as old as civilization. The Maya developed sophisticated arithmetic to study the stars and the weather, the ancient Greeks used geometry to estimate the size of the earth with remarkable accuracy, and the Chinese mathematician Liu Hui calculated pi to five decimal places two millennia before computers had been invented. And mathematics is alive and well today, with new discoveries made every day, sometimes about problems that are easy to understand but surprisingly difficult to solve. Some problems lie around for centuries waiting to be solved: Johannes Kepler made a guess in 1611 about how a pile of spheres could be packed most densely into three-dimensional space; it took four centuries until Thomas Hales proved that Kepler was right. And mathematicians love to expand old problems and turn them into new ones: Marina Viazovska won a Fields Medal in 2022, equivalent to a Nobel Prize, for solving an even harder version of Kepler's problem! Much of the power of mathematics comes from how it enables us to understand things that we can't see or experience directly. And throughout the history of mathematics, abstract ideas have proven to be unexpectedly useful in solving concrete problems. Mathematicians have been playing with prime numbers since antiquity; who would have thought that they would become an essential ingredient of modern cryptography? Who would have thought that complex numbers, first discovered in the 1500s and derided as "imaginary," would turn out to be exactly the right tools to describe real world phenomena like radio signals and electrical circuits? Even infinity, literally the biggest mathematical concept of all, is useful: Georg Cantor's revolutionary discovery that infinity itself comes in different sizes introduced ideas that have become indispensable for the study of computers and computer algorithms. Every year, the Abel Prize, the Gödel Prize and the Turing Award honor far-reaching mathematical discoveries. Sometimes these discoveries are brand new ideas, and sometimes they are applications of mathematics to solve real-world problems. In this collection, recipients of these awards will show you both the beautiful abstract ideas they study, and the amazing power they have to transform the modern world.
How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)
This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int
At its meeting in April 1990 at the University of Cambridge, the Executive Committee of the International Mathematical Union (IMU) decided that the largely unorganized archives of the Union should be properly arranged and catalogued. Simultaneously, the Executive Committee expressed the wish that a history of the Union should be written [1). As Secretary of the Union, I had proposed that these issues be dis cussed at the Cambridge meeting, but without having had in mind any personal role in the practical execution of such projects. At that time, the papers of the IMU were stored in Zurich, at the Eidgenossische Technische Hochschule, and I saw no reason why they could not remain there. At about this time, Professor K. Chandrasekharan produced a handwritten article titled "The Prehistory of the International Mathematical Union" [2), and it seemed to me that this might serve as the beginning of a more compre hensive history. I had first thought that Tuulikki MakeUiinen, who during eight years as the Office Secretary ofthe IMU had become well acquainted with the Union, would do the arranging of the archives in Zurich. She had a preliminary look at the material there, but it soon became clear that the amount of work required to bring order to it was too great to be accomplished in a few short visits from Helsinki. The total volume of material was formidable.
As modern mathematics has been developed by mathematicians over the past several hundred years, it is interesting to trace the academic genealogy of mathematicians — especially since all mathematicians learnt mathematics from their teachers. In this book, 750 mathematicians are listed along with the detailed descriptions of 464 famous mathematicians of the 19th and 20th centuries. In addition, interesting life stories and mathematical achievements are included with photographs.
The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com .