This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.
The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
This book contains the full text of the letters from Emil Artin to Helmut Hasse, as they are preserved in the Handschriftenabteilung of the Göttingen University Library. There are 49 such letters, written in the years 1923-1934, discussing mathematical problems of the time. The corresponding letters in the other direction, i.e., from Hasse to Artin, seem to be lost. We have supplemented Artin's letters by detailed comments, combined with a description of the mathematical environment of Hasse and Artin, and of the relevant literature. In this way it has become possible to sufficiently reconstruct the content of the corresponding letters from Hasse to Artin too. Artin and Hasse were among those who shaped modern algebraic number theory, in particular class field theory. Their correspondence admits a view of the ideas which led to the great achievements of their time, starting from Artin's L-series and his reciprocity law towards Hasse‘s norm symbol, local class field theory and the Local-Global Principle. These letters are a valuable source for understanding the rise and development of mathematical ideas and notions as we see them today. The book is a follow-up of our earlier book on the correspondence between Hasse and Emmy Noether. It is thus the second of a series which aims to open access to the rich collection of Hasse's mathematical letters and notes contained in the Göttingen Handschriftenabteilung.
The name Emmy Noether is one of the most celebrated in the history of mathematics. A brilliant algebraist and iconic figure for women in modern science, Noether exerted a strong influence on the younger mathematicians of her time and long thereafter; today, she is known worldwide as the "mother of modern algebra." Drawing on original archival material and recent research, this book follows Emmy Noethers career from her early years in Erlangen up until her tragic death in the United States. After solving a major outstanding problem in Einsteins theory of relativity, she was finally able to join the Göttingen faculty in 1919. Proving It Her Way offers a new perspective on an extraordinary career, first, by focusing on important figures in Noethers life and, second, by showing how she selflessly promoted the careers of several other talented individuals. By exploring her mathematical world, it aims to convey the personality and impact of a remarkable mathematician who literally changed the face of modern mathematics, despite the fact that, as a woman, she never held a regular professorship. Written for a general audience, this study uncovers the human dimensions of Noethers key relationships with a younger generation of mathematicians. Thematically, the authors took inspiration from their cooperation with the ensemble portraittheater Vienna in producing the play "Diving into Math with Emmy Noether." Four of the young mathematicians portrayed in Proving It Her Way - B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky - also appear in "Diving into Math.".
This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.
Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden’s record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States which revealed fascinating and often surprising new information about van der Waerden. Soifer traces Van der Waerden’s early years in a family of great Dutch public servants, his life as professor in Leipzig during the entire Nazi period, and his personal and professional friendship with one of the great physicists Werner Heisenberg. We encounter heroes and villains and a much more numerous group in between these two extremes. One of them is the subject of this book. Soifer’s journey through a long list of archives, combined with an intensive correspondence, had uncovered numerous details of Van der Waerden’s German intermezzo that raised serious questions and reproaches. Dirk van Dalen (Philosophy, Utrecht University) Professor Soifer’s book implicates the anthropologists’ and culture historians’ core interest in the evolution of culture and in the progress of human evolution itself on this small contested planet. James W. Fernandez (Anthropology, University of Chicago) The book is fascinating. Professor Soifer has done a great service to the discipline of history, as well as deepening our understanding of the 20th century. Peter D. Johnson, Jr. (Mathematics, Auburn University) This book is an important contribution to the history of the twentieth century, and reads like a novel with an ever-fascinating cast of characters. Harold W. Kuhn (Mathematics, Princeton University) This is a most impressive and important book. It is written in an engaging, very personal style and challenges the reader’s ability of moral and historical judgment. While it is not always written in the style of ‘objective’ professional historiography, it satisfies very high standards of scholarly documentation. Indeed the book contains a wealth of source material that allows the reader to form a highly detailed picture of the events and personalities discussed in the book. As an exemplar of historical writing in a broader sense it can compete with any other historical book. Moritz Epple (History of Mathematics, Frankfurt University)
This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.
Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
