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One of the greatest accomplishments in the history of cryptography occurred in 1940 when a Swedish mathematician broke the German code used for strategic military communications. This story has all the elements of a classic thriller: a desperate wartime situation; a moody and secretive mathematical genius with a talent for cryptography; and a stunning mathematical feat, mysterious to this day. Arne Beurling, the man who inherited Einstein's office at Princeton's Institute for Advanced Study, was the figure who played this role at a crucial moment in world history. Though the cracking of the code from the Geheimschreiber (G-Schreiber) device is every bit as impressive as the breaking of the Enigma code by the Poles and English, this secret has been kept for over 50 years! Through the eyes of a former head of Sweden's signal intelligence organization, Bengt Beckman, the reader will learn about the events leading up to the breakthrough and make the acquaintance of not only a remarkable mathematician, but also a remarkable human being. Arne Beurling was a leading international figure who achieved beautiful results in mathematical analysis. By the arrival of World War II, he was one of the most powerful and original mathematicians in the world and widely considered a genius. During his military service, he demonstrated a flair for code and was well known within Swedish cryptology circles. The natural choice of the Swedish intelligence service was to place Beurling at the center of the group charged with breaking the G-Schreiber code. His single-handed effort "broke the unbreakable". Using only teleprinter tapes and cipher text, he deciphered the code that the Germans believed impossible to crack--in two weeks! The feat, in a word, was astonishing. Many wonder how he did it. But Beurling took his secret to the grave, retorting when asked, "A magician does not reveal his secrets."

The author, Bengt Beckman, for many years was the head of the cryptanalysis department of the Swedish signal intelligence agency. In writing this book, he made extensive use of its archives. He also interviewed many people who participated in the Swedish wartime intelligence effort. He describes in detail Beurling's attack on the G-Schreiber system as well as attacks on several other wartime crypto systems, noting high points from the history of Swedish cryptology.

The book will appeal to a broad audience of readers, from historians and biography buffs to mathematicians to anyone with a passing interest in cryptology and cryptanalysis. This English edition has been translated by Kjell-Ove Widman, Director of Sweden's Mittag-Leffler Insitute. Also on cryptography and available from the AMS is "Cryptography: An Introduction." ... Read more

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Conferences on Algebra, Analysis, Applied Math and Topology ... Read more

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The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources.Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical results in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. "Ramanjuan: Letters and Commentary" was selected for the "Choice" list of Outstanding Academic Books for 1996. ... Read more

Customer Reviews (1)

Get personal with Ramanujan through letters
Ramanujan was most certainly the most talented mathematician of this century. With essentially no formal training, he managed to discover an enormous number of formulas, many of which were quite different from those previously known. The story of how he came to the attention of the mathematical community and was brought into "formal" mathematical circles is an interesting one. Given the colonial nature of the relationship between England and India, it would have been "natural" for the English mathematicians to consider an untrained colonial native to be beneath them. However, to their credit, there is no evidence that the English mathematicians ever felt or acted this way.
This book is the story of Ramanujan told through the letters that were written by and about him. While many are very formal, you still see the personalities emerging. G.H. Hardy is at times in awe of Ramanujan's ability, proving to be a person of high quality as he tries as best he can to aid him in adapting to British society and to doing mathematics in a formal way. Many others are also involved, and it is clear that they do have a genuine interest in his welfare as a person and as a mathematician. The commentary included among the letters is very helpful in establishing a context for the text. The authors do a very good job in explaining the circumstances of the letters. Some deal with social conditions and others are as simple as a description of what a word means.
What is most impressive about the book is that there is no undercurrent of colonial class consciousness running through the material in the letters. Given the situation in the early part of the twentieth century, that would have been typical of most English men of the times and it is a tribute to the mathematicians that they avoided it. Not many others would have been so noble.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

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This extraordinary volume contains a large part of the mathematical correspondence between A. Grothendieck and J-P. Serre. It forms a vivid introduction to the development of algebraic geometry during the years 1955-1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process.In the book, the reader can follow the creation of some of the most important notions of modern mathematics. The letters also reflect the mathematical and political atmosphere of this period. They are supplemented by J-P. Serre's notes, which give explanations, corrections, and references to further results.The book is a unique bilingual (French and English) volume. The original French text is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right. The book also includes several facsimiles of original letters. The original French volume was edited by Pierre Colmez and J-P. Serre. The English translation for this volume was prepared by Catriona Maclean with the assistance of Leila Schneps and J-P. Serre.The book should be useful to specialists in algebraic geometry, mathematical historians, and to all mathematicians who want to experience the unfolding of great mathematics. ... Read more

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John von Neumann was perhaps the most influential mathematician of the twentieth century. Not only did he contribute to almost all branches of mathematics, he created new fields and was a pioneering influence in the development of computer science. During and after World War II, he was a much sought-after technical advisor. He served as a member of the Scientific Advisory Committee at the Ballistic Research Laboratories, the Navy Bureau of Ordinance, and the Armed Forces Special Weapons Project. He was a consultant to the Los Alamos Scientific Laboratory and was appointed by U.S. President Dwight D. Eisenhower to the Atomic Energy Commission. He received the Albert Einstein Commemorative Award, the Enrico Fermi Award, and the Medal of Freedom. This collection of about 150 of von Neumann's letters to colleagues, friends, government officials, and others illustrates both his brilliance and his strong sense of responsibility. It is the first substantial collection of his letters, giving a rare inside glimpse of his thinking on mathematics, physics, computer science, science management, education, consulting, politics, and war. With an introductory chapter describing the many aspects of von Neumann's scientific, political, and social activities, this book makes great reading. Readers of quite diverse backgrounds will be fascinated by this first-hand look at one of the towering figures of twentieth century science. Also of interest and available from the AMS is John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More and Invariant Measures. Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. ... Read more

Customer Reviews (2)

Does not cover CS
John von Neumann was a brilliant man, making significant contributions to quantum physics and higher mathematics.However, as this book says, "Von Neumann is best known in the general public for his work in computer design.His activity in this field is very well documented in the work of W. Aspray.Aspray's book contains quotations from many of von Neumann's letters concerning computer science; thus the current volume contains just a small selection of von Neumann's letters related to computers".

If you're interested in von Neumann as a computer scientist, buy John von Neumann and the Origins of Modern Computing (History of Computing) instead.

Insight into the Thinking of a Renaissance Man
John von Newman was one of the Renaissance Men of our century. He produced significant contributions in the areas of : Logic, Quantum Mechanics, Economics, Armaments, and Computer Science. As a case in point, the computer you are using to read this is almost certainly one based on von Newmann architecture. His work on the development of atomic weapons was as important as his development of the social concept of Mutually Assured Destruction which was the fundamental precept of the Cold War. Had he lived longer he would almost certainly have received a Nobel Prize in economics for his development of game theory. (He died at age 54, probably because of exposure to radiation.)

This book is a compendium of letters that he wrote. It contains letters on many subjects written to a wide collection of people from scientists to plitical leaders, business leaders and declining an invitation to give a speech.

In addition to the letters there is a 40 or so page preamble about him as a person and summarizing some of the work that he did. Largely unknown outside the technical areas in which he worked John von Newmann was a towering figure in twentieth century science. This book will not get a wide distribution, but it provides interesting insight into his thinking. ... Read more

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Gerhard Gentzen (1909-1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called "proof theory" but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today.The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945.Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for "German logic", and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smorynski on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smorynski explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program.This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. ... Read more

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Wallis was one of the most original mathematicians of the seventeenth century and he left his mark on mathematics in many ways. He introduced arithmetical limits into mathematics (his famous infinite-product expression for $\pi$ is an example). His researches (for example, the means whereby he obtained the aforementioned product) led directly to Newton's work on the binomial theorem and quadratures. He was the first to see the significance of fractional and negative exponents, and he is responsible for the introduction of such symbols as $\infty$ and such terms as hypergeometric series. He was very influential politically, very quarrelsome, and at the center of the scientific life of his time (for instance, it was owing to his advice that the Gregorian calendar was not introduced earlier into England, as he did not like the Pope). This second edition includes Foreword by E. N. da C. Andrade, a Bibliography and an Index. ... Read more

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For over two centuries, the work of the St. Petersburg mathematicians in number theory has constituted a glorious contribution to mathematics. The Russian book, The St. Petersburg School of Number Theory, is about the life and work of prominent members of this school, such as Chebyshev, Korkin, Zolotarev, Markov, Voronoi, and Vinogradov. These mathematicians are indeed a very distinguished group. Their work in number theory is of the highest quality and continues to have lasting significance.This English translation acquaints the reader with the most important works of these six eminent members of the St. Petersburg school. A short biography is given for each of them, followed by an exposition of some of his most significant contributions. Each contribution features the author's original terminology and notation and is followed by commentary. Certain works receive relatively complete expositions, while others are dealt with more briefly.With a Foreword written for the English edition, this volume will appeal to a broad mathematical audience, including mathematical historians. It is particularly suitable for graduate students and researchers interested in number theory. ... Read more

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This volume is a collection of papers by Robert Steinberg. It contains all of his published papers on group theory, including those on ``special representations'' (now called Steinberg representations), tensor products of representations, finite reflection groups, regular elements of algebraic groups, Galois cohomology, universal extensions, etc. At the end of the book, there is a section called ``Comments on the Papers''. The comments by Steinberg explain how ideas and results have evolved and been used since they first appeared. ... Read more

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V.S. Varadarajan has made significant contributions to a remarkably broad range of mathematical subjects which include probability theory, various mathematical aspects of quantum mechanics, harmonic analysis on reductive groups and symmetric spaces, and the modern theory of meromorphic differential equations. The papers included in this volume have been selected to highlight these contributions. For other wonderful titles written by this author see: Euler through Time: A New Look at Old Themes, Supersymmetry for Mathematicians: An Introduction, The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis, and Algebra in Ancient and Modern Times. ... Read more

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Weeks' volume is a translation from the Latin of the third and last edition of Waring's Meditationes algebraicae. Weeks incorporates many corrections and additions that had appeared separately. The appendix offers the only critical review of Meditationes ever published, written in 1923 by Franz X. Mayer. ... Read more

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This book contains essays on Ramanujan and his work , as well as important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader.

The book opens with the only four existing photographs of Ramanujan, presenting historical accounts and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes.

Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the Journal of the Indian Mathematical Society. The last half of the book begins with a section on "Ramanujan's Manuscripts and Notebooks". Included is an important article by G. E. Andrews on Ramanujan's lost notebook.

The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's "Ramanujan and pi", and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson.

This volume complements the book Ramanujan: Letters and Commentary, Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see these AMS publications, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.

Copublished with the London Mathematical Society. ... Read more