NORBERT WIENER: A MATHEMATICIAN AMONG ENGINEERS

Norbert Wiener (1894–1964) is well known by the general public as the founder of Cybernetics, by mathematicians as one of the first north-American mathematicians who win international prestige — as the person who formalized Brownian motion, solved the Zaremba problem and was the author of two seminal papers devoted to Generalized Harmonic Analysis and Tauberian Theorems — and by engineers as the person who proposed much of the Fourier analysis used by them and contributed to the foundation of the statistical theory of communication — which includes the use of wave filter theory, information theory and prediction theory in control and communications as well as the automation of all types of electronic devices.

Wiener's research, which was frequently motivated by physics, engineering, or biology, was a clever mixture of Fourier analysis and probability theory. His contributions to electronics through his work on filtering (that is, the separation of noise from a message), and the theory of prediction made him very valuable to electronics engineering. In addition, Wiener addressed many other topics, including the formalization of the Brownian motion, ergodic theory, wave filter theory, and information theory. Taking all these ingredients together, he ventured to create a new scientific paradigm: cybernetics.

This book contains a detailed explanation of Wiener's life, his many colleagues, and the historical context in which he lived, as well as Wiener's work. It also contains a large appendix about 'Wiener, Shannon, and the rise of a Digital World'. The main focus of the book is on Wiener's work related to electrical and electronic engineering and the way he used his mathematics to create the main concepts and techniques of the statistical theory of communication. In particular, the author presents Wiener surrounded by the engineers that worked at MIT with whom he maintained strong contact. It was in this atmosphere that information theory arose, and Wiener was a main influence on the people who developed that theory.

Contents:

• Foreword
• About the Author
• Childhood and Youth: From Child Prodigy to Doctor in Philosophy
• Beginnings as a Mathematician
• Life Among Engineers
• Climbing Mathematical Olympus
• Mathematics for War
• Cybernetics: The Return to Philosophy
• Appendix: Wiener, Shannon, and the Rise of a Digital World
• Chronology
• Doctoral Students of Wiener
• Bibliography
• Name Index
• Subject Index

Readership: Undergraduate and graduate students, researchers and practitioners in the fields of mathematics, physics, electrical and electronic engineering, and even biologists, physicians, and philosophers. It will also be useful to people interested in the history of science and technology.

'I am a mathematician with an interest in the history of mathematics and of mathematicians. As such, I loved this book. It is a fascinating tour of the life and work of Norbert Wiener. It is a book written for someone who knows a reasonable amount of mathematics and has an interest in Wiener's life and his times. In short, it is a book written especially for me. But I do hope and expect that others will also delight in this book.' - Allan PinkusProfessor EmeritusDepartment of Mathematics, Technion

'Writing a book about Norbert Wiener is a most delicate task. Jose María Almira has achieved this challenge with tact, accuracy and sharpness. This book presents a very fair analysis and description of the complex personality of Norbert Wiener, mixed with a pedagogical and illuminating description of his mathematical contributions. The book will be of interest to anybody interested in the human aspects of mathematics and sciences in the XXth century, and on their role in society.' - Jean MawhinProfesseur Ordinaire ÉmériteInstitute of Mathematics and PhysicsUniversité catholique de Louvain, Belgium

'I found the book fascinating. It is a unique combination of Wiener biography, what happens to child prodigies, pure mathematics, stories about Wiener's many colleagues, and critical issues of importance to information and electrical technology practitioners. The author has a compelling, natural talent for telling these stories. Norbert Wiener is a major contributor to electrical engineering and many of its everyday concepts are due to him. The book does a good job in portraying Wiener, but it is only one third biography. The rest is technology and half of that is pure mathematics. It is simply a good book and it brings electrical engineering to life.' - John B AndersonProfessor Emeritus in Digital Communication, Electrical and Information Engineering DepartmentLund University, Sweden

'It is not surprising that Norbert Wiener, a critical figure in the history of 20th century mathematics, science, and technology, has already inspired several biographies to supplement his own two autobiographies. What then can a new study of Wiener add? Jose Maria Almira's book gives us a compelling and emphatic answer! Writing with enthusiasm, Almira accurately and entertainingly captures not only the life and times of Wiener, but also how Wiener used mathematics to solve engineering problems and create his masterpieces.' - Asuman G AksoyCrown Professor of Mathematics and George R Roberts FellowDepartment of Mathematical SciencesClaremont McKenna College, California

'In Norbert Wiener: A Mathematician among Engineers, ALMIRA JOSE MARIA escapes the usual criticisms that other biographies of Norbert Wiener might get. He presented a very fair analysis and description of the complex personality of Norbert Wiener, mixed with a pedagogical and illuminating description of his mathematical contributions. Another original feature of this biography, announced in the title, is a very pertinent analysis of the links between Wiener's mathematical contributions and engineering problems, and his (sometimes difficult) collaboration with many engineers and scientists.The book will be of interest to anybody interested in the human aspects of mathematics and sciences in the XXth century, and on their role in society.' - Jean MawhinProfesseur Ordinaire ÉmériteInstitute of Mathematics and Physics, Université catholique de Louvain, Belgium

Key Features:

• The book contains both a detailed account of Wiener's biography and an extensive explanation of his use of mathematics to solve engineering problems
• Although the mathematics are explained, this is done with an elementary exposition, so that many technical details are avoided. The mathematics are presented in such a form that the reader can understand how Wiener's ideas evolved, and see them as a natural and integrated flow
• A discussion of the Militarization of Science in the USA (and Wiener's thoughts on that issue) is included
• An extensive appendix where Wiener's and Shannon's contributions to the rise of a Digital World are explained and confronted, is included
• The book contains many boxes with extra explanations about the characters appearing in the book as well as about mathematics and engineering ideas and problems. Thus, a two-level reading can be made: one can just read the main text or can also read the boxes
• The book contains a detailed bibliography, which is decomposed in different blocks: one for Wiener's original work, another about biographical papers and books about of Wiener, etc. This facilitates to the interested readers a choice of further reading depending on their own interests