Norbert Wiener (1894–1964) was an American mathematician who worked in many fields of mathematics, mostly applied, and is credited with the invention of cybernetics. He was an early example of a child with a “tiger parent” who dominated his education and planned out his life for him. A contemporary example is Ken Ono; see his autobiography *My Search for Ramanujan*. There are eerie parallels in their careers, including their fathers assigning each of their children a career that was to be their specialty. Wiener’s autobiography appeared originally in two volumes, *Ex-Prodigy: My Childhood and Youth* (1953) and *I Am a Mathematician: The Later Life of a Prodigy* (1956). The present book is an omnibus of these two volumes and includes a historical introduction by Ronald R. Kline, a historian of science at Cornell.

The first volume covers Wiener’s life from birth to his marriage at age 31. Wiener’s mother was an American of German-Jewish descent. Wiener’s father Leo was a Russian Jewish immigrant to the US who took a lot of odd jobs when he first arrived but eventually became head of Slavic Languages and Literature at Harvard. He was intellectually restless and had wide interests, including being a serious amateur in mathematics. He developed a theory of education that involved unrelenting pressure, little praise, and harsh criticism for any failings. He applied this to his first-born, Norbert, with great success. Norbert entered college at age 11 and received a Ph.D. from Harvard at 18. Leo was convinced that Norbert was an ordinary child who had benefitted from Leo’s educational theories; he never understand that Norbert was really a child prodigy. Leo’s theories had no success with his next two children, but he blamed that on their being girls. His last child was also a boy, but by that time he delegated the child’s education to Norbert, who would not apply the same methods.

Norbert’s career (chosen by his father) was to be philosophy, which he satisfied by taking a Ph.D. in mathematical logic under Josiah Royce and Karl Schmidt at Harvard. He then had a traveling fellowship for several years, starting with a course of study in philosophy and logic under Bertrand Russell at Cambridge. Russell convinced him that he needed to know more mathematics if he wanted to be a philosopher of mathematics, so he also took courses under G. H. Hardy, whom he adored. He then went to Göttingen and studied under David Hilbert and Edmund Landau. He did not like Landau at all and is very dismissive of him in this book, but he greatly admired Hilbert.

After that he was at loose ends; World War I was starting, the job situation was dismal, and he took some odd jobs such as encyclopedia writer. Finally he got a position at MIT (which back then was strictly an engineering school and did no math research), where he stayed the rest of his life. He gradually began to feel free of his father’s dominance, starting with his time in Europe, but didn’t really feel independent until his marriage. He gives his wife, Margaret Engemann, tremendous credit for building up his self-confidence.

The second volume has a different nature, and focuses on his professional work rather than his family. It backtracks to age 24 and overlaps some of the first volume. Wiener did a great deal of traveling all over the world as a visiting scholar, and he includes a detailed account of each trip, including the scholarly environment at each place and a description of the people he worked with.

Wiener, like his father, had varied interests, and was a great interdisciplinarian who collaborated with many other scientists, not all mathematicians. He even took an interest in number theory. Prompted by a discussion with A. E. Ingham, he and his student Ikehara developed an especially simple and illuminating proof of the Prime Number Theorem based on Fourier transforms, that was the standard proof for many years. Being at MIT he was exposed to many practical problems, and he was gregarious and talked to other scientists and engineers wherever he was and took an interest in their problems. The book has very accessible descriptions of the types of work he did and why the problems were important. His work in cybernetics started in World War II with the design of automatic tracking systems for anti-aircraft guns; he is credited with inventing the term and the field of cybernetics. (Despite the title of the book, only the last part of his life was in cybernetics.)

Wiener is well-known among mathematicians for his absent-mindedness and for his high self-regard, but these don’t come through in this work. Hans Freudenthal wrote of him that “He spoke many languages but was not easy to understand in any of them.” This book, in contrast, is easy to understand. Wiener seems to have made a special effort to be understandable by the layman, especially in the mathematical descriptions in the second volume. The first volume is written in a slightly stuffy, old-fashioned style, with lots of broad generalizations about people, especially the Jews, and is also very curmudgeonly. The second volume is much more straightforward and relaxed.

Wiener has been the subject of several biographies, and it’s worth consulting these also, because (as Kline points out in the Foreword) Wiener omitted several important facts about himself. There’s a recent biography by Montagnini, *Harmonies of Disorder*. Two older but valuable biographies are Conway & Siegelman’s *Dark Hero of the Information Age: In Search of Norbert Wiener, Father of the Cybernetic Age* (Basic Books, 2005) and Heims’s *John von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death* (MIT Press, 1980).

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is allenstenger.com. His mathematical interests are number theory and classical analysis.