This book provides the first detailed account of Riemann's life along with analysis of his major works and their reception. These themes are presented in a chronological flow that takes into account numerous others who played important roles in Riemann's brief life and career. Among the more prominent figures who influenced Riemann's work were Gauss, Dirichlet, and Jacobi, but several others, including the physicist Wilhelm Weber, also played a major part. Special attention is given to the last four years of Riemann's life, which he and his wife Elise mainly spent in Italy, where he died. Her role in supporting Richard Dedekind and Heinrich Weber, the editors of Riemann's posthumous papers, is one of the many new aspects covered in this book.

Drawing on family letters and other archival documents, the biographical chapters bring the reader into Riemann's often tumultuous personal life. Money and other mundane problems were a constant cause of concern, but even more serious were the health problems he suffered all his life. Socially awkward, he often withdrew from his peers while seeking solace in his work or that of others. Riemann was a voracious reader, but the present account offers a detailed picture of what he read and when. Plenty of mysteries still remain, but here for the first time one gains a sense of the extraordinary intellectual adventure that dominated Riemann's life.

To help orient the reader, the book begins with an Introduction describing the landscape of German mathematics before Riemann arrived on the scene and ending with a chronological list of key events in his life. The remainder of the book has a three-part structure. Part I tells the story of Riemann's life in four chapters, corresponding to four distinct phases in his career. Part II delves into his better-known mathematical works, treated at first chronologically in Chapters 5 to 8. These are followed by an examination of Riemann's work on physical topics in Chapter 9, and closing with Chapter 10, which discusses Gaussian themes and their connections with Riemann's work. Part III deals with aspects of Riemann's legacy in two chapters. Chapter 11 traces the activities of seven important pupils and followers of Riemann up until the early 1880s. Chapter 12 then picks up the story told in the final section of Chapter 4, which describes the initial plans to publish Riemann's Collected Works. How that project was eventually brought to fruition by Dedekind and Weber forms part of the remarkable story of their lifelong friendship.

The biographical parts of this book Chapters 1 to 4 and 12 are intended for the general reader. They are not totally "jargon-free", but will interest anyone with a taste for intellectual history. The remaining parts of the book aim to describe Riemann's work in the language of his time, which often means quoting him directly. A short section on "Reading Riemann" appears at the end of Chapter 5. For a serious historical account, one should always keep the author's voice in mind, even if, as in Riemann's case, the meaning of his words was at times unclear.

The first full account of Riemann's life and scientific achievements Places the great mathematician's life and work in historical context Provides a new interpretation of his mathematical legacy

Autorentext

David E. Rowe is professor emeritus for history of mathematics and natural sciences at Johannes Gutenberg University in Mainz. Much of his research has focused on the Göttingen mathematical tradition and the career of Felix Klein. In 2025, he published The Erlangen Program, an account of Klein's most famous work and its reception history. He documented the career of Hilbert's first doctoral student, Otto Blumenthal: Ausgewählte Briefe und Schriften (2 volumes, Springer 2018, 2019). His biography, Emmy Noether - Mathematician Extraordinaire, was published by Springer in 2021. He and Joseph Dauben served as general editors of a six-volume Cultural History of Mathematics (Bloomsbury, 2024). In 2025, Rowe and Jan Hogendijk received the Kenneth O. May Medal from the International Commission for the History of Mathematics for outstanding lifetime contributions to the field.

Inhalt

Preface: Riemann's Life and Legacy. Introduction: Riemann's Times. Part I Riemann's Life.- 1 Riemann's Formative Years, 18261847.- 2 Years of Adventure, 18481853.- 3 Years of Struggle, 18541858.- 4 Triumph and Tragedy, 18591866.- Part II Riemann's Works.- 5 Riemann's Doctoral Dissertation.- 6 Riemann's Habilitation Texts.- 7 Elliptic and Abelian Functions.- 8 Zeta-Function and Paris Paper.- 9 Mathematical Physics.- 10 Gaussian Influences.- Part III Riemann's Legacy.- 11 Riemann's Pupils and Followers.- 12 Editing Riemann's Collected Works.