Dirichlet: A Mathematical Biography

ISBN-13: 9783030010713 / Angielski / Twarda / 2019 / 311 str.

Uta C. Merzbach

Opis

This is the first extensive biography of the remarkable German mathematician, Peter Gustav Lejeune Dirichlet (1805-1859). Dirichlet, who is credited with being one of the first mathematicians to give the modern, formal definition of a function, made deep contributions to number theory, including creating the field of analytic number theory. He is also known for his contributions to the theory of Fourier series and other topics in mathematical analysis. This monograph includes personal information about his life and the lives of some of his notable associates and how their lives were intertwined. In alternating chapters, a more mathematical guide to his publications and lectures is presented.This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.

Recenzje

"Uta Merzbach's mathematical biography of Dirichlet is a thoroughly researched volume that describes in detail the life, labors, and legacy of this remarkable mathematician, with full details of his family, friends, and colleagues, as well as descriptions of the general mathematical scene and of the various cities in which he lived. It also contains extensive and accessible summaries of his mathematical writings." (Robin Wilson, The Mathematical Intelligencer, Vol. 42 (4), 2020)
"The book under review is an outstanding piece of work and an important contribution to the literature on the history of mathematics in the 19th century." (Franz Lemmermeyer, zbMath 1412.01003, 2019)

Spis treści

Preface.- Acknowledgments.- Abbreviations and Conventions.- Rhineland.- Paris.- First Success.- Return to Prussia.- Early Publications.- Berlin.- Publications: 1829 - 1830.- Maturation.- Publications: Autumn 1832 - Spring 1839.- Expanding Interactions.- Publications: 1839 - 1845.- A Darkling Decade.- Publications: 1846 - 1855.- Göttingen.- Aftermath.- Lectures.- Centennial Legacy and Commentary.- Bibliography.- Index.

Blurb

This is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 – 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This unified approach is exemplified in a paper that effectively launched the field of analytic number theory. The same orientation pervaded his teaching, which had a profound influence on the work of many mathematicians of subsequent generations.

Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet’s life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.