Bernhard Riemann 1826-1866: turning points in the conception of mathematics

This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle — for mathematics and physics alike — to be a matter of ‘understanding the world through its behavior in the infinitely small.’ This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. Presents the work of Bernhard Riemann from a historical perspective Discusses the impact of Riemann's work on later math, physics, and philosophy Examines the philosophy of Reimannian thought INDICE: Preface.- Note to the Reader.- List of Illustrations.- Translator's Remarks.- Introduction.- Complex Analysis.- Real Analysis.- Geometry; Physics; Philosophy.- Turning Points in the Conception of Mathematics.- Bibliography.- Name Index.

• ISBN: 978-0-8176-4776-6
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 380
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés