This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemanns ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemanns work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Preface.- Introduction.- 1.Athanase Papadopoulos: Looking backward: From
Euler to Riemann .- 2.Jeremey Gray: Riemann on geometry, physics, and
philosophy some remarks.- 3.Hubert Goenner: Some remarks on a contribution
to electrodynamics by Bernhard Riemann.- 4.Christian Houzel: Riemann's Memoir
Über das Verschwinden der Theta-Functionen.- 5.Sumio Yamada: Riemann's work
on minimal surfaces.- 6. Athanase Papadopoulos: Physics in Riemann's
mathematical papers.- 7.Athanase Papadopoulos: Cauchy and Puiseux: Two
precursors of Riemann.- 8.Athanase Papadopoulos: Riemann surfaces: Reception
by the French school.- 9.Ken'ichi Ohshika: The origin of the notion of
manifold: from Riemann's Habilitationsvortrag onward.- 10.Franck
Jedrzejewski: Deleuze et la géométrie riemannienne : une topologie des
multiplicités.- 11.Arkady Plotnitsky: Comprehending the Connection of Things:
Bernhard Riemann and the Architecture of Mathematical Concepts.- 12.Feng
Luo: The Riemann mapping theorem and its discrete counterparts.- 13.Norbert
A'Campo, Vincent Alberge and Elena Frenkel: The RiemannRoch theorem.-
14.Victor Pambuccian, Horst Struve and Rolf Struve: Metric geometries in an
axiomatic perspective.- 15.Toshikazu Sunada: Generalized Riemann sums.-
16.Jacques Franchi: From Riemannian to Relativistic Diffusions.- 17.Andreas
Hermann and Emmanuel Humbert: On the Positive Mass Theorem for closed
Riemannian manifolds.- 18.Marc Mars: On local characterization results in
geometry and gravitation.- 19.Jean-Philippe Nicolas: The conformal approach
to asymptotic analysis.- 20.Lizhen Ji: Bernhard Riemann and his work.
Lizhen Ji is a specialist in geometry and the author and editor of numerous books and articles. He currently teaches at Michigan and at several universities in China, and serves as an editor for several journals. Athanase Papadopoulos is the author/editor of 100 papers and over 20 books on mathematics and the history of mathematics. Directeur de Recherche at the CNRS, he has also been a visiting scholar at several universities and research centers (Princeton, MPI Bonn, ESI Vienna, CUNY New York, USC Los Angeles, etc.). Sumio Yamada has worked extensively in the US and Japan (Tohoku in Sendai, followed by Gakushuin in Tokyo). He is the author of several research articles. Lizhen Ji, A. Papadopoulos and S. Yamada have engaged in several fruitful scientific collaborations.
