Geometry in History

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Plato on Geometry and the Geometers.- Topology and Biology: From Aristotle to Thom.- Time and eriodicity from Ptolemy to Schrödinger: Paradigm Shifts vs Continuity in History of Mathematics.- Convexity in Greek Antiquity.- On the Concept of Curve: Geometry and Algebra, fromMathematicalModernity to MathematicalModernism.- From Euclid to Riemann and Beyond: How to Describe the Shape of the Universe.- A Path in History, from Curvature to Convexity.- The Axiomatic Destiny of the Theorems of Pappus and Desargues.- Projective Configuration Theorems: Old Wine into New Wineskins.- Poincaré’s GeometricWorldview and Philosophy.- Perturbing a Planar Rotation: Normal Hyperbolicity and Angular Twist.- René Thom and an Anticipated h-Principle.- Rigid and Flexible Facets of Symplectic Topology.- Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective.- Basic Aspects of Differential Geometry.- The Global Study of Riemannian-Finsler Geometry.- The Poincaré Conjectureand Related Statements.- A Glimpse into the Problems of the Fourth Dimension.- Memories fromMy Former Life: The Making of a Mathematician.- Index.

The editors are mathematicians whose work is well known (Dani in dynamics and ergodic theory, and Papadopoulos in geometry and topology of low dimensions). They are the authors of many research articles and monographs, and they edited several books. They have a broad view on the current research on geometry, on the history of the subject and on its impact in modern research. Dani is the editor-in-chief of Ganita Bharati (Bulletin of the Indian Society for History of Mathematics).