Mathematical Reasoning and Visualization -- Visualization in Logic and Mathematics -- From Symmetry Perception to Basic Geometry -- Naturalism, Pictures, and Platonic Intuitions -- Mathematical Activity -- Mathematical Explanation and Proof Styles -- Tertium Non Datur: On Reasoning Styles in Early Mathematics -- The Interplay Between Proof and Algorithm in 3rd Century China: The Operation as Pr…
Introduction: The Birth and Growth of a Community -- History or Heritage? An Important Distinction in Mathematics and for Mathematics Education -- Ptolemy’s Mathematical Models and their Meaning -- Mathematics, Instruments and Navigation, 1600–1800 -- Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions -- The Mathematics and Science of Leonhar…
Mathematics, Art and Architecture -- Mathematics, Art and Architecture -- From Tiling the Plane to Paving Town Square -- Mathematics in Contemporary Arts — Finite and Infinity -- De Insana Geometria -- Ovals in Borromini’s Geometry -- Fractals: A Resonance between Art and Nature -- Mathland — From Topology to Virtual Architecture -- Visual Mathematics and Computer Graphics -- Introduction…
Prologue: A journey to Rome -- The musician's son -- A gifted young Tuscan -- To Rome and the Jesuits -- A Surveyor of Inferno -- The spheres from the tower -- From Pisa to Padua -- Signs in the sky -- De Revolutionibus Orbium Coelestium -- Lecturer and designer -- A professor's commitments -- Modern physics is born -- A new star in an unchanging sky?- Drawing close to a court -- The balls fall…
Question and Method -- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field -- Paths toward Algebraization — The Field of Limits: The Development of Infinitely Small Quantities -- Culmination of Algebraization and Retour du Refoulé -- Le Retour du Refoulé: From the Perspective of Mathematical Concepts -- Cauchy’s Compromise Concept -- Development of Pure…
Parte 1 -- Un cifrario del XVIII secolo -- La prima macchina cifrante al mondo -- Damm, Hagelin e Gyldén -- Intercettazione di segnali radio e analisi crittografica prima del 1939 -- Guerra -- Entra in scena Arne Beurling -- La flotta russa del Baltico -- Segnali misteriosi -- Telescriventi -- L’analisi di Beurling -- La G-Schreiber e gli “app” -- Crittoanalisi sistematica -- Esce di sce…
The Main Theorem: Cyclic Algebras -- The Paper: Dedication to Hensel -- The Local-Global Principle -- From the Local-Global Principle to the Main Theorem -- The Brauer Group and Class Field Theory -- The Team: Noether, Brauer and Hasse -- The American Connection: Albert -- Epilogue: Käte Hey.The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept…
Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (espec…
1 The Graeco-Roman World -- 2 The Roman world from the end of the republic to the end of the empire -- 3 The Middle Ages -- 4 From the age of the great transoceanic discoveries to the new measurements of the Earth .90 -- 5 The Figure and the size of the Earth in the XVIII Century -- 6 From the French Revolution to the artificial Satellites -- Epilogue -- The concept of Geoid -- The mathematical…
The Role of Mathematics in Physical Sciences — Interdisciplinary and Philosophical Aspects -- Mathematics and Physics: Reflecting on the Historical Role of Mathematics -- Oliver Heaviside’s “Dinner” -- Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity -- John von Neumann on Mathematical and Axiom…