Plato's Ghost (eBook)

The Modernist Transformation of Mathematics

Jeremy Gray (Autor)

eBook Download: PDF

2008
528 Seiten
Princeton University Press (Verlag)
978-1-4008-2904-0 (ISBN)

Infos

Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincare, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naive set theory and the revived axiomatic method-debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Autor

Jeremy Gray is professor of the history of mathematics and director of the Centre for the History of the Mathematical Sciences at the Open University. His books include Worlds Out of Nothing and János Bolyai, Non-Euclidean Geometry, and the Nature of Space.

Produkt-Details

• Erscheint lt. Verlag: 2.9.2008
• Zusatzinfo: 36 b/w illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Geschichte
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Technik
• Schlagworte: abductive reasoning • abstract algebra • Alessandro Padoa • Algebra • Antinomy • aphorism • appearance and reality • A priori and a posteriori • Axiom • Axiom of reducibility • Bernhard Riemann • Big O notation • Burali-Forti paradox • Characteristica universalis • Classical Logic • classical mathematics • conjecture • Continuum Hypothesis • Contradiction • Conventionalism • counterexample • Crispin Wright • David Hilbert • Decision problem • Dirichlet Integral • Divisibility rule • Edmund Husserl • Equation • Ernst Zermelo • Euclidean Geometry • Felix Hausdorff • Fictionalism • For All Practical Purposes • Foundations of mathematics • G. E. Moore • Generality of algebra • Geometry • Gettier problem • Gödel's Incompleteness Theorems • Gottlob Frege • Halting Problem • Hermann Weyl • Hilbert's program • Homogeneous Coordinates • idealization • ideal type • Intuitionism • Intuitionistic Logic • Jordan Curve Theorem • Josiah Royce • Leonard Nelson • Logical Investigations (Husserl) • Logical Positivism • logicism • mathematician • Mathematics • Mathesis Universalis • Max Dehn • Mental Space • Moore method • neutral monism • Nominalism • Non-Euclidean geometry • P-adic number • Paradoxes of set theory • Philosophical investigations • Philosophical Language • Philosophy • philosophy of mathematics • Pierre Duhem • pragmaticism • Primitive notion • Principia Mathematica • Pure Mathematics • real number • Richard's paradox • Riemannian Geometry • Riemann surface • Russell's paradox • SCHOLASTICISM • Science and Hypothesis • scientific notation • Scientism • set theory • Significant figures • Sign (mathematics) • Skolem's Paradox • Special case • Theorem • theory • Theory Choice • The Philosopher • The Principles of Mathematics • transcendental arguments • Turing Machine • Utilitarianism • Wilhelm Ackermann • Zeno of Elea • Zeno's paradoxes • Zermelo–Fraenkel set theory
• ISBN-10: 1-4008-2904-6 / 1400829046
• ISBN-13: 978-1-4008-2904-0 / 9781400829040