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.
By:
Jeremy Gray
Imprint: Princeton University Press
Country of Publication: United States
Dimensions:
Height: 254mm,
Width: 178mm,
Spine: 38mm
Weight: 1.247kg
ISBN: 9780691136103
ISBN 10: 0691136106
Pages: 528
Publication Date: 22 September 2008
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Hardback
Publisher's Status: Active
"Introduction 1 I.1 Opening Remarks 1 I.2 Some Mathematical Concepts 16 CHAPTER 1: Modernism and Mathematics 18 1.1 Modernism in Branches of Mathematics 18 1.2 Changes in Philosophy 24 1.3 The Modernization of Mathematics 32 CHAPTER 2: Before Modernism 39 2.1 Geometry 39 2.2 Analysis 58 2.3 Algebra 75 2.4 Philosophy 78 2.5 British Algebra and Logic 101 2.6 The Consensus in 1880 112 CHAPTER 3: Mathematical Modernism Arrives 113 3.1 Modern Geometry: Piecemeal Abstraction 113 3.2 Modern Analysis 129 3.3 Algebra 148 3.4 Modern Logic and Set Theory 157 3.5 The View from Paris and St. Louis 170 CHAPTER 4: Modernism Avowed 176 4.1 Geometry 176 4.2 Philosophy and Mathematics in Germany 196 4.3 Algebra 213 4.4 Modern Analysis 216 4.5 Modernist Objects 235 4.6 American Philosophers and Logicians 239 4.7 The Paradoxes of Set Theory 247 4.8 Anxiety 266 4.9 Coming to Terms with Kant 277 CHAPTER 5: Faces of Mathematics 305 5.1 Introduction 305 5.2 Mathematics and Physics 306 5.3 Measurement 328 5.4 Popularizing Mathematics around 1900 346 5. Writing the History of Mathematics 365 CHAPTER 6: Mathematics, Language, and Psychology 374 6.1 Languages Natural and Artificial 374 6.2 Mathematical Modernism and Psychology 388 CHAPTER 7: After the War 406 7.1 The Foundations of Mathematics 406 7.2 Mathematics and the Mechanization of Thought 430 7.3 The Rise of Mathematical Platonism 440 7.4 Did Modernism'""Win""? 452 7.5 The Work Is Done 458 Appendix: Four Theorems in Projective Geometry 463 Glossary 467 Bibliography 473 Index 503"
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 Jnos Bolyai, Non-Euclidean Geometry, and the Nature of Space.
Reviews for Plato's Ghost: The Modernist Transformation of Mathematics
In Plato's Ghost, he has ... present[ed] us with an ambitious and in many respects remarkable synthesis of the modern transformation of mathematics via structural and set-theoretic notions, together not only with its logic and philosophy but also with related developments in artificial languages and psychology... I can certainly recommend Plato's Ghost highly as a rich resource and point of departure for readers who want to learn more about this exciting period in the development of modern mathematics. -- Solomon Feferman American Scientist This accessible, rigorous volume belongs in every serious library. -- J. McCleary Choice In a book aimed at the educated public, the author presents an impressive amount of data--both of the kind mathematicians with some awareness of the history of their subject may be aware of, and of an entirely different kind, coming from the outskirts of mathematics, from philosophy, from physics, or from the popularization of mathematics, which will likely be new even to historians of mathematics. -- Victor V Pambuccian Mathematical Reviews
- Commended for Choice Magazine Outstanding Reference/Academic Book Award 2009.
- Short-listed for Choice Magazine Outstanding Reference/Academic Book Award 2009
- Short-listed for Choice's Outstanding Academic Books 2009 (United States)
- Shortlisted for Choice Magazine Outstanding Reference/Academic Book Award 2009.
