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
Poincaré, and many others. He describes the lively debates surrounding
novel objects, definitions, and proofs in mathematics arising from the
use of naïve 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.
