The Ghost of Plato. The Modernist Transformation of Mathematics

“Plato’s ghost” is the first book that is considered the development of mathematics from 1880 to 1920 as a result of the influence of modernism, similar to what happened in art, literature and music. Jeremy Gray traces the growth of mathematical modernism in interaction with physics, philosophy, theology, psychology and ideas about real and artificial languages. The author shows how modernism led to solving many problems, and also posed even deeper and, ultimately, insoluble issues.
Gray demonstrates how mathematicians-Modernists believed that they advanced further than anyone else, only to make deeper mistakes. He tells the story of these ambitious and brilliant mathematicians, including Richard Dedecinda, Henri Lebeg, Henri Poincare, David Gilbert and many others. He describes lively debates around new objects, definitions and evidence in mathematics that arose as a result of the use of the naive theory of sets and a revived axiomatic method - debates that have grown into modern arguments in philosophy, including a crisis of foundations and mathematical Platonism.
"Ghost Plato" is a compulsory reading for mathematicians and mathematics historians. The book can be fruitfully used as an addition to various courses of philosophy, including the philosophy of mathematics and logic, the history of analytical philosophy and the philosophy of science