Morris Kline (1908-1992) studied mathematics at New York University, earning his doctorate in 1936. He taught at NYU from 1938 to 1975. He was also associate editor of Mathematics Magazine and Archive for History of Exact Sciences. Among his books written for the general reader are Mathematics in Western Culture, Mathematics in the Modern World, Why Johnny Can’t Add, and Why the Professor Can’t Teach.
Mathematics: The Loss of Certainty (Barnes & Noble Rediscovers Series)by Morris Kline
Mathematics: The Loss of Certainty, originally published in 1980, refutes the myth that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. As Morris Kline points out, there is not one universally accepted concept of mathematicsthere are many conflicting/i>… See more details below
Mathematics: The Loss of Certainty, originally published in 1980, refutes the myth that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. As Morris Kline points out, there is not one universally accepted concept of mathematicsthere are many conflicting ones.
Yet the effectiveness of mathematics in describing and exploring physical and social phenomena continues to expand. Mathematical activity is flourishing as never before, with the rapid changes in computer science and the search for quantitative relationships in the social and biological sciences. “Are we performing miracles with imperfect tools?” Kline asks provocatively.
Two nineteenth-century developmentsnon-Euclidean geometry and quaternionsforced mathematicians to realize that mathematics is not a series of self-evident truths about nature produced by infallible reasoning. They found, for example, that several different geometries fit spatial experience equally well. All could not be truthsa realization that impelled mathematicians to investigate the nature of their axioms and “unassailable” reasoning. To their surprise, they found that the axioms were arbitrary and inadequate and their proofs were woefully defective.
To rebuild the foundations of mathematics and to resolve the contradictions, four schools of thought emergedeach differing radically in their views of what mathematics is. The book traces the history of mathematics’s fall from its lofty pedestal of unshakeability and explores the reasons for its continuing mysterious effectiveness. Kline explains in nontechnical language the drastic changes that have taken place in our understanding of “pure” as well as “applied” math, and the implications for science and for human reason generally.
Praise for Mathematics: The Loss of Certainty
“What we have here is a first class and impassioned war of ideas.”
“Immensely readable the copestone of his achievements .The story he has to tell is intensely dramatic, and he tells it well.” William Barrett, The New York Times Book Review
“Kline’s probing, exciting history is a revelation and an education, whose major revelation is a fluid art full of perplexity, doubt and even petty politics. No one who pretends to be informed should miss this valuable book.” Roger Dionne, Los Angeles Times
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