Mathematics: The Loss of Certainty

Mathematics: The Loss of Certainty is a book by Morris Kline on the developing perspectives within mathematical cultures throughout the centuries.This book traces the history of how new results in mathematics have provided surprises to mathematicians through the ages. Examples include how 19th century mathematicians were surprised by the discovery of non-Euclidean geometry and how Godel's incompleteness theorem disappointed many logicians.

Kline furthermore discusses the close relation of some of the most prominent mathematicians such as Newton and Leibniz to God. He believes that Newton's religious interests were the true motivation of his mathematical and scientific work. He quotes Newton from a letter to Reverend Richard Bentley of December 10, 1692:When I wrote my treatise about our system The Mathematical Principles of Natural Philosophy, I had an eye on such principles as might work with considering men for the belief in a Deity; and nothing can rejoice me more than to find it useful for that purpose.He also believes Leibniz regarded science as a religious mission which scientists were duty bound to undertake. Kline quotes Leibniz from an undated letter of 1699 or 1700:It seems to me that the principal goal of the whole of mankind must be the knowledge and development of the wonders of God, and that this is the reason that God gave him the empire of the globe.Kline also argues that the attempt to establish a universally acceptable, logically sound body of mathematics has failed. He believes that most mathematicians today do not work on applications. Instead they continue to produce new results in pure mathematics at an ever-increasing pace.