Mathematics: The Loss of Certainty is a book by Morris Kline

Morris Kline

Morris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.Kline grew up in Brooklyn and in Jamaica, Queens...

 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, e.g. how 19th century mathematicians were surprised by the discovery of non-Euclidean geometry

Non-Euclidean geometry

Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...

 or how Goedel's incompleteness theorem disappointed many logicians.