Mathematics, The loss of certainty
Morris Kline  Oxford University Press, 1980  ISBN: 0195030850

Mathematics has an air of being the most secure form of knowledge. In Mathematics, The Loss of Certainty, however, Morris Kline shows that this is not necessarily deserved. He shows how, rather than mathematics being an obvious progression of knowledge, in fact many ideas in the subject were strongly resisted when first introduced, and even when accepted often rested on insecure foundations. He explains how Euclidean geometry turned out not be as 'obviously true' as people thought, how calculus was based on the shaky ground of infinitesimals, and how grudgingly imaginary numbers came to be accepted as a valid way to do calculations.
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