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Turning Points in the History of Mathematics pp 85–93Cite as

Birkhäuser

Philosophy of Mathematics: From Hilbert to Gödel

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Abstract

The nineteenth century witnessed a gradual transformation of mathematics—in fact, a gradual revolution, if that is not a contradiction in terms. Mathematicians turned more and more for the genesis of their ideas from the sensory and empirical to the intellectual and abstract. Although this subtle change already began in the sixteenth and seventeenth centuries with the introduction of such nonintuitive concepts as negative and complex numbers, instantaneous rates of change, and infinitely small quantities, these were often used (successfully) to solve physical problems and thus elicited little demand for justification.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Hardy Grant & Israel Kleiner

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  1. Hardy Grant
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  2. Israel Kleiner
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Correspondence to Hardy Grant .

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Grant, H., Kleiner, I. (2015). Philosophy of Mathematics: From Hilbert to Gödel. In: Turning Points in the History of Mathematics. Compact Textbooks in Mathematics. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-3264-1_10

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