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I know that studying the evolution and history of a certain subject is a way of resolving the complexity of that subject. So I want to ask about references that describe the history and evolution of the foundation of mathematics as well as its philosophy and milestones of each part. For example, set-theory may be naive of axiomatic; and axiomatic have many versions. Each version is sufficient for explaining certain branch in mathematics. I want another reference emphasizing the application of each version in mathematics itself.

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Some references :

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I recently read a scholarly book relevant to this question.

Jeremy Gray, Plato's Ghost: The Modernist Transformation of Mathematics

The transformation in question goes from 1880 to 1910 (roughly speaking). Gray discusses how mathematics was done before, the turmoil surrounding the change, and how it was done after.

Recommended. But not for the faint of heart.

[Post copied from https://math.stackexchange.com/a/2000433/442 ]

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There is a good book on foundations with emphasis on history: Abraham Fraenkel and Yehoshua Bar-Hillel, Foundations of set theory. Original is in German. But a second revised edition, which has one more author, Azriel Levy, has been translated into English.

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