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Recently I got interested in the foundational crisis of mathematics. As a theoretical physicist (so, not a mathematician), I am looking for a book that gives a historical take on the matter while also providing a basic understanding of the logic and math concepts that sparked the crisis and those that ultimately solved it.

Thanks in advance for any suggestions!

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If you are interested in a history of both foundational questions and their mathematical background, there is a book of one of the most prominent historians of mathematics, Ivor Grattan-Guinness, The search for Mathematical Roots. 1870-1940- Logic, Set Theories and the Foundations of Mathematics from Cantor to Russel to Godel, Princeton University Press, 2000.

This book is really profound and particular, because it gives a detailed account of the mathematical aspects, not only of philosophical aspects, and a comprehensive treatment of the history of logic in that period.

As for the philosophical and foundational aspects, there are many good books that introduce to philosophy of mathematics, as books indicated above in the comments. I can mention in particular a source book, a classical reference, well-known selected readings book, where you can find classical important articles about the subject, that is Benacerraf P., Putnam H. (eds.), Philosophy of Mathematics- Selected readings, Cambridge University Press, 2° ed., 1982.

[edit] I see that you are Italian, I too. So you can read also, in Italian, Gabriele Lolli, La guerra dei trent'anni (1900-1930)-Da Hilbert a Gödel, ETS, 2011.

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