From Kant to Hilbert: A Source Book in the Foundations of Mathematics is an autodescriptive title. It is a collection of papers, books, letters, notes, and other writings by mathematicians influential and forgotten, translated when necessary into English, that track the development of nineteenth-century mathematics, which really means mid-1700s to early-1900s mathematics. I've just finished the first volume, and begun on the second. The title references another very influential source book, From Frege to Godel, edited by Jean van Heijenoort, which covers mathematical logic between the two figures. Mathematical logic and foundations are intertwined essentially, though with their differences, and Ewald lays this out nicely in the preface; it does a good job of providing that second perspective. I'm likely going to read my copy of the second volume together with van Heijenoort's, as both roughly cover the same period of time.

Mathematics and philosophy have historically been in great dialogue, and this first volume presents many paradigms of that. If one heard a list of just some of the thinkers represented—Berkeley, D'Alembert, Kant, Bolzano, Peirce—it could be easily mistaken for a philosophy source book. Of course many of the topics discussed pertain intimately to both disciplines.

You may have plenty of moments which are those flashes of inspirations. Berkeley is always a powerhouse. Lambert's quasiprediction of non-Euclidean geometry. Kant's toying with the idea that the inverse square law is the a priori ground of the three-dimensionality of space and not vice-versa—this is a fascinating thing to consider. Seeing how the minds of an age wrestle with the twin ideas of imaginary numbers and infinitesimals tearing apart the accepted mathematical notions is a Miltonian scene. I still don't fully understand quaternions.

I'd tentatively say that a solid understanding of mathematical foundations is prerequisite for pursuing modern philosophy. I don't have this yet, and so I don't pursue modern philosophy. I struggle especially with how to interpret the consequences of Godel, which I'm sure is partially because I don't understand everything in logic leading to him, and also because it's naturally difficult. Certainly there's a lot more to learn. This book was a part of that.