The Principles of Mathematics

Rating:
Summary: Dated, but still a gold mine.
Review: 10-Point Rating: (8.75)
One of the claims of the analytical school of western philosophy is that math is reducible to logic, specifically the logic of groups, classes, or sets. In this vein, I can think of no better introduction than Russell's Principles of Mathematics. Although many of the ideas he proposes are intellectually outdated, Russell's method is rigorous and his presentation is lucid. While this book is not for everyone, no serious student of mathematical foundations should be without it. The chapters on zero and the concept of continuity are especially insightful.

Rating:
Summary: Essential reading
Review: An essential reading for every student of Philosophy of Mathematics.

Rating:
Summary: Spliting Hairs Infinitesimally
Review: He doesn't do much theorem proving, but he tackles
head on all the basic problem of mathematics that were known
a hundred years ago. It was how well he did everything
that makes this still a must read if you love mathematics.
There is actually only one equation in his book that I can think of:
and it is of a Clifford geometry measure! This man was a mathematician's
mathematician and a metamathematics master in the language of
philosophy as well! The pages are falling out and I still
go to this and Sommerville when I want inspiration or understanding of really hard issues.