J. Ferreiros

This book covers the period 1850-1940, but the twentieth-century portions are much less thorough. The book begins by discussing the different schools of German mathematics ca. 1850; it may be useful to keep a scorecard here. Then it delves into close readings of Riemann, with his analytically-motivated precursors to set theory and topology, followed by discussions of Dedekind and Cantor. After this, the history becomes a number of short threads about Peano, Hilbert, Russell, Zermelo, and Gödel.

It was very interesting to trace the philosophical shift from concept-extension to predicativity, and to see the lexical progression from manifold (mannigfaltigkeit) to system to set (menge). This makes me want to go back and read other things with fresh eyes, such as Lakoff and Nunez's Where Mathematics Comes From and Devlin's Math-as-Gossip thesis.

Highly recommended.
Read before this book: some knowledge of set theory to be able to follow along.
Read after this book: Constructibility?… (mehr)