Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures

A nice read and rather in line with some of the stuff i lately read about it. Brown argues for a more experimental view of mathematics, where mathematicians are not the people rigorously proofing everything, but the ones who contribute to our understanding of mathematics. Pictures, conjectures, intuition etc playing an essential role. The nice thing is that a lot of great mathematicians seem to agree with this view. It is contrary to the 'proofs only' approach that i encountered when studying math, and which at that time felt like a mathematicians form of machismo.
Interesting read in this perspective is Ulam's Adventures of a mathematician.

A rather unusual account of the foundations of mathematics; Brown covers all of the traditional schools (platonism, logicism, formalism, constructivism, intuitionism), but stands out by taking a stand for a modified form of platonism that's quite attractive. One of his concerns is the status of diagrams in proofs, and he makes interesting observations. It seems he does not know Peirce very well (he's consistently misspelt Pierce); Brown could have found some helpful tools and concepts in Peirce's writing.

Fantastic book. Fascinating questions are raised and addressed, in an easy to read and convincing style. If the topic interests you, this is a good place to start.