Mathematics Form and Function

In this book, Saunders Mac Lane attempts to answer some questions about mathematics; it's origins, how it is organized, whether or not mathematics has formalisms that come from facts, how mathematics develops, how does someone evaluate the depth and importance of mathematical research, what should be the standards of rigor and finally, why is mathematics effective?

That final question goes a lot deeper than some would think. It ties itself right into epistemology, and how we know things that we know. At the same time, it covers a great deal of mathematical ideas. Starting at counting it goes into Peano axioms and other things. It structures itself differently from other books that survey mathematics in that it seems to organize the show more information by subject rather than chronologically.

At the end of the book, Mac Lane answers the questions he put forth in the introduction of the book. All in all it was a satisfying and interesting read. show less