I just finished reading The Annotated Turing: A Guided Tour Through Alan Turing’s Historic Paper on Computability and the Turing Machine. Charles Petzold does an excellent job explaining one of the most important papers and proofs in all of mathematics and logic. I thouroughly enjoyed Petzold’s explainations intermixed with history about Turing.  He carefully crafts a story about Alan Turing in the annotations, taking important events in Turing’s short life and molding them into segues to various concepts in the paper itself.  Jumping back and forth from history to math in this way proved to be a very interesting way to read a mathematical proof (and I mean that in a good way).  

The math and logic can be a bit rigorous.  We are talking about the paper that established one of the core principles of formal math: that it is impossible to create a general algorithm to determine any truth.  Until 1936, most mathematicians thought that this was indeed possible.  A famous mathematician, David Hilbert, had issued a challenge known as the Entscheidungsproblem.  Turing, and Alonzo Church, independently answered the call by proving Hilbert’s assertion wrong.  While Church used a more formal mathematical approach, Alan Turing basically invented modern computer science to provide the concepts needed to prove that no such universal algorithm could exist.  On the path to this conclusion, he also proved that there must exist real numbers that cannot be computed.  Think about that one for a bit!  It is difficult to overstate the importance and impact Turing and his paper have had on our world in general, and in the subjects of mathematics and computer science in particular.

I highly recommend this book.  While the logic gets difficult in spots, one can skim over these sections and get to the point.  Petzold did right by Turing in this annotated version of his paper.  Its an informative and enjoyable read.

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