Some more long introductory remarks and commentary throughout readings of the closing pages of the chapter culminating in the explanation of the "punchline" conclusion of the chapter which is: "Necessary truth is the subject matter of mathematics. It is not the reward we get for doing mathematics". This is a good exploration of fallibility, the relationship of physics to mathematics and how science is, in a sense, logically prior to mathematics (and logic for that matter!)...all because proof is a physical process.