The Nature of Mathematics and the Irrationality of the Square Root of Two

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.