OUTTAKES

Since the first draft of the second edition was too long (some 800 pages, which had to be cut down to 600), I found myself sacrificing some material that I was very reluctant to part with. I decided to put the cuts that were too extensive and seemed too good to omit entirely into a web page. The following links contain that material. It is mostly historical matter of secondary importance, or mathematical detail that would have complicated the discussion too much, had I left it in the textbook. Clicking on any of the fifteen links below will bring up a pdf file (for which, of course, you'll need the Acrobat Reader or equivalent). The highlighted links show which section of the book the material came from.

Section 3.1 : Plato's defense of highly abstract topics in education (from his Laws).

Section 3.5: A sketch of the life of a remarkable seventeenth-century Mexican woman intellectual.

Section 4.3: The one "classical" woman mathematician I didn't discuss in the textbook, and the reason why I didn't.

Section 6.2: What a computation with the Chinese Shang numerals may have looked like, and the square-root algorithm.

Section 6.9: A fifteenth-century reaction to the great marvel—Hindu-Arabic numerals!

Section 7.2: An early Greek neo-Platonist on number theory and music.

Section 8.1: Fermat's method of infinite descent and his "last theorem" for the case n = 4.

Section 10.1: The summary of the history of Greek mathematics by Eudemus and Proclus.

Section 10.3: Some legends about Archimedes' life, death, and tomb.

Section 11.1: The Heron/Archimedes theorem on the area of a triangle in terms of its sides. Details of the proof.

Section 11.2: Map of a Roman town, from the sixth century CE.

Section 12.2: Two mechanical methods of drawing, from the Renaissance and the Enlightenment periods.

Section 13.4: Interpolation in early Chinese mathematics.

Section 13.5: Ancient Greek algebra. (This entire section was omitted from the textbook.)

Section 15.1: Cauchy on permutation groups.