"Lecture" for Week 5

A whirlwind tour through 1000 years ...

China and India

• Here is my personal musical take on the Chinese remainder theorem (The current home of RESIDUE_INT is here.)
• The other most famous contribution of classical China is Gaussian elimination for solving systems of linear equations, 16 centuries before Gauss. Stillwell will get to that in Sec. 6.2, and I will in a much later week on the history of linear algebra.
• Katz has a section on Indian contributions to trigonometry. Indian mathematicians from Bhaskara I to the 14th century worked at calculating tables of sines, etc., presumably for applications to astronomy and navigation. To this end they developed various approximation and interpolation formulas that are understandable today but must have been nonobvious and ingenious at the time.

The Islamic period

This week's reading, especially the Islamic part, is full of unfamiliar and complicated names. It's good we don't have a final exam, right? I feel I ought to be providing some guidance as to which are the most important figures from the Islamic culture. My list is

• Al-Kwarizmi
• Omar Khayyam
• Avicennna and Averroes, who weren't primarily mathematicians (mentioned in long footnotes in the Medieval chapter)
I have to admit that the main criterion for getting on this list is that I had heard of the person before doing the reading the first time. Perhaps the most striking or inspiring thing about these periods is that some individuals did do significant mathematics in such isolation, in societies that were not conducive to it.

The medieval period

Continuing the list of famous figures:
• Fibonacci. I made an attempt to find out why Leonardo of Pisa is called "Fibonacci". Both Katz and Allen say that the name was not applied to him until the 19th century; Katz obviously dislikes the name and brings it up as seldom as possible. But Carl Boyer's history-of-math book says that it just means "son of Bonaccio" -- Leonardo being himself one of those rich merchants' sons that he and his successors made a living teaching, according to Katz p. 214.
• Oresme (Katz tells us to pronounce it "o-REM"). Betraying my physics background (and my years as a calculus teacher), I find him to be the most interesting figure of this period. Apparently he was the first to draw graphs of functions representing quantities other than positions, and had some understanding of the relations between position, velocity, and acceleration.