Resources for Math 3510, Fall 2010
I have placed three books on 2-hour reserve in Carlson Library. (Search by name: hewitt.)
- The Crest of the Peacock, by George Gheverghese
This important book takes an important first step towards filling a
large gap in the literature on the history of mathematics. Most
books accessible to undergraduates pay scant attention to the
mathematics that was not developed in Europe. Although far from
comprehensive, Joseph gives a good account not only of how other
cultures developed mathematical ideas centuries before they were
rediscovered in Europe, but also why their approach was often subtly
different than the European approach.
- Journey through Genius, by William Dunham.
Dunham believes that just as a course in the history of art would be
meaningless unless you look carefully at the art produced by the
greatest artists, so a course in the history of mathematics would be
meaningless unless you look at the mathematics produced by the
greatest mathematicians. Dunham looks at works of genius, from
Thales to Cantor. He walks you through the proofs of major theorems
as orginally given by their discoverers, using the tools available
at the time. He also includes biographical sketches and broader
historical context. In many ways it would be profitable to read
this book in parallel with our textbook.
- Mathematics and its History, by John Stillwell.
I confess that I have not read this book. I include it for the
obvious reason that its author also wrote our textbook. I intend to
read it this semester to see how he expands and elucidates some of
the issues raised in out textbook.
There are many websites with historical accounts, mathematical and
otherwise. Here I mention only two.
For us this site is by far the most valuable. Here you will find
biographies, maps, timelines, and much, much more.
This site is extremely important, and extremely flawed. You should
not let the flaws deter you, but neither should you ignore them.
Use Wikipedia as a starting point. Need to learn about Cyrus the
Great or the Counter-reformation? Wikipedia is a great place to
start. But don't stop there! read the article then follow-up
by heading to some of the references listed in the end. Always
verify information found at Wikipedia against other sources.
There are two other textbooks which may be helpful:
- Math through the Ages, expanded edition, by William
Berlinghoff and Fernando Gouvêa.
The NCTM standards call for the intergration of the history of math
into K-12 curriculum, and so this book was written with K-12
teachers in mind. It has two parts. In the first part they provide
a sweeping overview of the history of mathematics. In the second
they look in depth at individual topics. They try to answer
questions such as where our arithmetic symbols came from, or how our
concept of fractions evolved.
- A History of Mathematics, second edition, by Victor
This is a fairly comprehensive undergraduate treatment of the
history of mathematics. You may find it particularly usefull when
we discuss topics such as the Egyptian method of arithmetic
(section~1.3); Iraqi sexagesmials (section~1.3); Bhaskara's
solutions of Pell's equation (section~6.7); Cardano's
formulas (section~9.3); projective geometry (sections~10.1
and~11.5); and many others.
There are some BBC radio programs that help give us a glimpse of life
in the ancient world, and in particular the role of science and
mathematics. (Look for the Listen Now buttons on the pages
They begin with a high-level view of 3000 years of ancient Iraqi
history, focusing on the empires based at Babylon. There is a
discussion of Babylonian science and mathemtics beginning around
the 28-minute mark.
- There is a series entitled A history of the world in 100
objects. Each 15-minute episode focuses on a single object
from the British Museum. Here are a few that relate directly to our
There are 97 others. Enjoy!
- Cuneiform tablets.
The tablet featured here records an allotment of beer, the currency
of ancient Iraq, before money was invented. The object illustrates
how writing was invented by the accountants, and only later
exploited by the poets and mathematicians.
- Rhind papyrus.
Unlike Iraq very few written objects survive rom ancient Egypt. This
episode describes one of the most important. It is in essence a
self-study guide for the civil service exams, and hence illustrates
the main goal of math education for the past 5000 years.
- Rosetta stone.
How can we read objects such as the Rhind papyrus today, when the
language it was written in has not been spoken for 2000 years?
Because of the Rosetta stone. (You can read more about the
deciphering of the Rosetta stone in chapter~5 of The Code
Book, by Simon Singh.) How can we read the clay tablets from
ancient Iraq, whose languages have been extinct even longer?
One of the voices you will hear frequently at the BBC is that of
Eleanor Robinson. She has a fabulous article in the American Mathematical
Monthly which shows what can go wrong when mathematicians try
their hand at historical reconstruction. This piece concerns the most
famous mathematical tablet from ancient Iraq, the so-called
There is a useful atlas with which you can trace, for example, the flow
of european history starting in
year 400, just before the fall of the western Roman
Empire. Also useful is Europe: 10 centuries in 5 minutes.
Charlie Gunn's view inside hyperbolic space.