THE 2001 MAA NORTH CENTRAL
SECTION SUMMER SEMINAR |

**THE HISTORY OF MATHEMATICS
V. Frederick Rickey, Lecturer**

**JULY 24-27, 2001
BEMIDJI STATE UNIVERSITY
BEMIDJI MINNESOTA**

Details of registration, housing, etc.

This summer short course consisted of a number of different types of activities, including the following:

- A public lecture on the palimpsest of Archimedes.

- Lectures on different aspects of the history of the calculus.
- Examples of how to use history in the classroom.
- Ideas about teaching history of mathematics courses.
- Finding history on the internet and judging its quality.
- A book display.
- Time to talk.

**1. A public lecture on the palimpsest of
Archimedes. **Thursday, July 26, 8:00 pm in Hagg-Sauer hall, room 113.
All other lectures will take place in this same room.

**Title:
****The Archimedes Palimpsest**

Abstract:
On 29 October 1998, Christie's auction house in New York City sold a tenth
century manuscript that contained several works by Archimedes, including the
unique surviving copy of his wonderful work that we call "The Method."
This talk will focus on the remarkable history of this manuscript, including, a
description of its discovery and publication by Heiberg early in the last
century, its sale at Christie's, its display at the Walter's Art Gallery in
Baltimore and the Field Museum in Chicago, and what is happening to the
manuscript now. The manuscript itself will be described as well as its contents.
The mathematical content of this public lecture will be fairly low and it will
be accessible and of interest to a wide audience, especially those with an
interest in old books.

An English translation of The Method can be found in The Works of Archimedes, edited by T. L. Heath and published by Dover. This is fairly hard reading but worth the effort for it will make it clear that Archimedes was doing problems that we would now classify as calculus, but that he had not created the subject. The best survey of the mathematics of Archimedes is in chapter 2 of

The Historical Development of the Calculusby C. H. Edwards, Jr. A popular exposition isArchimedes: What Did He Do Besides Cry Eureka?by Sherman Stein (MAA, 1999; here is a review). The auction catalog (Christie’s, 29 Oct 1998, #9058) is most interesting but is now out of print but should be available in art museum libraries. A popular introduction to manuscripts is Medieval Craftsmen. Scribes and Illuminators by Christopher De Hamel (University of Toronto Press, 1992).On the web: The Walters: http://www.thewalters.org/archimedes/

Prof. Rorres: http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

There is much else about Archimedes and this famous palimpsest on the web, but I consider these to be the two best sites.

**2. Lectures on different aspects of the
history of the calculus.**

- Early examples of integration and differentiation.
- What Newton and Leibniz did.
- The Bernoullis and Euler.
- Cauchy and Weierstrass develop foundations.
- Cantor’s leap from Calculus to Set Theory.
- Robinson and Non-Standard Analysis.

Abstracts and suggested readings for each of these talks is available.

**3. Examples of how to use history in the
classroom.**

One of the best ways of using historical information is in the classroom. It is an excellent motivator for the student. It can be used in a variety of ways and several of these will be discussed.

A number of classroom examples will be presented. Here are some potential topics:

- What to say on the first day.
- Bolzano's Intermediate Value Theorem.
- The shape of the bridge and the catenary.
- Why the sine has a simple derivative.
- What shape should a clepsydra be?
- The geometric and harmonic series.
- The irrationality of e.
- Perrault and the tractrix.
- Liouville on non-elementary integrals.
- Cauchy’s famous wrong theorem.

This is undoubtedly more than can be done in an hour, but I thought you might like some choice.

**4. Ideas about teaching history of
mathematics courses.**

Hopefully we will have some free wheeling discussions on the topic of teaching history of mathematics courses. Several years ago, Victor Katz and I gave a minicourse on teaching history of mathematics courses, and so I am placing the web pages for that course here. Unfortunately, not all of the links are live; please bear with me while I work on these pages.

Also available here are the web pages for the history of mathematics course I taught at Bowling Green several years ago.

**5. Finding history on the internet and
judging its quality.**

A new resource --- and also a new problem --- for all teachers is the use of the internet. We now need to help our students learn to use it wisely. Here are some www exercises that I drew up to help people develop judgment as to the quality of things on the internet. This should be a topic that all can contribute to.

**6. A book display.**

Mathematicians love books and historians of mathematics go absolutely wild over them. Consequently we must absolutely have a book display. Here is a book list of things that it would be nice to have. Some of these are in the Bemidji State University Library and will be available to us. But look at the list and bring something along. So that we don't have multiple copies please send email to Ivy Knoshaug: iknoshaug@bemidjistate.edu indicating what you will bring. Naturally you are encouraged to bring some of your favorite items that are not on this list.

**7. Time to talk. **

Talking about the history of mathematics and whatever things interest you is a vital part of this seminar so longish breaks have been scheduled in. I am most willing to talk to you whenever I am free.

Prepared by V. Frederick Rickey, July 8, 2001. Send suggestions to fred-rickey@usma.edu .