III.5    Suggested Projects

Most students are turned off by the prospect of writing a paper, for it seems that it is going to be a big chore (remember, most mathematics students have written precious few papers, especially about mathematics). However most students pick out a project that interests them and then they really get into it.

My experience has been that by indicating on day one, right in the syllabus, that I expect a high quality product, that the students will produce. I tell students that I expect their papers to be well written and that if I receive a poorly prepared paper, I will simply return it without grading it. This threat has worked for me; I have never had to return a paper.

I suggest that you pass out a list of projects to the students to give them guidance on major projects for the course. After passing out the list, I make comments on the topics, indicating some of the pitfalls of writing a paper for a History of Mathematics course. First off, it must involve history and it must involve mathematics. They have troubles with both requirements. Try to impress on the students that it is not sufficient just to mention a whole bunch of mathematical topics the individual worked on, but that they must actually explain enough of the mathematics so that one of their peers could understand (what I really want to see evidence of is that they have understood the mathematics they are writing about).

However, on the projects listed below I give some bibliography to get started. I do not give this information to the student right away as I feel an important part of the project is to find some sources. However, after the students give their project titles to me and mention the literature that they have looked at, then I suggest additional items that they should look at. This usually proves to be a time consuming task as one must deal with each student individually. Also, I often go to the library and work with them as I want them to observe my bibliographic skills in action.

I used to have them do two papers, but I found it was too much work, for them and for me. They actually do a better job with just one.

My preference is that students do a research project on some topic in the history of mathematics, for I believe that this gives them a broader experience. It also makes it easier to incorporate mathematics. Here are a few suggestions:

However, many students prefer to write about an individual. This is fine with me, but some care needs to be taken so that they can incorporate some mathematics in their paper. I caution my students that I know a lot about Newton, Leibniz and Euler and so they will have trouble writing a paper that will impress me (also these topics are far too big for a student project, if they want to do them, then they must trim the topic down). Here are a few suggestions of interesting individuals along with some excellent references.

Note that these are (relatively) modern mathematicians. I believe students will learn much more if they choose an individual from the past two centuries.

By far the most interesting papers are produced by students who delve into some original source. They gain much from doing this: confidence gained in reading original mathematics, awe in the way that things used to be done, and reverence for the rare books which they get to handle. These are experiences that they can pass on to their own students.

The projects below were chosen because the original sources that are listed to get them started are available either in our library at Bowling Green or easily available through the OhioLink interlibrary loan system. Projects using original sources have become much easier as an abundance of original sources is now available on line. Thanks to Google Books many out of copyright sources are available in full text on line. In addition EEBP (Early English Books Online), which is available as a data base in many libraries contains everything (almost literally) published in England before 1700, regardless of language.

This last is a favorite. A student came to me indicating that he wanted to write about one of the Bernoulli's. I cautioned him that one of the requirements of the paper was that they had to use an original source and that I was unaware of any Bernoulli papers that were available in English (he couldn't read Latin or French). He proved me wrong and found a wonderful paper:

Leslie Bradley, Smallpox inoculation: an eighteenth century mathematical controversy. Translation and critical commentary, [Nottingham] University of Nottingham, Adult Education Dept., 1971. The originals, in French, are readily available in Die Werke von Daniel Bernoulli, Bd. 2.

His effort won a writing award from the Ohio Section of the MAA.

Fernando Q. Gouvêa has a nice bunch of suggestions that use original sources.

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If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .
Posted 2 December 1996. Revised 4 January 2003 and December 2008.