101 Historical Research Projects about Collegiate Mathematics
V. Frederick Rickey
Department of Mathematical Sciences
United States Military Academy, West Point, NY 10996
It is easy to summarize research on the history of collegiate mathematics: Some work has been done, some work is being done, but much work needs to be done.
Today I would like to make some comments about each of these categories, putting the stress on what needs to be done. The work that has been done falls into several broad categories:
Each of these deserve our attention, but to begin, I would like to offer some advice for individuals who want to participate in this broad research program.
1. Advice on Doing History
My first experience with institutional history came in 1984-85 when I was on sabbatical at the University of Vermont. Roger Cooke had just published his book on The Mathematics of Sonya Kovalevskaya (Springer 1984) and when we were talking about research projects for the year he said that there was one mystery man left from the book about Kovalevskaya, and that was Josef Perott (1854-1924), about whom Roger Cooke has written recently. We knew that Perott had taught at Clark University from 189? to 1921, so contacted the archivist, Stewart Campbell, and then headed down to see what we could find. It did not take us long to realize that Clark University was far more interesting than Josef Perott. During the 1890s, Clark University had the best mathematics department in the country (Sylvester had left Johns Hopkins, Harvard was just an undergraduate school, and the yet to be created University of Chicago, had not yet stolen Clark's faculty). The results of this research are published as "W. E. Story of Hopkins and Clark," pp. 29-76 in A Century of Mathematics in America — Part III (AMS, 1989). This work deals completely with graduate level mathematics education, for Clark had no undergraduates, but it did clearly demonstrate to me how fascinating institutional research is.
I learned a number of things from doing this research which should be of interest to anyone contemplating doing some work on institutional history, indeed, in doing history of any sort:
Roger and I worked hard to identify all the individuals who received degrees from Clark University, but in the mid 80s that meant that we had to go to the library and dig out what we could. Just for fun, I decided to see what new information I could learn about these individuals today. So I googled them and quickly came up with a good deal of information. It then occurred to me that these individuals could make fine research subjects, for all were involved in college teaching.
2. Histories of mathematics departments
The trilogy of volumes, A Century of Mathematics in America, contains papers about a number of mathematics departments (Harvard, Yale, Chicago, Princeton, Stanford, Berkeley and NYU in volume 2 and the Institute for Advanced Studies, Columbia, MIT, Michigan and Texas in volume 3). Thus it provides a good place to read some histories that have warranted publication. Quite a number of schools now have histories of the mathematics department on their web pages. Here are those that I have located: (undoubtedly there are more):
In addition I have been collecting data for a history of the Department of Mathematical Sciences at the United States Military Academy. It has been my practice to place my research notes on the web. This has had the advantage that it is an easy way to organize these notes. An unexpected consequence is that other people have found these pages by doing web searches and have then written to me with additional information or with questions that prompt additional research. I would encourage you to do likewise. Let me stress, that while you will find a lot of data on these pages, you will not find a history of the department. To write a history the data must be reworked into a story about the department that gives the reader a real sense of what has transpired over the years.
Perhaps the best choice for a history research project is to write about your own department and then place the information on the web, with links from your department's web page. What should a history contain? This partly depends on how ambitious you wish to be. Here are some suggestions:
If you are frustrated in the meager amount of historical resources that are available to you, then I ask you to think of the future. Start a plan for the department to save and archive important documents. Faculty files should never be discarded, but preserved in the college or university archives (to be closed to researchers for some number of years).
3. Histories of mathematical organizations
The Mathematical Association of America has pushed its sections to prepare histories. These vary widely as one might expect. By remarking that Jim Tattersall has written a rather nice history of the Northeastern section, those of you who recognize his name as someone deeply involved in historical research, you know it is worth looking at.
The Ohio section has one of the most detailed histories, and again, someone interested in history was involved, namely Dave Kullman. The Ohio section has another interesting project entitled Ohio Masters of Mathematics which contains biographies of individuals somehow involved with the state. This project deserves emulation, for it is interesting to read and of use to mathematicians everywhere, for if someone is interested in one of these individuals they are likely to find these web pages through a search.
The Michigan section has prepared some rather nice web pages about the history of the section. One thing that is treated is the history of the Michigan Mathematics Prize Competition. There are many collections of competition questions and these often contain some information about the origin of the competition. Perhaps the most carefully studied of the competitions is the Putnam. The zeroeth competition between Harvard and West Point is nicely chronicled by Chris Arney and George Rosenstein, Michelle Isenhour and another by Arney.
Among the printed histories that of the EDAPELsection, prepared by David Zitarelli at Temple, is by far the best.
If your section has not prepared a history or if you are not satisfied with its quality, this is a good place to begin doing history. I suggest you find someone experienced and team up with them. You can learn about history by doing, but observing has its own rewards.
Does your school have a mathematics club? Writing its history would be a manageable task if the club has kept some documentation. The club may well have a book listing officers and members. They may have kept announcements of their events, both social and academic. Were there any members who have now gained some fame? Were there famous speakers? Look in your schools yearbooks, there may well be a picture of the mathematics club (and faculty too)
Perhaps this is a good place to issue a caveat. There is much more to history than making lists, in fact, that is not history at all. But it can be the raw data needed to write a good history. Histories are stories. One wants to write about, say, your department in a way that gives the spirit of the place as well as contains a good deal of mathematical detail. How have the course descriptions in the college catalog changed over the years? There are lots of things to include. Make the history readable, interesting, and filled with detail.
A very interesting web site is the Mathematical Genealogy Project that Harry Kuntz has created. Mathematicians seem to enjoy knowing about their mathematical ancestors and this web page is simply a list of individuals, their advisors, and their doctoral students. On several occasions I have commented that here is data just waiting for someone to do something interesting with. What does it tell us historically? I wish I had suggestions. Think about it.
4. Histories of mathematics courses
Now we come to the hard part. The really interesting questions are hard, so have not been done.
How often have you heard the statement "Calculus books are all the same!" But is this really true? I am old enough to see that they have changed, changed considerably in my lifetime. I have also looked at enough old books – L'Hospital, Euler, Agnesi, Lacroix, Cauchy, as well as many others – to know that calculus books have changed considerably over the centuries. But no one has studied how they have changed. This is a Herculean task. Fortunately, George Rosenstein has undertaken the onerous task of preparing a catalog of early American calculus textbooks.
George M. Rosenstein, Jr, "The best method. American calculus textbooks of the nineteenth century," A Century of Mathematics in America, Part III, 77-109. MR1025342 (91c:01037).
That is a start, but only a start. Perhaps this task is simply too big. One way to break it down is to just study one portion of the books. In this paper, Rosenstein looked at how limits were treated in books straddling the 19th and 20th centuries. Bill Austin, Don Barry and David Berman have studied when related rates problems entered the curriculum.
Craig Bauer of York College of Pennsylvania is engaged in an interesting project. As is fitting for the newest member of the editorial board of Cryptolgia, he is investigating the history of college and university courses on cryptology. The earliest of these seem to be around the time of World War II. Some were government sponsored, some were by invitation only and secret. He is investigating all that went on in the universities. I look forward to reading what he writes on this fascinating topic.
What is the history of teaching history of mathematics courses in colleges and universities? Which states require prospective high school teachers to take a course in the history of mathematics? It is sad that the answer to this last question is not available. What has been the most used textbook in such courses over different periods?
We could continue to ask about the history of every course in the curriculum, but I think you get my point. Very little research has been done on this topic. So much needs to be done.
5. Other mathematical topics
Several years ago I drew up a list of research questions about the mathematics department at West Point; perhaps they will set you thinking about projects that you could do about your institution.
Here are a few more questions that deserve study:
Have you seen plaster models of surfaces in cabinets in mathematics departments? What are they for? A number of books discuss them, but does anyone have any documentation that they were ever used in the classroom, and more importantly, how they were used.
Do you know anyplace that has any glass stereopticon slides? I have some produced by L. C. Karpinski and others produced under the direction of David Eugene Smith
How has the introduction of the Graduate Record Exam impacted the college teaching of mathematics?
How has the level of rigor in college mathematics classes changed over the years?
How has assessment changed historically? Of course, it was called "testing" not so many years ago, but a closer look should turn up a lot of interesting information.
Well, I certainly have posed a bunch of questions. I don't know if I have posed 101 Projects for Historical Work, but then, as you know, there are two kings of mathematicians: those who can count, and those who can't.
Comments about this paper and suggestions for other historical research topics to include would be most welcome. Send me, Fred Rickey, and email.