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:

1. Advice on Doing History
2. Histories of mathematics departments
3. Histories of mathematical organizations
4. Histories of mathematics courses
5. Other historical topics

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:

• Choose a modest size project, one that can be done in a reasonable amount of time. As you can tell from the above dates, it took five years from the inception of this research until it reached print. We both had tenure, but five years is too long for young scholars. Go ahead and contemplate large projects, but do small ones. To cite a personal example, for some years I have been working on a volume of historical notes for calculus teachers. What I should have done was to publish the notes as I completed them, and then compiled a book when the volume of these notes was sufficient.
• Get to know your librarians. This is really important. They are the professionals at finding things out. Tell them what you are most interested in and what your broad interests are. Then they can help you out when information crosses their path.
• Be persistent. Before we made our first visit to Clark, Roger and I did our homework and learned as much as we could about the school, the mathematics program, and the faculty. One thing we knew was that the library had created a card catalog listing all faculty publications. This is quite a reasonable thing for a budding graduate school with a superior faculty to do. So on our first trip to Clark, I asked about that catalog. Where was it? The archivist had no idea. No one knew what I was talking about. I asked the university historian, William A. Koelsch, on the next trip. He did not know what I was talking about. On a later trip, we were having tea with the archivist and university historian. I mused aloud "I wonder what happened to that file cabinet with a list of all faculty publications?" Somehow, I struck a chord. Professor Koelsch said, "Do you mean that cabinet behind Stewart's desk?" I jumped up and dashed to the librarian's office. Pulled out a random drawer, and there was the information that I wanted. Now rather than compiling our own list of publications by the mathematics faculty and students, we could simply photocopy what had already been compiled.
• Read, read, read!  On several occasions, Victor Katz and I have presented a minicourse on teaching history of mathematics classes, and the most important piece of advice I give the participants is "Start reading now!". Several participants have come back to me later and remarked how valuable this advice is. You need to read broadly and deeply. If you are going to research the history of your own department, and this is a wonderful beginning project, then you need to seek out every history of your school that has been written and read it. Alas, you probably will not learn much about the mathematics department, but this background will give you a good perspective from which to view the mathematics department. You need also to read the professional journals to see what good history looks like. You definitely should read Historica Mathematica and I would suggest, at the minimum, that you also read Isis, the premier history of science journal.
• Be serious about your research. This is not an avocation, not something to be taken lightly. This is your life! Never ask a librarian a question when you do not have time to hear the answer and pursue the topic. You are not under a deadline to complete this research, so take your time and do it right.
• Learn to use all available resources. Mathematicians are not good library users. They have never had to be, for their thesis advisors told them what to read and then when they got out on their own, they developed a network that provided information about what needed to be read. But doing historical research is different. One absolutely must develop superior library skills.
• Learn to use rare book rooms and archives. If you are going to do historical research, then much of the material that you will want to access will be in the rare book room or archives of some library. Today, due to the internet, it is much easier to learn where relevant archives are located. Perhaps you will be fortunate enough to locate a "finding aid" on line. If so, read it carefully and try to judge what should be examined first. Then email the archivist and tell about your project and what you would like to look at and when you plan to visit. Explain your plan broadly and the librarian can likely provide more things than you could have located by yourself. Perhaps a personal story will drive this point home: When Roger Cooke and I were working on the Clark project, I wanted to visit Johns Hopkins, for that is where William Story had been before moving to Clark. I was particularly interested in the founding of the American Journal of Mathematics for both Story and J. J. Sylvester were involved. I called the archivist and had about a half hour conversation about the research that I was involved in and why I wanted to visit the Hopkins archives. When I arrived the archivist had already pulled the archival boxes of most interest to me, and also opened a dozen or so drawers in the card catalog and parted the cards at things she thought were relevant to my research. This shows the value of advance preparation, seriousness about your research, and establishing the fact that you are a dedicated researcher. One of the first things I do when visiting an archive is to ask "I would like to wash my hands. Where is the men's room?". This shows the librarian that I am experienced at using a rare book room and respect the value of the materials that I have asked to see. Also remember the rule: pencils only. Get all your pens out of sight before entering an archive.
• Become an expert at using the internet and library databases.

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.

• Jacob William Albert Young (1865-1948) received the first PhD in mathematics from Clark.
• Frederick Carlos Ferry (1868-1956) earned a PhD from Clark in 1898 and then returned to his alma mater, Williams College, where he taught Latin, Greek, and Mathematics, and served as Dean. He moved to Hamilton College. There is archival material at Williams
• Thomas Franklin Holgate (1859-1945), after receiving a PhD from Clark, became a professor at Northwestern.  The archival material at Northwestern, where he was professor and dean, contains a "History of the Mathematics Department at Northwestern University, 1855-1905."

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):

• History of the History of Mathematics Department at Brown
• Bowling Green State University
• History of the Colorado College Math Department by John Fauvel.
• History of the Mathematics at Dartmouth by Bancroft H. Brown. [A. S. Hardy]
• University of Georgia has a nice page
• Harvard
• Madison College. Here is an interesting idea. Pick a school that no longer exists and find out what happened to it.
• History of Math and Stat at Nebraska
• Ohio State
• A History of Mathematics at Rutgers. Written by Charles Weibel in 1995 [Adrain was there]
• University of Saskatchewan
• A History of the Mathematics at Union College
• United States Naval Academy Mathematics Department History
• History of the Mathematics Department at Virginia Tech
• Union College. Written by Theodore A. Bick in August 1993.
• University of Wisconsin - Stevens Point

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:

• Create a list of the department heads, when they served, and biographical information about them. What did they publish? If they are deceased, try to find family members. Has a nachlass been preserved? If they are still alive you should interview them,  but don't do this until you have learned a great deal about them and have a list of questions to ask them. Also be cautious that memory is fallible; on this point you may wish to read a lovely paper by Liliane Beaulieu in Osiris.    
  • Liliane Beaulieu, "Bourbaki's art of memory," Osiris, second series, vol. 14 (1999), 219-251. Available in JSTOR.
• Collect similar information about the other departmental members, concentrating on those that seem to have played the most important role in the department. Looking at these statistics can tell some things, e.g., about the growth spurts the department underwent. If your department is old or large this can be a daunting task; I know, for my department had more than 200 faculty members in the nineteenth century and far more in the twentieth.
• Collect information about courses taught. Were new courses introduced to accommodate new faculty members? Were there courses taken off the books? Why?
• Which textbooks were used? This can be a big task but it can be very rewarding. At West Point the noted textbook author Charles Davies was on the faculty for 21 years, retiring in 1837 at age 39, so that he could devote his time to writing (and also because of ill health). He wrote 50 textbooks which appeared in some 500 "editions" and many of these have been preserved in the library. More importantly, many of them contain annotations by instructors that reveal precisely which material was covered in class in a given year.
• What actually happened in the classroom? Sadly, I cannot cite any nineteenth centuries of what actually happened in the classroom. I would delight in references to counterexamples.
• Does your department have a colloquium? If you are so fortunate to have the tradition of asking speakers to write an abstract of their presentation in a notebook then you have a valuable resource (Oberwohlfach has several shelves full of them). How did the faculty preserve and expand their skills? Were they active in NCTM and the MAA?

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.

• Bill Austin, Don Barry and David Berman, "The lengthening shadow: The story of related rates," Mathematics Magazine, vol. 73, no. 1 (Feb. 2000), 3-12.

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.