Research Projects in USMA's Mathematical History

These research projects posed here divide roughly into two types. The first deal with the history of the Department of Mathematical Sciences at USMA, and the second deal with the books that are available in the USMA library. It is anticipated that this list will be increased as additional questions occur. Suggestions for additional projects would be welcome.

By design, these are projects that can be attacked by people who have not had previous experience in historical research. There is research here that can be done by cadets with a serious interest in mathematics and its history. The same projects can be done by faculty, with increased scope or greater depth. Many of them could develop into publishable works depending on what results turn up. The sources needed for these projects are in English, but if you read French, come running; there are lots of interesting things to do dealing with the early USMA curriculum.

If you are interested in working on one of these problems or have another line of inquiry that you would like to explore, please contact Prof. V. Frederick Rickey, Thayer 246: .

The Department

1.    What is the "Thayer Method" of teaching?  The "Thayer Method" is often mentioned at West Point, but what historical documentation do we have for it? Has the phrase changed meaning over time?

2.    What are the Olivier Models?  These are the models in the large glass cases dispersed around the department. We know some of their history, but how were they used in the classroom at West Point? In general, what can be said about the use of other classroom aids --- including the blackboard, the slide rule, the computer. Was USMA the first place in this country to use a blackboard?

3.    How does the USMA curriculum compare to elsewhere? This is a question that needs to be relativized to a given period (so many people can work on different eras). There were times when USMA was way ahead of the rest of the country and times when it was behind. It would be interesting to see how we compare.

4.    Captions explaining photographs.  MAJ Kirk Bensen has posted lots of photographs from the Howitzers on the web at  http://dean_math2/mathhist/ . Some of these are self explanatory, but others need some words of explanation. It may require some digging to properly document these photographs and explain what is pictured.

5.    Oral history. Several former department heads are still alive as well as other individuals who have had long contact with the department. It would be interesting to conduct a number of interviews with them to learn what their memories are of the department and what they feel about the changes that have taken place since they left. They could also provide valuable information about the oral tradition of the department when they arrived. There is much to be learned here, but it might require determination and persistence to get the information. In particular, oral history requires a lot of work because you want to have a pretty good idea what the questions are before you ask the questions, for memories often do not agree with facts.

6.    Investigate the history of probability and statistics in the mathematics curriculum at West Point. When did it first enter the curriculum? What textbooks were used and who taught the courses. Where did the teachers get their knowledge of the field? How have things changed over the years?

7.    Robert C. Yates (1904-1963) taught at West Point from 1942 to 1954, initiated "New Instructor Training" in the department, and wrote at least five books and sixty papers. Two of these have been reprinted in the NCTM Classics in Mathematics Education Series: The Trisection Problem and Curves and Their Properties. It would be interesting to have a complete bibliography of his works, a biography, and an evaluation of his impact on the department. His son, Dan, is a mathematician and he could be contacted for information about his father. The son visited the department several years ago.

8.    Charles Nicholas wrote "The Green Death," as it was 'affectionately' called by cadets. He was department head (1959 to 1967) when he wrote this series of Special Topics Memoranda that served as the calculus text at USMA. How did this work compare to what was being taught at other colleges at the time? Were they as rigorous as other texts of the period? What is now known of Nicholas's service as Deputy Assistant Director of the CIA, and what role did his knowledge of mathematics play in that position?

9.    The correspondence of Charles Davies needs to be transcribed and studied. I suggest that it be done as web pages. A harder project would be to study the changes that took place in this textbooks. Fortunately the library has many copies of his works that have been marked up by the instructors and cadets who used them.

10.     How much mathematics did Thaddeus Kosciuszko know? What kind of mathematics, if any, did one need to know to build fortifications? Marguerita Herman in her delightful book,  Ramparts: Fortification From the Renaissance to West Point, indicates that a good deal of geometry was sometimes used. Precisely what was that geometry and how did military engineers learn it?

11.    Sylvanus Thayer. There are so many research projects about Thayer that it is hard to know where to begin. Much correspondence survives from his trip to Paris where he visited the Ecole polytechnique and bought the books that are the heart of the mathematics collection here at West Point. What did he learn in Paris about mathematics that he put into effect here?

The Library

1.    Geometry books from Legendre to Davies. The first geometry textbooks used at West Point were those of Legendre, and they were written in French. The work was translated into English several times.

2.    Maria Agnesi's Analytical Institutions (1802) is in the library. It is this (mis)translation that gave rise to the curve known as "The Witch of Agnesi." It would be interesting to read the calculus sections of this book and to analyze their content and compare them with other mid-eighteenth century texts (the Italian original dates from 1848). What influence, if any, did this work have on the calculus curriculum at West Point?

3.  The works of Charles Maseres. A number of his works are in the library and they appear to be quite interesting. They contain translations of a number of important works from Jakob Bernoulli on probability to a discussion of Rhapson's method of solving equations. Maseres has translated these works into English, but they are virtually unknown today.

4.    Descriptive Geometry entered this country through West Point and there are a large number of books on this topic in the library. But what is descriptive geometry? Did it really evolve into engineering drawing? Was it really vital for a military engineer to know these things?

In connection with an Institute on the History of Mathematics and Its Use in Teaching which Victor Katz, of the University of the District of Columbia, and I conducted, I drew up a list of research questions for the participants to attack. These projects turned out to be quite successful and I hope the above questions and projects will be too.

This page was posted September 15, 1999.