Research Projects

At this History Institute we would like each of you to do some research in the history of mathematics. Even in the limited time available, there are projects where progress can be made, but care needs to be taken to narrowly focus them. The following are our suggestions. They are designed to take advantages of the resources available here at American University. Take these as initial ideas and develop them in any way you choose; often what you do will change after you start doing it. We would like you to work in teams of three on these projects. You will be asked to make a report on your research during the third week.
  1. What sort of reputation did Artemas Martin (1835-1918), the bibliophile who collected many of the mathematics texts in the American University Rare Book Room, have as a mathematician during his lifetime? Take a look at some of his works and give your own appraisal of him as a mathematician. What biographical information on him can you find? See B. F. Finkel, A Mathematical Solution Book, and a 1964 MA thesis at AU by Emily Lampert for some biographical information. Was Martin listed in American Men of Science or other biographical works?

  2. Louis C. Karpinski (1878-1956), longtime historian at the University of Michigan is renown for his Bibliography of mathematical works printed in America through 1850 (1940). Less well known is that it was published "with the cooperation for Washington libraries of Walter F. Shenton." The only paper he published in the American Mathematical Monthly was "The First English Euclid," 35(1928), 505-511. Shenton taught at The American University from about 1925 until he died in the 1960s. There is a box of his papers at AU. Would be interesting to know more about him. Do people around DC still remember him? What might be in the University of Michigan library about him?

  3. Suppose a history of mathematics course were being taught 100 years ago. What would the content of that course be and how would it differ from courses being taught today? How would our appraisal of ancient mathematics differ? Of seventeenth-century mathematics? What schools offered history of mathematics courses and how are they described in the catalogues. What were the textbooks like then (see those of Ball, Cajori, Gow, Fink, etc.; see AMM 9(1902), 280-283 for a review of Ball).

  4. It is widely held in the mathematical community today that all calculus books are the same. Look at a selection of calculus books over the past three centuries and see if they have differed and precisely how. Some books to consider are Ditton (1706), Bayes (1736), L'Hospital (1740), MacLaurin (1742), Hodgson (1756). You can choose some nineteenth-century texts by searching the card catalogue. Also see a paper by Rosenstein in volume 3 of A Century of Mathematics in America, edited by Peter Duren et al.

  5. What are the mathematical implements on the cover of Katz's book? More generally, what is the picture about. This project will lead you into the art history literature. Perhaps the following will get you started: Hugh Kenner, "The phantom skull," Art & Antiquities, Summer 1988, p. 128.

  6. What is the history of the 17 plane symmetry groups? Are they all represented in the Alhambra in Spain? When was the mathematical classification done and by whom?

  7. One of the books that the young Newton read was Oughtred's Clavis mathematicae; first English translation, The Key of the Mathematicks (1647). Wallis describes the book in chapter XV of his 1685 A Treatise of Algebra. How accurate is the description of Wallis? What might Newton have learned from this work? Another project would be to consider the quality of the history of algebra presented by Wallis.

  8. Edmund Gunter coined the words "cosine" and "cotangent." What can you find about this in The Works of Edmund Gunter? Also, how was the "cross-staffe" mentioned on the title page used for?

  9. How do the articles on the history of mathematics in the history of science journal Isis differ over the years? Can you notice a change in the style of doing history?

  10. A frequently asked question is "Why do we use m for slope?" What does Descartes have to say about this? The first Latin edition of Descartes is in the library. Are lines treated there? [To the best of my knowledge, both "m" and "slope" were first used in mid nineteenth-century textbooks.]

  11. Rafael Bombelli dealt with the irreducible case of cubic equations in his Italian L'Algebra of 1579. What is in this book?

  12. What can be learned by comparing various editions of Euclid's elements? You should definitely restrict you attention to several propositions or to at most one book of Euclid. What are the advantages and disadvantages of the translation of Heath?

  13. The free Black mathematical practitioner Benjamin Banneker taught himself arithmetic through "double position." What does this mean? How much mathematics would he have known? Take a look at some arithmetic books that he might have read and see what conjectures you can make.

  14. The above project leads to the broader issue of what arithmetic texts contain in general (of course these same questions can be asked of algebra and geometry texts). How widely used were nineteenth-century arithmetic texts in this country? How many were printed? How many editions were there? What did `edition' mean then? How did the people learn arithmetic, or did they? This is a very open ended project, so you will need to narrow it down quickly.

  15. Very few women are mentioned in history of mathematics texts. Is this because they did not have any interest in mathematics? What can you learn from the Ladies Diary (1831) or from the Ladies, Farmers, and Mathematical Almanac (1863-1866). Did any women contribute to the journal The Mathematical Visitor (1877-1881).

  16. Who was Oliver Byrne and how good a mathematician was he?

If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .