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Mathematics Education at West Point: The First Hundred Years - Charles Davies, Mathematics Professor, 1823-1837

Author(s): 
V. Frederick Rickey and Amy Shell-Gellasch

Charles Davies was born 22 January 1798 in Washington, Connecticut. When he was a youth, the family moved to Black Lake, in northern New York State, where he was educated in local schools. During the war of 1812, when the Chief of Engineers, Joseph G. Swift, was preparing the defense of Ogdensburg, he met Davies’ father, the County Sheriff, and took an interest in young Davies and “personally aided in securing his appointment” at West Point.[1] Davies came to West Point in December 1813 and graduated in December 1815. There were no openings in the Corps of Engineers when he graduated so he took a less desirable position in artillery, serving a year in garrison duty before being transferred to the Corps of Engineers in August 1816. He resigned from the Army on 1 December 1816 to accept a position at West Point teaching mathematics.[2] He served under department heads Andrew Ellicott and David Douglas, and then taught natural and experimental philosophy for two years, before becoming professor of mathematics in May of 1823 when Douglas became professor in philosophy.

While at West Point, Davies started a long and lucrative career as the author of text books, first for use at the Academy, and then across the country. The ones used at West Point were:

1826 Elements of Descriptive Geometry, with Their Application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces.

1828 Elements of Geometry and Trigonometry. Translated from the French of A. M. Legendre, by David Brewster. Revised and Adapted to the Course of Instruction in the United States.

1830 Elements of Surveying. With the Necessary Tables.

1832 A Treatise on Shades and Shadows, and Linear Perspective.

1833 The Common School Arithmetic, Prepared for the Use of Academies and Common Schools in the United States, and also for the Use of the Young Gentlemen who may be Preparing to enter the Military Academy at West Point.

1835 Elements of Algebra: Translated from the French of M. Bourdon. Revised and Adapted to the Course of Mathematical Instruction in the United States.

1836 Elements of the Differential and Integral Calculus.

1837 Elements of Analytical Geometry: Embracing the Equations of the Point and Straight Line, the Conic Sections, and Surfaces of the First and Second Order.[3]

Not surprisingly, the effort of producing eight books in eleven years left Davies exhausted and with a severe bronchial infection. Thus he resigned in May of 1837 so that he could tour Europe, restore his health and then “continue to write and revise wildly successful mathematics textbooks.”[4]

All of the works listed above, except the arithmetic, were used as textbooks at West Point, as well as many other schools. This is due in part to the dozens of West Point graduates who taught mathematics at schools across the country.[5] More importantly, these books were vastly superior to other texts that were available at the time. Historian Florian Cajori wrote that the books of Davies “were, as a rule, perspicuous, clear, and logically arranged. They were not too difficult for the ordinary student, and contained elements of great popularity.”[6] Aggressive marketing techniques also led to the widespread use of the books. Davies “saw himself simultaneously as a professor and a businessman, like two touching circles with one inside the other.”[7]

The 1828 text, Elements of Geometry and Trigonometry, was his most popular book. In the period 1828-1895 it appeared in 33 editions/printings and some 300,000 copies.[8] In his lifetime Davies published 49 different titles.[9] If we include his editing of Edward Courtenay’s posthumous Treatise on the Differential and Integral Calculus, and on the Calculus of Variations, then Davies published an even 50 books. These appeared in at least 492 editions/printings. They covered the ground from elementary arithmetic through college mathematics (though none was higher than calculus). By 1875, A. S. Barnes & Co.[10], (a firm that flourished by publishing the Davies texts) had sold about 7,000,000 texts by Davies, and were selling about 350,000 every year.[11] Is it any wonder then that he dominated mathematics textbook writing in the nineteenth century?

In 1831 two other translations of Bourdon’s Algebra appeared, one by Farrar at Harvard and one by Edward C. Ross. Ross (1801-1851) taught at the Academy his last year as a cadet and graduated in 1821. He remained at West Point as a mathematics instructor until 1833. After leaving the Academy, Ross went on to teach mathematics at Kenyon College in Ohio and then the Free Academy in New York City.[12]

The Ross translation, Elements of Algebra Translated from the French of M. Bourdon, for the use of cadets of the U.S. Military Academy (1831), was significant in that it freed the cadets from the necessity of studying French in order to read their mathematics texts. The Ross translation was used until Charles Davies produced his own in 1835 — based partly on that of Ross. Davies’ text, in various editions, was used for the rest of the century. In 1893, it was supplemented by A Treatise on Algebra by Charles Smith that was used until 1905. The use of the algebra text of Davies for 65 years reveals something about education at West Point. The Academic Board had absolute control over the curriculum and once they got a curriculum in place during Thayer’s years as Superintendent, they were very reluctant to change it. They tinkered a bit, but made few substantial changes. (See the appendix for a listing of texts used at West Point and the date they were introduced into the curriculum.)



[1]Henry Eugene Davies, Davies Memoir. A Genealogical and Biographical Monograph on the Family and Descendants of John Davies of Litchfield, Connecticut. Privately Printed, 1895.

[2]This is curious, for in 1809 Ferdinand Hassler was forced to resign the professorship because he was not in the army. Probably the law changed in the meantime.

[3]For information about editions of these books, see Albree et al.

[4]Amy K. Ackerberg-Hastings, Mathematics is a Gentlemans Art: Analysis and Synthesis in American College Geometry Teaching, 1790-1840, Ph.D. dissertation, Iowa State University, 2000. University Microform 9977308.

[5]A list of USMA graduates who taught mathematics at other schools and the schools where they taught is being compiled. The information is available at http://www.dean.usma.edu/math/people/rickey/dms/OldestSchools.html.

[6]Florian Cajori, The Teaching and History of Mathematics in the United States, Washington, Government Printing Office, 1890, p. 120.

[7]Amy K. Ackerberg-Hastings, p. 216. Chapter five of this work, “The two circles will touch each other internally: Charles Davies and the art and business of teaching geometry,” History of Undergraduate Mathematics in America: Proceedings of a Conference Held at the United States Military Academy, West Point, New York, June 21-24, 2001, edited by Amy Shell-Gellasch. See pp. 215-276, for the best available biography of Davies.

[8]Amy K. Ackerberg-Hastings, "Charles Davies, mathematical businessman", pp. 119-132 in Shell-Gellasch. Almost all of the books of Davies appear in multiple “editions” but many are so alike that they should be called “printings.”

[9]Davies’ earliest texts were translations of French authors. These then evolved into text attributed to Davies alone, and eventually he wrote his own text from scratch.

[10]Note that this is not the Barnes of Barnes and Nobles fame.

[11]First Century of National Existence; the United States as They Were and Are . . . by an Eminent Corps of Scientific and Literary Men. Illustrated with Over Two Hundred and Twenty-Five Engravings. San Francisco: L. Stebbins. 1875, p. 268. Available on the web through the Humanities Text Initiative: http://www.hti.umich.edu.

[12]Arney, Chris, West Point's Scientific 200: Celebration of the Bicentennial, Palmetto Bookworks, 2002, pp. 57-58.

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