Historically Speaking: 4. George Washington and Mathematics Education

The fourth installation of the Historically Speaking reprint series is from October 1954. In it, Edmund E. Ingalls discussed the mathematical knowledge of a person probably familiar to most readers, the first President of the United States, George Washington, and another gentleman perhaps not as well-known in the 21st century, Nicholas Pike:

Edmund E. Ingalls, “George Washington and Mathematics Education,” Mathematics Teacher, Vol. 47, No. 6 (October 1954), pp. 409–410. Reprinted with permission from Mathematics Teacher, ©1954 by the National Council of Teachers of Mathematics. All rights reserved.

Click on the title to download a pdf file of the article, “George Washington and Mathematics Education.”

Ingalls had an interesting academic background, having earned two degrees from Yale University—a bachelor's degree in philosophy and a master’s degree in forestry. He then went on to earn degrees in mathematics, an MS from the (then-State) University of Iowa and a PhD from the University of Michigan. He served more than 30 years as a mathematics professor at Albion College in Michigan. With an avid interest in the history of mathematics, he accumulated an extensive collection of mathematics books printed before 1850. He died in 1978 at the age of 85.

In the 1930s, Ingalls was consulted by a textile mill superintendent, who asked for an easier method of determining the weight in ounces per yard of a roll of cloth, one that saved time and avoided the frequent arithmetical errors inherent in the existing method. Ingalls published his solution in “A Slide Rule Solution of a Woolen Mill Problem” in the MAA publication Mathematics News Letter [Ingalls 1933].^[1]

In the Historically Speaking article, Prof. Ingalls reported that he surprisingly learned about a letter from George Washington to Massachusetts textbook author Nicholas Pike as he was conducting research on Pike while consulting Euphemia Vale Smith’s 1854 History of Newburyport. Nicholas (sometimes spelled Nicolas) Pike (1743–1819) was a graduate of Harvard College, with both bachelor’s and master’s degrees from that institution. For many years, he was the principal of the grammar school in Newburyport, Massachusetts, where he also served at times as town clerk and justice of the peace. He was known for his rigid discipline in the classroom, where he passed on the basics of the classical education he had himself received at Harvard. [Smith 1854, p. 327; Alexanderson and Klosinski 2019, p. 353] He is best known for publishing, in 1788, his A New and Complete System of Arithmetic, Composed for the Use of the Citizens of the United States [Pike 1788]. At least 17 printings of the book and two abridgments were sold by the 1830s, indicating it was quite popular in the early American republic [Robin Halwas Limited 1997].

The title page of this textbook appears as the background of the lovely cover of a recent issue of the AMS Bulletin. (A cleaner, clearer copy is inside [Alexanderson and Klosinski 2019, p. 350].) Sometimes mistakenly credited with being the first American arithmetic text, as George Washington does in his letter, and as Pike himself believed, his book was in fact preceded by several others. But it is generally considered to be “the first popular English language arithmetic by a person born in the colonies” [Alexanderson and Klosinski 2019, p. 349] and “the standard mathematical manual in New England schools” during his lifetime [Zitarelli 2019, p. 1]. And, as Professor Ingalls hints, the first edition contained recommendations from professors and presidents of Harvard, Dartmouth and Yale Colleges, the secretaries of state of South Carolina and New York, and the governor of Massachusetts, among others. It was undoubtedly with the hope that the book would receive another prestigious recommendation that Nicholas Pike sent a copy of the published volume to George Washington.

Of course there was also a hint of patriotism in seeking an endorsement from General Washington. In the 1780s in the new United States, there was a “general heightening of national consciousness” and a belief that “the nation’s education institutions should reflect the achievement of independence and its opportunity to create a model democracy” [Clements and Ellerton 2015, p. 103]. Frank Swetz points out that even the title of the book reflects the “nationalistic pride of the times and a concern with the place of mathematics in the process of nation building” [Swetz 1993, p. 491]. As Washington wrote to Pike, “I flatter myself that the idea of its being an American production . . . will induce every patriotic and liberal character to give it all the countenance and patronage in his power” [Ingalls 1954, p. 409].^[2]

V. Frederick Rickey, emeritus professor of mathematics from the United States Military Academy at West Point, spent several years studying Washington’s mathematical education and activities in collaboration with one of the editors of Washington’s papers, Theodore J. Crackel, and historian of early American mathematics, Joel Silverberg [2013; 2015]. Rickey had a conversation with Convergence associate editor Betty Mayfield and co-editors Danny Otero and Amy Ackerberg-Hastings about the context for Pike’s approach to Washington:

One might expect a text on commercial arithmetic to be rather dry and, perhaps, boring. Ezra Stiles, President of Yale College, described it as “a Book suitable to be taught in Schools of Utility to the Merchant” [Pike 1788, p. 2]. And the text did include instruction and exercises on topics such as square measure, measures of wine and beer barrels, and converting currency. But Pike’s text is more interesting than it may at first appear.

For one thing, it may have been the first mathematics text in the United States to use a decimal point. The United States government had just instituted decimal coinage in 1786 [U.S. Metric Association 2015], and Pike included examples of using this new decimal currency. (However, some critics have noted that Pike devoted only four pages to the new system of currency, and in general he did not present material that was relevant or easy to digest for his intended students [Clements and Ellerton 2015, pp. 111–113].) He also included material far beyond what we would call arithmetic: There were sections on trigonometry, conic sections, algebra, number theory, and even infinite series. He posted interesting problems related to the age of the moon, and to determining the date of Easter.

What Nicholas Pike did not know when he wrote to General Washington was that Washington did a lot of work in arithmetic in the late 1740s. He had a very good knowledge of elementary arithmetic and geometry, as well as some knowledge of trigonometry—in an old style that is very difficult for us to understand today. What we do not know is exactly where Washington learned his mathematics. We do know that his father purchased an indentured servant, John Hobby, in 1736 and apparently hoped that Hobby might tutor his son. Young George Washington also studied arithmetic at schools in Fredericksburg and Popes Creek, Virginia. And he owned a copy of a 1727 text, The Young Man’s Companion; or, Arithmetic Made Easy, by William Mather [Crackel, Rickey, and Silverberg 2013].

Washington had good reason to study mathematics: In his time, every landowner was a surveyor—because he had to be [Frisinger 1976]. And George Washington was a very large landowner, perhaps one of the largest in the country. He apparently taught himself the mathematical tools he needed for surveying.

So George Washington’s interest in Pike’s arithmetic book was more than patriotic. He had a knowledge and appreciation for much of the mathematics in the text and its use. And as Edmund Ingalls points out, his letter “contains comments which are quotable in discussions of some of our present mathematics-education problems” [Ingalls 1954, p. 409].

References

Alexanderson, Gerald L. and Leonard F. Klosinski. 2019. About the Cover: Early American Arithmetics. Bulletin of the American Mathematical Society n.s. 56: 349–353.

Anning, Norman. 1954. Geometric Progressions in America and Egypt. The Mathematics Teacher 47: 37–40.

Clements, M. A. (Ken), and Nerida F. Ellerton. 2015. Decimal Fractions and Federal Money in School Mathematics in the United States of America, 1787–1810. In Thomas Jefferson and his Decimals 1775–1810: Neglected Years in the History of U.S. School Mathematics, 103–141. Cham, Switzerland: Springer.

Crackel, Theodore J., V. Frederick Rickey, and Joel Silverberg. 2013. George Washington’s Use of Trigonometry and Logarithms. Proceedings of the Canadian Society for History and Philosophy of Mathematics 26: 98–115.

Crackel, Theodore J., V. Frederick Rickey, and Joel Silverberg. 2015. Reassembling Humpty Dumpty: Putting George Washington’s Cyphering Manuscript Back Together Again. In Research in History and Philosophy of Mathematics: The CSHPM 2015 Annual Meeting in St. Catharines, Ontario, edited by Maria Zack and Elaine Landry, 79–86. Proceedings of the Canadian Society for History and Philosophy of Mathematics/Le Société Canadienne d’Histoire et de Philosophie des Mathématiques. Cham, Switzerland: Birkhäuser.

Frisinger, H. Howard. 1976. Mathematics and Our Founding Fathers. Mathematics Teacher 69: 301–307.

Ingalls, Edmund E. 1933. A Slide Rule Solution of a Woolen Mill Problem. Mathematics News Letter 8: 54–56.

Ingalls, Edmund E. 1954. George Washington and Mathematics Education. Mathematics Teacher 47(6): 409–410.

Pike, Nicholas. 1788. A New and Complete System of Arithmetic, Composed for the Use of the Citizens of the United States. Newburyport, MA: John Mycall.

Robin Halwas Limited. 1997. American Mathematical Textbooks 1760–1850. London.

Smith, Mrs. E. Vale. 1854. History of Newburyport; from the Earliest Settlement of the Country to the Present Time. With a Biographical Appendix. Boston: Dambrell and Moore.

Swetz, Frank J. 1993. Back to the Present: Ruminations on an old Arithmetic Text. Mathematics Teacher 86: 491–494.

U.S. Metric Association. 2015, 13 November. Conversion to Decimal Currency.

Zitarelli, David. 2019. The Arithmetic of Nicholas Pike. Online supplement to A History of Mathematics in the United States and Canada, vol. 1, 1492–1900. Providence, RI: MAA Press Imprint of the American Mathematical Society.