Mathematics and Statistics
Jared Mansfield, 1759-1830
In the brief span of nine years, Jared Mansfield made important mathematical contributions to Ohio and to the young United States.
Jared Mansfield came from an established New England family. The first members of his family to settle in the new world came to New Haven, Connecticut, in 1639. Several of his male forebears graduated from Yale College during the 18th century, and Jared began his Yale career in 1777. Unfortunately, his father died while he was a student, and perhaps due to the lack of his father’s guidance, he committed, "serious errors of conduct ... [and was] expelled from Yale during Jan. of his Senior year for complicity in a theft of books from the library ... [and] other discreditable escapades" . Somehow Mansfield was reinstated. The mathematics education he received at Yale (algebra, trigonometry, surveying, navigation, conic sections, fluxions, and possibly an introduction to Newton’s Principia) was of a high quality in the pre-Revolutionary American colonies. Today, the Yale University Art Gallery displays the Mansfield portrait by Robert Walker Weir.
After graduation, Mansfield followed several of his ancestors as Rector of the Hopkins Grammar School. The Hopkins School was designed to prepare the sons of the colony’s upper classes in languages (Latin and Greek) and in mathematics and the liberal arts for entrance into Harvard , Yale, and the small number of other American colleges. In the last two decades of the eighteenth century, Mansfield also directed other preparatory schools in New Haven and Philadelphia.
But Mansfield’s most important accomplishment in the 1790s was the composition of a remarkable and eclectic collection, Essays, Mathematical and Physical (published in New Haven in September 1801) . A partial list of the topics Mansfield discussed will show how wide his interests were: philosophical inquiries into negatives, zero and infinity; trigonometry; nautical astronomy; a theory of the tides; curves; fluxions; ballistics; and the motions of the moon. This book so impressed Thomas Jefferson that, in 1802, he appointed Mansfield to the inaugural faculty of the United States Military Academy at West Point, and then a little more than a year later, to be the Surveyor General of the United States.
From November, 1803 until the Spring of 1812, Mansfield based his work as Surveyor General first in Marietta, Ohio, and after October, 1805, in "the dirty little village" that was to become Cincinnati. General Rufus Putnam, "the Father and Founder of Ohio," had been the first Surveyor General in the Old Northwest. But, complaints had arisen about the accuracy of Putnam’s work, and Mansfield was appointed in an attempt to fix some of the problems. (Also, it would be interesting to know if politics played any part in his appointment: Putnam was a Federalist, whereas Mansfield, like Jefferson, was a Democrat/Republican.)
Mansfield selected the point where the Great Miami River opens into the Ohio River as the foot of his first principle meridian; today, this meridian is the boundary between Ohio and Indiana. In this and in his subsequent work, Mansfield faithfully followed the basic principles of scientific surveying - the principles upon which the lands were surveyed across the country as the nation expanded through the rest of the nineteenth century. From each principle meridian (running North-South), a system of base lines (running East-West) were defined in order to establish what were essentially coordinates for the region; corrections were made for the latitude. This was the basis on which townships and sections, that stretched across the nation, were established. I believe that of the regions Mansfield actually surveyed, about half were in what is now Ohio and the other half in present-day Indiana.
For the surveying work, the United States government provided Mansfield with certain astronomical instruments. Mansfield’s son claimed (in 1879) that his father’s home in Cincinnati was "the first real observatory in the United States" , but that is in dispute. In addition to making a way for his work and his family on the American frontier, during his tenure as Surveyor General, Mansfield published three mathematical papers:
"A Calculation of the Orbit of the Comet, which Appeared Lately; Together with Some General Observations on Comets," Memoirs of the Connecticut Academy of Sciences 1 (1810), 103-110.
"Of the Figure of the Earth," Memoirs of the Connecticut Academy of Sciences 1 (1810), 111-118.
"Observations on the Duplication of the Cube, and the Trisection of an Angle," Memoirs of the Connecticut Academy of Sciences 1 (1810), 119-123.
One of Mansfield’s most important contributions to mathematics and mathematics education in Ohio was his son, Edward Deering Mansfield (1801-1880); but that is another story!
The region where Mansfield, Ohio, is now located was first settled by Europeans in 1808, but reportedly Jared Mansfield was not among these pioneers. Clashes between Native Americans and the settlers in this part of Ohio were quite common, at least until the end of the War of 1812. I do not know how the settlers came to name their community after Jared Mansfield.
When the Mansfield family returned from Cincinnati to New Haven, the War of 1812 had just started. During the War, the fortunes of the United States Military Academy fell to a very low ebb. At the conclusion of the War, President James Madison led a major reform effort of the Academy at West Point, and one aspect of this rebuilding was Jared Mansfield’s appointment as Professor of Natural Philosophy. Mansfield spent the years 1814 to 1828, teaching physics as his contribution to the Academy’s rebirth under Colonel Sylvanus Thayer (revered at West Point as "The Founder of the Academy"). When Mansfield retired, the USMA Class of 1828 commissioned a portrait by Thomas Sully, which hangs in the West Point Museum today.
When he retired, Mansfield moved out to Cincinnati to be near his son. On a return visit to New Haven, Mansfield died on Februray 3, 1830, and there is a monument to his memory in the Grove Street Cemetery there.
Article by Joe Albree
Auburn University at Montgomery
- Albree, Joe (2002). "Jared Mansfield (1759-1830): Janus Figure in American Mathematics." 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). West Point: Department of Mathematical Sciences. pp. 73-94.
- Mansfield, Edward D. (1879). Personal Memories. Social, Political, and Literary with Sketches of Many People, 1803-1843. Books for Libraries Press (Reprinted 1970).
- Mansfield, Jared (1801). Essays, Mathematical and Physical: Containing New Theories and Illustrations of some Very Important and Difficult Subjects of the Sciences. Never Before Published. New Haven: William W. Morse.