Advances in mathematics during the U.S. Revolutionary War

SUMMARY: The American Revolutionary War saw advances in mathematics, cryptography, and education.

The American Revolutionary War was a political and armed conflict between Great Britain and the British colonies on the North American continent between 1775 and 1783. Colonists who sought to end British rule and declare their political and economic independence supported the establishment of thirteen colonial governments, each of which, in turn, sent representatives to Philadelphia to set up the Second Continental Congress.

This congress debated the state of political and economic ties to Britain, plied for support from other European powers, and discussed the possibilities and potential of a collective effort to make the separation official. Shortly after its inception, the Second Continental Congress formed a Continental Army and issued the Declaration of Independence. These actions announced the birth of a new nation: the United States of America. The War of American Independence also called the American Revolutionary War, saw fierce fighting in a wide variety of locations throughout the new nation and on the soil of virtually every new state. Some key battles were fought in Lexington, Concord, and Boston, Massachusetts; Saratoga and Ticonderoga, New York; Trenton, New Jersey; King’s Mountain and Cowpens, South Carolina; and Yorktown, Virginia, among many other places.

The war lasted almost a decade and ended with the Treaty of Paris, which was signed at the Palace of Versailles in 1783 and recognized the sovereignty of the United States of America. There are many statistics available that relate to aspects of the war, including casualties and cost. For instance, some report that the British spent about £80 million while incurring a national debt of 250 million pounds, while the United States spent approximately $135 million, of which $37 million became the national debt. Mathematics was used in a wide variety of ways, including in the design and implementation of artillery and in planning strategy and tactics. Mathematicians fought in the war, conducted surveys, and created and decoded ciphers. The mathematics educational system also changed significantly as a result of the war.

French Mathematicians

Many historians agree that the Americans would have been unable to win the war without the political and military support of France and other allies. Louis-Antoine de Bougainville (1729-1811) was a French mathematician who became the first Frenchman to sail around the world. After election to the Royal Society of London in 1756, he turned to a career in which he participated in numerous wars, including the Revolutionary War.

His astronomical observations became important to later explorers. He stated, “Geography is a science of facts: one cannot speculate from an armchair without the risk of making mistakes which are often corrected only at the expense of the sailors.” During the Revolutionary War, he was a commodore who supported the U.S. side.

French mathematician Silvestre François Lacroix (1765-1843) was the most influential mathematics author of his time. In 1752, he wrote a calculus book, Traité du calcul–intégral, which brought him recognition within the mathematical community for his clear exposition and updates to differential and integral calculus.

American Mathematicians

U.S. Army geographer Simeon DeWitt (1756-1834) subscribed to The Mathematical Correspondent, generally regarded as the first U.S. special-interest scientific publication. DeWitt was a student at Rutgers University when British troops burned the college buildings. He continued his study of mathematics and surveying on his own and was appointed the geographer of the army by General George Washington. After the war, he became surveyor-general of New York State.

During the American Revolution, rather than devising new mathematical theories, important mathematical minds like Benjamin Franklin (1706-1790) and David Rittenhouse (1732-1796) focused on real-world applications of mathematics relevant to the war efforts. Navigation, logistics, surveying, mapmaking, and code-breaking gained significant advancements using algebra, trigonometry, and geometry.

Education

Mathematics education changed dramatically in the United States during and after the war. Before the war, students usually learned mathematics from British works, although Americans like Isaac Greenwood (1702-1745) had written arithmetic texts. Advanced mathematics included algebra, geometry, trigonometry, calculus, and surveying techniques. Many colleges were shut down during the war because students and professors served as soldiers, and buildings were used for other purposes. However, some members of the army were trained in mathematics during the war. After the war, new primary schools and colleges were established.

Between 1776 and 1815, numerous mathematics texts were published in the United States. Some of these were reprints of English works, and others were compilations or new works by American writers. In 1788, American Nicholas Pike (1743-1819) published his text, The New and Complete System of Arithmetick: Composed for the Use of the Citizens of the United States, which contained both arithmetic and geometry. It was popularized by patriotic recommendations. There was also a change in women's education. Before the war, it was thought that mathematics beyond simple arithmetic was unnecessary for women. After the war, mathematics educational opportunities began slowly to increase, as women were educated in mathematics to help in family businesses.

Bibliography

Apfeldorf, Michael. "Mathematics and Primary Sources: Historic Codes, Ciphers, and Computational Thinking, Part I." Library of Congress Blogs, 20 Mar. 2018, blogs.loc.gov/teachers/2018/03/mathematics-and-primary-sources-historic-codes-ciphers-and-computational-thinking-part-i. Accessed 1 Oct. 2024.

Tarwater, Dalton. The Bicentennial Tribute to American Mathematics. The Mathematical Association of America, 1977.

Tolley, Kim. The Science Education of American Girls. Routledge, 2003.

Weber, Ralph. “James Lovell and Secret Ciphers during the American Revolution.” Cryptologia, vol. 2, no. 1, 1978.

Zitarelli, David. “The Bicentennial of American Mathematics Journals.” The College Mathematics Journal, vol. 36, no. 1, 2005.