Benjamin Peirce

Benjamin Peirce (April 4, 1809, Salem, Massachusetts – October 6, Cambridge, Massachusetts, 1880) was the first internationally known American-born mathematician and is sometimes called "the father of American mathematics". He was the first to recognize as an important mathematical structure the linear associative algebra He derived several of its properties and gave "Peirce's decomposition"—the decomposition of a semi-simple associative algebra into a direct sum of simple algebras.

Peirce was also a highly respected astronomer who helped determine the orbit of the newly discovered (1846) planet Neptune and calculated the perturbations produced between its own orbit and those of Uranus and other planets.

Benjamin Peirce is the father of Charles Sanders Peirce, a well-known philosopher and mathematician.

Life

Benjamin Peirce graduated from Harvard in 1829 and accepted a teaching position with George Bancroft at his Round Hill School in Northampton, Massachusetts. Two years later, at the age of twenty-two, Peirce was asked to join the faculty at Harvard as a tutor in mathematics. In 1833 Peirce received his M.A. from Harvard. In 1842 he became Harvard's Perkins Professor of Mathematics and Astronomy, a position he held until his death in 1880.

In the year he received his M.A. (1833), Peirce married Sarah Hunt Mills; four sons were born to the couple. The eldest, James Mills Peirce, was for forty-five years a prominent mathematician at Harvard; Charles Sanders Peirce, was known for his work in mathematics and physics, but also recognized for his discoveries in logic and philosophy; Benjamin Mills Peirce, brilliant but undisciplined, died in early manhood; and Herbert Henry Davis Peirce was a Cambridge businessman.

In 1847 Benjamin Peirce was appointed to a five-man committee by the American Academy of Arts and Sciences to plan and organize what was to become the Smithsonian Institution. From 1849 to 1867 Peirce served as consulting astronomer to the newly created American Ephemeris and Nautical Almanac. Peirce was also one of the 50 founders of the National Academy of Sciences (1863). He stimulated the forming of the Harvard Observatory by lecturing on Encke's Comet in 1843 and was an organizer of the Dudley Observatory, Albany, N.Y.

In 1852 he began a long association with the U.S. Coast Survey, a US government service that was renamed to Coast and Geodetic Survey in 1871, under the directorship of Peirce. Starting as director of longitude determinations, he eventually became superintendent (from 1867 until 1874). In 1871 Peirce convinced Congress to mandate a transcontinental geodetic survey along the 39th parallel (that passes approximately through Baltimore-Denver-San Francisco).. In addition, he oversaw the first geodetic map of the US.

Before the American Civil War, Peirce was a pro-slavery Democrat with many good friends in the South. When the war started in 1861 with the taking of Fort Sumter (near Charleston SC) by the Confederates, Peirce changed his mind and became a strong Union supporter. Peirce was a deeply religious man, he clung to the fundamental doctrine of a personal, loving God, to whom he made frequent reference in even his most technical books and papers.

Peirce's science

Peirce is mainly remembered for his work on the linear associative algebra of 1870. But before that he did other important work. When he was not yet twenty he found an error in the proof of his countryman Nathaniel Bowditch's translation of Pierre-Simon Laplace's Traité de mécanique céleste [Treatise on Celestial Mechanics]. From then on he assisted regularly in the proof-reading of the translation.

In his early years of teaching, Peirce wrote a series of elementary textbooks in the fields of Trigonometry, Sound, Geometry, Algebra, and Mechanics. All these texts were used in his own courses at Harvard as soon as they came out, but only the Trigonometry be- came widely popular. These textbooks, although considered terse and difficult, had a lasting influence on the teaching of mathematics in America.

In addition Peirce wrote on a wide range of topics, mostly astronomical or physical. Some of the problems he discussed were: the motion of two adjacent pendulums, the motion of a top, the fluidity and tides of Saturn's rings, and Encke's comet of 1843.

Peirce's work on the orbits for Uranus and Neptune was triggered by the discovery of Neptune in 1846. In 1846 Le Verrier concluded from certain irregularities in the orbit of Uranus that there must exist another, yet unobserved, planet. He predicted its orbit and position. His prediction was quickly verified by the observation of a new planet which was baptized Neptune. Peirce, however, pointed out that two solutions of the problem were possible and that Neptune would not have been discovered at all, except that by chance both possible locations lay at that particular time in the same direction from the earth. Later, however, it was found that both men were wrong: Le Verrier because he had simply made an error in his calculations which resulted in a wrong orbit; Peirce because he accepted this wrong orbit as mathematically valid, and from it derived a second solution. Le Verrier had indicated the correct direction in which to look, but had predicted the wrong distance. Nevertheless, the net result of the controversy was to gain for Peirce international recognition as a mathematician and astronomer.

Peirces advanced treatise A System of Analytical Mechanics of 1855 was considered one of the most important mathematical books produced in the United States up to that date and was praised as being the best book on the subject at the time.

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