Benjamin Peirce

Mathematician, physicist, and astronomer, Benjamin Peirce (1809-1880) has been called the "fatherof American mathematics." He distinguished himself as superintendent of the U.S. Coast Survey. Peircewas a professor at Harvard College from 1833 until his death, and contributed to the founding of its observatory.

Peirce is remembered for calculating the exact location and path of the planet Neptune, using a series of lengthy and complex mathematical equations. He also tracked and calculated the paths of many comets and charted the phases of the moon for the United States government. Soon after the discovery of Saturn's rings in 1850, he calculated and published his assessment of the possible composition of the rings. Peirce's work and his writings on practical mathematics extended to the fields of astronomy, mechanics, and geology. His contributions to the field of theoretical mathematics included commentary on hypercomplex number theory.

A Prominent Puritan

Benjamin Peirce was born in Salem, Massachusetts, on April 4, 1809. He was the third child of Benjamin Peirce and the former Lydia Ropes Nichols and was descended from a long line of Puritans. The Peirce family came from Norfolk County, England, to Watertown, Massachusetts, around 1634. The Peirces were craftsmen, weavers, shopkeepers, farmers, and East India traders. The elder Benjamin Peirce served as a state legislator and later joined the staff at Harvard as a distinguished librarian.

Peirce attended Salem Private Grammar School. There he came under the influence of the mathematician and scientist Nathaniel Bowditch, whose son attended school with Peirce. Bowditch let Peirce read proofs of his English translation of P.S. Laplace's astronomy treatise, Traite de Mecanique Celeste ( Celestial Mechanics ). The translation was published as Peirce was graduating from Harvard in 1829. Until 1839, Peirce contributed to revising and refining the Bowditch translation. Peirce had a lifelong professional relationship with Bowditch and later paid tribute to Bowditch in the introduction to a treatise Peirce wrote on analytical mechanics, calling him "the father of American geometry."

Harvard Professor

After graduating from Harvard, Peirce joined the teaching staff at Round Hill School in Northampton, Massachusetts. After two years at Round Hill, Peirce joined the faculty at Harvard, initially as a mathematics tutor. In 1833 he became professor of mathematics and astronomy at Harvard, and in 1842 he was named Perkins professor at the college.

So complex was Peirce's mind that it was difficult for all but the most proficient mathematicians to understand much of his work. The speed of his mental processes made it difficult for him to describe his work coherently with pen and paper. His lectures were far too advanced for many students to follow. Those students who heard him speak often said they felt awed by his commitment to the discipline of mathematics.

During his tenure at Harvard, Peirce published a variety of mathematics texts. These included Plane Trigonometry in 1835, Spherical Trigonometry in 1836, and Plane and Solid Geometry in 1837. He published his Treatise on Sound in 1836. In 1840 he published another text on plane geometry, followed in 1841 by the first volume of a text on mechanics; a second volume followed in 1846.

Peirce was instrumental in the founding of the Harvard College Observatory in 1839. When in March 1843 he observed a comet, he spearheaded an intensive effort to get a 15-inch telescope at the observatory. The telescope was installed in 1847, allowing Peirce better opportunity to study celestial phenomena. The telescope was instrumental in the discovery of the planet Neptune that year and in calculating its path. As the mathematics editor of the American Almanac, Peirce published his calculations and observations of the known orbits of comets in the almanac's 1847 edition.


Around 1840, a small but prominent cadre of American scientists and mathematicians assembled to seek support and funding for national development in science. The group was known sarcastically as Lazzaroni, or beggars. It had close ties to a formidable European scientific community. Peirce aligned himself with the Lazzaroni, who eventually became the nucleus of the American Association for the Advancement of Science. The association solicited leading industrialists for political backing and support for scientific advancement.

In 1843 Alexander Dallas Bache, a self-ordained leader of the Lazzaroni, became the second superintendent of the U.S. Coast Survey. The Coast Survey, authorized in 1807, was the first scientific agency established by the U.S. Government. Under the influence of the Lazzaroni, the Coast Survey helped spur the scientific movement in the United States. In 1852, at superintendent Bache's request, Peirce calculated the longitudes of various places in the United States.

Peirce and his colleagues in the educational and scientific communities persuaded Congress to authorize funding for the publication of the American Ephemeris and Nautical Almanac. A bureau for the publication was established in Washington, D.C., in 1849, and the project was delegated to Harvard College, with Peirce as consulting mathematician. The moon tables, as calculated by Peirce, were published in 1853 and described the phases of the moon through 1883.

In the 1840s Peirce joined with one of his former Harvard students, Benjamin Apthorp Gould, and a Swiss naturalist, Louis Agassiz, to lobby for expansion of the science facility at Harvard College. They were instrumental in the opening of Harvard's Lawrence Scientific School in 1847. Peirce, with his high-visibility projects during those years, contributed significantly to the development of a Harvard-based sphere of scientific influence.

In 1863, Peirce and the American Association for the Advancement of Science helped get Congress to establish the National Academy of Sciences. Peirce was among its 50 charter members. He was a member of the organizing committee and served as chairman of the mathematics and physics groups of the academy.

In 1867 Peirce relinquished his post as consultant for the American Ephemeris bureau to become superintendent of the U.S. Coast Survey. His three-year association with the Coast Survey is considered one of his most significant contributions. Among the far-reaching projects undertaken by the Survey under Peirce was surveying Alaska, which had just been purchased from Russia. Peirce also sent representatives worldwide to observe solar eclipses.

Astronomer of Note

Because of his exceptional competence in performing lengthy calculations and comprehending complex geometric concepts, Peirce made many calculations about objects in space. In 1847 he published a work containing the known orbits of comets. That same year he performed a series of extended calculations to determine the precise location, orbit, and weight of Neptune, which had been discovered in 1846.

In 1850 rings were discovered around Saturn, leading to much speculation about their composition. George Phillips Bond of the Harvard College Observatory, who discovered the rings, suggested that they might be fluid. Peirce contested that theory and put forth a comprehensive set of formulas to disprove it. He published an initial analysis of the nature of the rings in 1851. In 1866 he published his formulas for the rings in Memoirs of the National Academy of Sciences.

In 1852 Peirce described a hypotheses concerning probability, which came to be known as Peirce's criterion. Although his premise was ultimately disproved, he left an extraordinary amount of detailed calculations about probability. In the Astronomical Journal of December 31, 1858, he published a theory detailing the hyperbolic orbit of comets. His System of Analytical Mechanics, which he dedicated to Bowditch, was regarded well into the 20th century as definitive.

Peirce lectured widely, and during his lectures he routinely introduced new concepts. In an 1870 presentation called "Linear Associative Algebra," which he presented to the National Academy of Sciences, he introduced the terms idempotent and nilpotent. The former describes a number that approaches itself when calculated to a power of two or greater, and the latter refers to a number that approaches zero. He later self-published the speech, which contained his widely quoted statement: "Mathematics is the science which draws necessary conclusions." He also coined the phrase "indeterminate form" to describe the incalculable equation of zero divided by zero.

Peirce died on June 10, 1880, in Cambridge, Massachusetts. His final significant work, Ideality in the Physical Sciences, was published posthumously in 1881. It was the text of a lecture that he delivered early in 1879.

Peirce's use of mathematical calculations to predict accurately such phenomena as the recurrence of comets and the phases of the moon demonstrated the practicality of his knowledge. He performed his extensive calculations without the convenience of an adding machine, much less a calculator or computer.

Peirce married Sarah Hunt Mills on July 23, 1833. Together they had five children: James Mills, born in 1834; Charles Sanders, born in 1839; Benjamin Mills, born in 1844; Helen Huntington, born in 1845; and Herbert Henry Davis, born in 1849. The children, like their father, grew to be prominent citizens: a Harvard professor, a noted Harvard-based scientist and philosopher, a mining engineer, the wife of a realtor, and a foreign diplomat respectively.


Dictionary of American Biography, American Council of Learned Societies, 1928-1936.

Lenzen, V.F., Benjamin Peirce and the U.S. Coast Survey, San Francisco Press, 1968.


New Solidarity, August 22, 1986.


"Earliest Known Uses of Some of the Words of Mathematics," (February 5, 2001).