Benjamin Peirce

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Benjamin Peirce

Birthplace: Salem, Essex, Massachusetts, United States
Death: Died
Immediate Family:

Son of Benjamin Peirce and Lydia Ropes Peirce
Husband of Sarah Hunt Peirce
Father of Charles Sanders Peirce; James Mills Peirce; Herbert H. D. Peirce; 2 Peirce and 4 Peirce

Occupation: mathematician and astronomer
Managed by: Private User
Last Updated:

About Benjamin Peirce

Benjamin Peirce ( /ˈpɜrs/;[1] April 4, 1809, Salem, Massachusetts – October 6, 1880, Cambridge, Massachusetts) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philosophy of mathematics.

He was the son of Benjamin Peirce (1778-1881), later librarian of Harvard, and Lydia Ropes Nichols Peirce (1781–1868).

After graduating from Harvard, he remained as a tutor (1829), and was subsequently appointed professor of mathematics in 1831. He added astronomy to his portfolio in 1842, and remained as Harvard professor until his death. In addition, he was instrumental in the development of Harvard's science curriculum, served as the college librarian, and was director of the U.S. Coast Survey from 1867 to 1874.


Benjamin Peirce is often regarded as the earliest American scientist whose research was recognized as world class.


In number theory, he proved there is no odd perfect number with fewer than four prime factors.

In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition.

Definition of mathematics

In the philosophy of mathematics, he became known for the statement that "Mathematics is the science that draws necessary conclusions." Benjamin Peirce's definition of mathematics was credited by Charles Sanders Peirce as helping to initiate the consequentialist philosophy of pragmatism.

Like George Boole, Benjamin Peirce believed that mathematics could be used to study logic. These ideas were developed by Charles Sanders Peirce, who noted that logic also includes the study of faulty reasoning.

In contrast, the later logicist program of Gottlob Frege and Bertrand Russell attempted to base mathematics on logic.


Benjamin Peirce proposed what came to be known as Peirce's Criterion for the statistical treatment of outliers, that is, of apparently extreme observations. His ideas were developed by Charles Sanders Peirce.

Benjamin Peirce was an expert witness in the Howland will forgery trial, where he was assisted by his son Charles Sanders Peirce. Their analysis of the questioned signature showed that it resembled another particular handwriting example so closely that the chances of such a match were statistically extremely remote.

Private life

He was devoutly religious, though he seldom published his theological thoughts. Peirce credited God as shaping nature in ways that account for the efficacy of pure mathematics in describing empirical phenomena. Peirce viewed "mathematics as study of God's work by God's creatures", according to an encyclopedia.

He married Sarah Hunt Mills, the daughter of U.S. Senator Elijah Hunt Mills. Peirce and his wife had four sons and one daughter :

James Mills Peirce (1834–1906), who also taught mathematics at Harvard and succeeded to his father's professorship.

Charles Sanders Peirce (1839–1914), a famous logician and polymath.

Benjamin Mills Peirce (1844–1870), who worked as a mining engineer before an early death.

Helen Huntington Peirce Ellis (1845–1923), who married William Rogers Ellis.

Herbert Henry Davis Peirce (1849–1916), who pursued a career in the Foreign Service


The lunar crater Peirce is named for Benjamin Peirce.


An Elementary Treatise on Plane and Solid Geometry, Boston: James Munroe and Company. Google Eprints of successive editions 1837–1873.

An Elementary Treatise on Plane and Spherical Trigonometry, Boston: James Munroe and Company. Google Eprints of successive editions 1840–1862.

Physical and Celestial Mechanics, Boston: Little, Brown and Company. Google Eprint of 1855 edition.

Linear Associative Algebra, lithograph by Peirce 1872. New edition with corrections, notes, and an added 1875 paper by Peirce, plus notes by his son Charles Sanders Peirce, published in the American Journal of Mathematics v. 4, 1881, Johns Hopkins University, pp. 221–226, Google Eprint and as an extract, D. Van Nostrand, 1882, Google Eprint.

Other References

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Benjamin Peirce's Timeline

April 4, 1809
Salem, Essex, Massachusetts, United States
Age 24
September 10, 1839
Age 30
Age 39
October 6, 1880
Age 71