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

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.[2]


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",[3]. 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 believe 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.[citation needed]


Benjamin Peirce proposed a Peirce's criterion for the statistical treatment of outliers, that is, of apparently extreme observations. His ideas were developed by Charles Sanders Peirce. [4]

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

As a person he was devoutly Christian, seeing "mathematics as study of God's work by God's creatures."[citation needed]

He married Sarah Hunt Mills, the daughter of U.S. Senator Elijah Hunt Mills.[5] The husband and wife had a daughter and three sons:

* Charles Sanders Peirce a famous logician,
* James Mils Peirce, who also taught mathematics at Harvard, and
* Herbert Henry Davis Peirce, who worked for Herter Brothers.


The lunar crater Peirce is named for Benjamin Peirce.


* Physical and Celestial Mathematics, (Boston: Little, Brown and Company, 1855)
* An Elementary Treatise on Plane and Spherical Trigonometry (1861)
* An Elementary Treatise on Plane and Solid Geometry (1865)
* Linear Associative Algebra (1880)


1. ^ "Peirce", in the case of Benjamin Peirce and his son C.S. Peirce, always rhymes with "terse" and so, in most dialects, is pronounced exactly like the English-language word "purse": About this sound Audio (US) (help·info). See "Note on the Pronunciation of 'Peirce'", The Peirce [Edition] Project Newsletter, Vol. 1, Nos. 3/4, Dec. 1994, Eprint.
2. ^ Stephen Stigler. Annals of Statistics. 1978.
3. ^ First line of Linear Associative Algebra
4. ^ Theory of Errors of Observation
5. ^ Adams, Henry. The Life of George Cabot Lodge. pg. 4–5. Boston and New York: Houghton Mifflin, 1911


* F. P. Matz, "B. O. Peirce: Biography," American Mathematical Monthly, 1895, № 2, 173–179.

* S. R. Peterson, "Benjamin Peirce: Mathematician and Philosopher," Journal of the History of Ideas, 16, 1955, 89–112.

* P. Meier and S. Zaibel, "Benjamin Peirce and the Howland Will", Journal of the American Statistical Association, 75, 1980, 497–506.

* Peirce, Benjamin. "Linear Associative Algebra", Van Nostrand, New York, 1882.

o Peirce, Benjamin (1881). "Linear Associative Algebra". American Journal of Mathematics 4 (Vol. 4, No. 1., pp 97–229. (1881): 97–229. http://www.jstor.org/stable/2369153. JSTOR.

* Benjamin Peirce, "Criterion for the Rejection of Doubtful Observations", Astronomical Journal II 45 (1852) and Errata to the original paper.

* Peirce, Benjamin (May 1877-1878). "On Peirce's criterion". Proceedings of the American Academy of Arts and Sciences 13: pp. 348–351. http://www.jstor.org/stable/25138498.

* Peirce, Charles Sanders (1870 [published 1873]). "Appendix No. 21. On the Theory of Errors of Observation". Report of the Superintendent of the United States Coast Survey Showing the Progress of the Survey During the Year 1870: pp. 200–224. . NOAA PDF Eprint (goes to Report p. 200, PDF's p. 215).

* Peirce, Charles Sanders (1982 [1986 copyright]). "On the Theory of Errors of Observation [Appendix 21, according to the editorial note on page 515]". in Kloesel, Christian J. W., et alia. Writings of Charles S. Peirce: A Chronological Edition. Volume 3, 1872-1878. Bloomington, Indiana: Indiana University Press. pp. 140–160.

* Stigler, Stephen M. (March 1978). "Mathematical Statistics in the Early States". Annals of Statistics 6: pp. 239–265. doi:10.1214/aos/1176344123. http://projecteuclid.org/euclid.aos/1176344123. JSTOR 2958876 MR483118

* Stigler, Stephen M. (1980). "Mathematical Statistics in the Early States". in Stephen M. Stigler. American Contributions to Mathematical Statistics in the Nineteenth Century, Volumes I & II. I. New York: Arno Press.

* Stigler, Stephen M. (1989). "Mathematical Statistics in the Early States". in Peter Duren. A Century of Mathematics in America. III. Providence, RI: American Mathematical Society. pp. 537–564.

External links

* Grattan-Guinness, Ivor, and Walsh, Alison (2005), "Benjamin Peirce", Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), Eprint.
* O'Connor, John J., and Robertson, Edmund F. (2005), "Benjamin Peirce", MacTutor History of Mathematics Archive, Eprint.


Mathematics Encyclopedia

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