Benjamin Peirce

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Benjamin Peirce

Peirce c. 1870
Born(1809-04-04)April 4, 1809
DiedOctober 6, 1880(1880-10-06) (aged 71)
SpouseSarah Hunt Mills
Children5, including Charles and Herbert
Alma materHarvard University
Known for
Scientific career
InstitutionsHarvard University
Superintendent of the United States Coast Survey
Academic advisorsNathaniel Bowditch
Notable studentsJoseph Lovering
InfluencedCharles Sanders Peirce
Signature of Benjamin Peirce.png

Benjamin Peirce ForMemRS HonFRSE (/ˈpɜːrs/;[1] April 4, 1809 – October 6, 1880) 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.

Early life[edit]

He was born in Salem, Massachusetts, the son of Benjamin Peirce (1778–1831), later librarian of Harvard, and Lydia Ropes Nichols Peirce (1781–1868).[2]

After graduating from Harvard University in 1829, he taught mathematics for two years at the Round Hill School in Northampton, and in 1831 was appointed professor of mathematics at Harvard. 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. In 1842, he was elected as a member of the American Philosophical Society.[3] He was elected a Foreign Member of the Royal Society of London in 1852.[4]


Benjamin Peirce is often regarded as the earliest American scientist whose research was recognized as world class.[5] He was an apologist for slavery, opining that it should be condoned if it was used to allow an elite to pursue scientific enquiry.[6]


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.

In the philosophy of mathematics, he became known for the statement that "Mathematics is the science that draws necessary conclusions".[7] Peirce's definition of mathematics was credited by his son, Charles Sanders Peirce, as helping to initiate the consequence-oriented philosophy of pragmatism. Like George Boole, Peirce believed that mathematics could be used to study logic. These ideas were further developed by his son Charles , 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.


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 further developed by his son Charles.[8]

Peirce was an expert witness in the Howland will forgery trial, where he was assisted by his son Charles. Their analysis of the questioned signature showed that it resembled another particular handwriting example so closely that the chance of such a match occurring at random, i.e. by pure coincidence, was extremely small.[citation needed]

Private life[edit]

He was devoutly religious, though he seldom published his theological thoughts.[9] Peirce credited God as shaping nature in ways that account for the efficacy of pure mathematics in describing empirical phenomena.[10] Peirce viewed "mathematics as study of God's work by God's creatures", according to an encyclopedia.[9] He was an avid juggler of diabolo and wrote about the physics of the game in Analytic Mechanics.[11]

He married Sarah Hunt Mills, the daughter of U.S. Senator Elijah Hunt Mills.[12] Peirce and his wife had four sons and one daughter:[13]

  • 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, polymath and philosopher,
  • 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, and
  • Herbert Henry Davis Peirce (1849–1916), who pursued a career in the Foreign Service.


The lunar crater Peirce is named for Peirce, as well as the asteroid 29463 Benjaminpeirce.

Post-doctoral positions in Harvard University's mathematics department are named in his honor as Benjamin Peirce Fellows and Lecturers.

The United States Coast Survey ship USCS Benjamin Peirce, in commission from 1855 to 1868, was named for him.[14]


See also[edit]


  1. ^ "Peirce", in the case of Benjamin Peirce and family, always rhymes with "terse" and so, in most dialects, is pronounced like the word "purse ". See "Note on the Pronunciation of 'Peirce'", The Peirce [Edition] Project Newsletter, Vol. 1, Nos. 3/4, Dec. 1994, Eprint.
  2. ^ Rossiter Johnson; John Howard Brown (1904). The twentieth century biographical dictionary of notable Americans ... The Biographical Society. pp. 269–. Retrieved August 28, 2011.
  3. ^ "APS Member History". Retrieved April 12, 2021.
  4. ^ "Fellow Details". Royal Society. Retrieved May 27, 2017.
  5. ^ Stigler, Stephen M. (1978). "Mathematical Statistics in the Early States". Annals of Statistics. 6 (2): 239–265. doi:10.1214/aos/1176344123. JSTOR 2958876.
  6. ^ Auspitz, Josiah Lee (Autumn 1994). "The Wasp Leaves the Bottle: Charles Sanders Peirce". The American Scholar. 63 (4): 602–618.
  7. ^ First line of Linear Associative Algebra
  8. ^ Peirce, Charles Sanders (1870/1871/1873).
  9. ^ a b Grattan-Guinness, Ivor and Walsh, Alison (2008), "Benjamin Peirce", Stanford Encyclopedia of Philosophy. Eprint.
  10. ^ Peirce, "Address of Professor Benjamin Peirce, President of the American Association for the Year 1853", Proceedings of the American Association for the Advancement of Sciences, Eighth Meeting [ = Volume 8], held at Washington D.C., May, 1854, published 1855, pp. 1–17, see especially pp. 12–15. Google Books Eprint
  11. ^ Notes and Queries (August 27, 1881 ed.). Oxford University Press. 1881. p. 176.
  12. ^ Adams, Henry. The Life of George Cabot Lodge. pp. 4–5. Boston and New York: Houghton Mifflin, 1911
  13. ^ Fisch, Max H. (1981), Introduction, Writings of Charles S. Peirce v. 1.
  14. ^ NOAA Legacy: Tools of the Trade: Coast and Geodetic Survey Ships: Benjamin Peirce


  • F. P. Matz, "B. O. Peirce: Biography," American Mathematical Monthly, 1895, № 2, 173–179. Google Eprint.
  • 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 (1852), "Criterion for the Rejection of Doubtful Observations", Astronomical Journal II 45 and Errata to the original paper. Link pages for their non-PDF images of the article and its errata.
  • Peirce, Benjamin (1872, 1881), Linear Associative Algebra. Lithograph edition 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, n. 1, 1881, Johns Hopkins University, pp. 221–226, Google Eprint, doi:10.2307/2369153 JSTOR and as an extract, D. Van Nostrand, 1882, Google Eprint, Internet Archive Eprint.
  • Peirce, Benjamin (1878), "On Peirce's Criterion", Proceedings of the American Academy of Arts and Sciences, v. 13 (whole series), v. 5 (new series), for May 1877 – May 1878, Boston: Press of John Wilson and Son, pp. 348–351. Google Eprint. JSTOR abstract.
  • Peirce, Charles Sanders (1870/1871/1873) "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. Coast Survey Report submitted February 18, 1871, published 1873 by the U.S. Government Printing Office, Washington, D.C. Reports 1837–1965. NOAA PDF Eprint (link goes to 1870 Report's p. 200, PDF's p. 215). Reprinted in pp. 140–160 of Writings of Charles S. Peirce: A Chronological Edition: Volume 3, 1872–1878, Christian J. W. Kloesel et al., eds., Bloomington, Indiana: Indiana University Press, ISBN 0-253-37201-1.
  • Stigler, Stephen M. (1980). "Mathematical Statistics in the Early States". In Stephen M. Stigler (ed.). American Contributions to Mathematical Statistics in the Nineteenth Century, Volumes I & II. Vol. I. New York: Arno Press.
  • Stigler, Stephen M. (1989). "Mathematical Statistics in the Early States". In Peter Duren (ed.). A Century of Mathematics in America. Vol. III. Providence, RI: American Mathematical Society. pp. 537–564.

External links[edit]

Government offices
Preceded by Superintendent, United States Coast Survey
Succeeded by