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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.
He was elected a Foreign Member of the Royal Society of London in 1852.
Benjamin Peirce is often regarded as the earliest American scientist whose research was recognized as world class. He was an apologist for slavery, opining that it should be condoned if it was used to allow an elite to pursue scientific enquiry.
In the philosophy of mathematics, he became known for the statement that "Mathematics is the science that draws necessary conclusions". 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.
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.
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 was an avid juggler of diabolo and wrote about the physics of the game in Analytic Mechanics.
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,
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, GoogleEprint and as an extract, D. Van Nostrand, 1882, GoogleEprint.
Tachytrope, curve in which the law of the velocity is given. Developed by Peirce.
^"Peirce", in the case of Benjamin Peirce and family, always rhymes with "terse" and so, in most dialects, is pronounced like the word "purse (help·info)". See "Note on the Pronunciation of 'Peirce'", The Peirce [Edition] Project Newsletter, Vol. 1, Nos. 3/4, Dec. 1994, Eprint.
^ abGrattan-Guinness, Ivor and Walsh, Alison (2008), "Benjamin Peirce", Stanford Encyclopedia of Philosophy. Eprint.
^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 BooksEprint
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, GoogleEprint, doi:10.2307/2369153JSTOR and as an extract, D. Van Nostrand, 1882, GoogleEprint, Internet ArchiveEprint.
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, ISBN0-253-37201-1.
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. 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. III. Providence, RI: American Mathematical Society. pp. 537-564.