Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who taught at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

for approximately 50 years. He made contributions to

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, and the

philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...

Early life

He was born in

Salem, Massachusetts Salem ( ) is a historic coastal city in Essex County, Massachusetts, United States, located on the North Shore (Massachusetts), North Shore of Greater Boston. Continuous settlement by Europeans began in 1626 with English colonists. Salem was one ...

, the son of first cousins Benjamin Peirce (1778–1831), later librarian of Harvard, and Lydia Ropes Nichols Peirce (1781–1868). After graduating from

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 Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

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 United States Coast Survey from 1867 to 1874. In 1842, he was elected as a member of the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

. He was elected a

Foreign Member of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

of London in 1852.

Research

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

slavery Slavery is the ownership of a person as property, especially in regards to their labour. Slavery typically involves compulsory work, with the slave's location of work and residence dictated by the party that holds them in bondage. Enslavemen ...

, opining that it should be condoned if it was used to allow an elite to pursue scientific enquiry.

Mathematics

In number theory, he proved there is no odd

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

with fewer than four

prime factor A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s. In algebra, he was notable for the study of

associative algebra In mathematics, an associative algebra ''A'' over a commutative ring (often a field) ''K'' is a ring ''A'' together with a ring homomorphism from ''K'' into the center of ''A''. This is thus an algebraic structure with an addition, a mult ...

s. He first introduced the terms

idempotent Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of pl ...

and

nilpotent In mathematics, an element x of a ring (mathematics), ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n=0. The term, along with its sister Idempotent (ring theory), idem ...

in 1870 to describe elements of these algebras, and he also introduced the

Peirce decomposition Peirce may refer to: * Charles Sanders Peirce (1839–1914), American philosopher, founder of pragmatism Schools * Peirce College, Philadelphia, formerly known as Peirce College of Business, Peirce Junior College and Peirce School of Business Admi ...

. 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 Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...

, as helping to initiate the consequence-oriented philosophy of

pragmatism Pragmatism is a philosophical tradition that views language and thought as tools for prediction, problem solving, and action, rather than describing, representing, or mirroring reality. Pragmatists contend that most philosophical topics� ...

. Like

George Boole George Boole ( ; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. H ...

, Peirce believed that mathematics could be used to study

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

. 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 Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philos ...

and

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

attempted to base mathematics on logic.

Statistics

Peirce proposed what came to be known as Peirce's Criterion for the statistical treatment of

outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...

s, that is, of apparently extreme observations. His ideas were further developed by his son Charles. Peirce was an

expert witness An expert witness, particularly in common law countries such as the United Kingdom, Australia, and the United States, is a person whose opinion by virtue of education, training, certification, skills or experience, is accepted by the judge as ...

in the

Howland will forgery trial The Howland will forgery trial (''Robinson v. Mandell'') was a United States, U.S. court case in 1868 where businesswoman Henrietta Howland Robinson, Henrietta "Hetty" Howland Robinson, who would later become the richest woman in America, conteste ...

, 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.

Private life

He was devoutly religious, though he seldom published his theological thoughts.Grattan-Guinness, Ivor and Walsh, Alison (2008), "Benjamin Peirce", ''Stanford Encyclopedia of Philosophy''
Eprint
Peirce credited God as shaping nature in ways that account for the efficacy of

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

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 The diabolo ( ; commonly misspelled ''diablo'') is a juggling or circus skills, circus juggling prop, prop consisting of an axle () and two cone, cups (hourglass/egg timer shaped) or cylinder, discs derived from the Chinese yo-yo. This object i ...

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 James Mills Peirce (May 1, 1834 – March 21, 1906) was an Americans, American mathematician and educator. He taught at Harvard University for almost 50 years. Early life and family Peirce was born May 1, 1834, in Cambridge, Massachusetts. He wa ...

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

(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. BenjaminPeirce

Eponyms

The lunar crater Peirce is named for Peirce, as well as the

asteroid An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...

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 , in commission from 1855 to 1868, was named for him.noaa.gov NOAA Legacy: Tools of the Trade: Coast and Geodetic Survey Ships: Benjamin Peirce
/ref>

Works

* ''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 Little, Brown and Company is an American publishing company founded in 1837 by Charles Coffin Little and James Brown in Boston. For close to two centuries, it has published fiction and nonfiction by American authors. Early lists featured Emil ...

. ''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

, 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
* 1872
A System of Analytical Mechanics

David van Nostrand David Van Nostrand (December 5, 1811 – June 14, 1886) was a New York City publisher. Biography David Van Nostrand was born in New York City on December 5, 1811. He was educated at Union Hall, Jamaica, New York, and in 1826 entered the publis ...

& Company, link from

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

Notes

References

* F. P. Matz, "B. O. Peirce: Biography," ''

American Mathematical Monthly ''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an exposi ...

'', 1895, № 2, 173–179. ''Google'
Eprint
* S. R. Peterson, "Benjamin Peirce: Mathematician and Philosopher," ''Journal of the History of Ideas'', 16, 1955, 89–112. * Peirce, Benjamin (1852)
"Criterion for the Rejection of Doubtful Observations"
''Astronomical Journal'' II 45 an
Errata to the original paper
Link pages for their non-PDF images o
the article
an
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

, published in the ''American Journal of Mathematics'' v. 4, n. 1, 1881, Johns Hopkins University, pp. 221–226, ''Google'
Eprint

JSTOR JSTOR ( ; short for ''Journal Storage'') is a digital library of academic journals, books, and primary sources founded in 1994. Originally containing digitized back issues of academic journals, it now encompasses books and other primary source ...

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 The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

'', 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

br>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
NOA
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, . * *

External links

* * * Grattan-Guinness, Ivor, and Walsh, Alison (2005), "Benjamin Peirce", ''

Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...

'', Edward N. Zalta (ed.)
Eprint
* O'Connor, John J., and Robertson, Edmund F. (2005), "Benjamin Peirce", '' MacTutor History of Mathematics Archive''
Eprint
* Hogan, Edward R. (2008), ''Of the Human Heart: A Biography of Benjamin Peirce'', Lehigh University Press

*

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

,
Benjamin Peirce
, 23 October 1880, p. 257 {{DEFAULTSORT:Peirce, Benjamin 1809 births 1880 deaths Charles Sanders Peirce American algebraists American number theorists American statisticians American astronomers 19th-century American mathematicians United States Coast Survey personnel National Oceanic and Atmospheric Administration Harvard University Department of Philosophy faculty Harvard University alumni Foreign members of the Royal Society Members of the United States National Academy of Sciences People from Salem, Massachusetts Mathematicians from Massachusetts Members of the American Philosophical Society