by Stephen M. Stigler

© Oxford University Press 2004 All rights reserved

**Adrain, Robert** (1775-1843), mathematician and university teacher, was born on 30 September 1775 in Carrickfergus, Ireland, the eldest of five children. His father, a teacher and maker of mathematical instruments, had emigrated from France, and his mother was of Scottish descent. Both of Adrain's parents died when he was fifteen and in order to support himself and his siblings he opened a school at Ballycarry. The school was a success, and led to a lucrative position as a private tutor. About 1795 he married Ann Pollock *(d.* in or after 1834); they had one daughter, Margaret, before political events intruded. In the Irish uprising of 1798 Adrain took up arms as an officer with the insurgent forces, and his employer, an officer of the crown, offered a price for Adrain's capture. Not long afterwards, Adrain was shot in the back by one of his own men, and was widely rumoured to be dead. Although severely wounded he survived, and with great difficulty escaped with his wife and infant daughter to New York.

Upon his arrival in America Adrain travelled to Princeton, New Jersey, to avoid the yellow fever then prevalent in New York. He taught at a Princeton academy for two years before moving on to a principalship in York, Pennsylvania, and then to a succession of other teaching positions. In 1805 he became principal of an academy in Reading, Pennsylvania, in 1809 a professor at Queen's College, New Brunswick, New Jersey, in 1813 a professor at Columbia College, New York city, and then in 1826, after a brief return to Queen's College, he moved to the University of Pennsylvania, Philadelphia, where he remained until 1834, becoming vice-provost in 1828. One of his students at Columbia remembered him as genial '"Old Bobbie" ... an Irish gentleman, of large size, broad beaming face, and silvery voice' *(Harper's,* 414, 1884, 820), but his career as a teacher was not without blemish. In 1834, he was forced to resign because of his inability to deal with noisy disorder in his classes, a contagion that became intolerable when it threatened to spread to other classes. By this time he had a total of seven children, and he moved his family back to New Brunswick. Then, from 1836 to 1840, he left his family to take up yet another teaching position at the Columbia College grammar school. He returned to New Brunswick in 1840. One of his sons, Garnett Bowditch Adrain (1815-1878), served as a member of the US congress in 1857-61.

Adrain has two claims to fame in the history of mathematics; one is as the editor of a series of mathematical periodicals that served as an impetus to serious mathematical research in America, the other is as the author of a short article in one of his journals that is recognized as one of the earliest original contributions to theoretical statistics. As early as 1804 Adrain was contributing to the first mathematical journal in America, the *Mathematical Correspondent,* and four years later in 1808 he founded his own, *The Analyst, or, Mathematical Museum.* Unlike most Americans Adrain was familiar with European research work, and his contributions to these and other periodicals that followed were at a higher level than those of others, introducing deeper problems and attempts at solutions in areas including Diophantine algebra, geometry, and elliptic integrals.

In the fourth number of the first (and only) volume of *The Analyst,* Adrain contributed a solution to a problem in surveying that was remarkable for the time, leading to his being frequently described as an independent co-discoverer (with C. F. Gauss and A. M. Legendre) of the method of least squares, a method for combining astronomical or geodetic observations so as to reduce the effect of unavoidable observational errors in determining theoretical constants. There is evidence that Adrain had read Legendre's 1805 treatment of least squares at the time, but Adrain's method of attack, starting with two derivations of the normal distribution for errors, was surely original with him and independent of both Legendre and Gauss. Adrain's manuscript, now lost, was apparently dated 1808, although the issue containing his result probably appeared in 1809, the same year as Gauss's publication of his version of the method. Adrain's work on this received no published notice until 1871 when it was rediscovered by Cleveland Abbe.

In other work Adrain published two articles on the figure of the earth in 1818 in the *Transactions of the American Philosophical Society,* and from 1811 onwards edited several American editions of C. Hutton's *Course in Mathematics.* He was elected to the American Philosophical Society in 1812 and the American Academy of Arts and Sciences in 1813. He died at New Brunswick on 10 August 1843.

STEPHEN M. STIGLER

**Sources **

S. M. Stigler, 'Mathematical statistics in the early states', *Annals of Statistics,* 6 (1978), 239-65

S. M. Stigler, ed., *American contributions to mathematical statistics in the nineteenth century,* 2 vols. (1980)

J. L. Coolidge, 'Robert Adrain and the beginnings of American mathematics', *American Mathematical Monthly,* 33 (1926), 61-76

C. Abbe, 'Historical note on the method of least squares', *American Journal of Science,* 3rd ser., 1 (1871), 411-15

M. J. Babb, 'Robert Adrain: man and mathematician', *General Magazine and Historical Chronicle,* 28 (1926), 272-84

J. Dutka, 'Robert Adrain and the method of least squares', *Archive for History of Exact Sciences,* 41 (1990-91), 171-84

G. B. Adrain, 'Robert Adrain, LLD', *United States Magazine and Democratic Review,* 14 (1844), 646-52

E. R. Hogan, 'Robert Adrain: American mathematician', *Historia Mathematica,* 4 (1977), 157-72

'Columbia College', *Harper's New Monthly Magazine,* 69 (1884), 813-31, esp. 820

D. J. Struik, 'Adrain, Robert', *DSB*

**Archives **

University of Pennsylvania, Philadelphia, Van Pelt Library

**Likenesses **

Verlynden, oils, 1822, Col. U.

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