Peacock, George

(1791-1858), mathematician and university reformer

by Harvey W. Becher

© Oxford University Press 2004 All rights reserved

Peacock, George (1791-1858), mathematician and university reformer, was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, co. Durham, one of eight children and the youngest of five sons of Thomas Peacock, perpetual curate and schoolmaster at Denton. He attended Sedbergh School and then, at the age of seventeen, Richmond School under the mastership of James Tate, formerly a fellow of Sidney Sussex College, a moulder of numerous outstanding Cambridge students, and a staunch whig. Having stood at the head of his class at Richmond, in the summer of 1809 Peacock read with John Brass, a Trinity undergraduate who was to become the sixth wrangler of 1811. Peacock was admitted as a sizar at Trinity College, Cambridge, on 21 February 1809 and matriculated in the following Michaelmas Term. In 1810 he won one of the Bell scholarships dedicated to needy sons of clergymen, and in 1812 he was awarded a college scholarship. The following summer he read mathematics with Adam Sedgwick, later to become Woodwardian professor of geology. Like Peacock, Sedgwick was a whig in politics and a strong supporter of reform in the university, and the two were to enjoy a lifelong friendship. Peacock graduated as second wrangler and second Smith's prizeman in 1813, became a fellow of Trinity in 1814 and received his MA in 1816. He was elected a fellow of the Royal Society in 1818, and joined the Astronomical Society in 1820 and the Geological Society in 1822. He was also ordained priest (1822) and gained a DD (1839). He was a mathematics lecturer at Trinity from 1815, a tutor from 1823 to 1839, and Lowndean professor of astronomy and geometry from 1837 until his death.

As an undergraduate Peacock was a founding member of the Analytical Society (in 1812). The society dedicated itself to importing into Cambridge, and developing, continental pure analytics, mainly from France. Enamoured with the French, it denigrated the fluxional notation and the easily intuited fluxions and fluxional mixed (applied) mathematics derived from Isaac Newton, who was revered as the embodiment of Cambridge mathematics and English culture. In an era dominated by fear of the French Revolution and Napoleon, the clerics who ruled Cambridge, primarily the heads of colleges, were suspicious of French mathematics, and doubted the motives of the reformers. In this atmosphere the Analytical Society accomplished little. However, in 1816 Peacock joined two of its leaders, Charles Babbage and John Herschel, in translating a French calculus textbook by S. F. Lacroix. In 1820, the trio published a book of examples to illustrate the theoretical calculus, in acquiescence to the Cambridge tradition of teaching by means of exemplification, as opposed to the French method of teaching via abstract principles that had earlier been advocated by the Analytical Society. This tactic of gaining influence through partial accommodation with the educational traditions of Cambridge was largely devised by Peacock. Supplemented by the collection of examples, the Lacroix translation, while updating Cambridge mathematics, also fitted into the Cambridge curriculum; consequently, the two publications had an immediate and long-lasting influence.

Peacock also ventured reform as moderator of the tripos. In the 1817 tripos, to the dismay of the Cambridge traditionalists, he stressed pure analytics. He also introduced the continental notation for differentiation. Even though he translated the foreign notation into the fluxional notation at the bottom of his papers, his employment of dy/dx raised an outcry against French mathematics from the university traditionalists to the point that Peacock feared some official proceedings against him. Peacock furthermore contrived to limit the viva voce portion of the tripos to allow more time for printed problem papers, in hopes of rewarding mathematical talent rather than memorization of standard bookwork. This endeavour failed when, under pressure from older members of the university, the other moderator and the examiners deserted Peacock. Likewise, they adhered to the traditional mathematics, much to the chagrin of Peacock who believed this vitiated any effect his own papers might have had. In the end, though historians almost universally point to Peacock's examination papers of 1817 as effecting the 'analytical revolution', Peacock himself concluded that they accomplished nothing.

In the tripos of 1819 Peacock and his fellow moderator, Richard Gwatkin, who had also been a member of the now defunct Analytical Society, again employed the continental notation, and from this point it became the norm at Cambridge. However, peeved by the students' lack of physical knowledge, Peacock decided to introduce a large dose of traditional mixed mathematics into the viva voce examination. He rationalized his retreat on the grounds that Gwatkin had forged ahead, and also on the grounds of political expediency: he hoped that his actions in 1819 would appease the powers that be whom he had alienated in 1817. He had been influenced by Jean-Baptiste Biot, the French physicist, who, while visiting Cambridge in 1818, had asserted that the French erred in neglecting Newton's Principia. In the same vein, Peacock pondered working Newton's optics into his college lectures. In mathematics education he was, from the start, a reformer who sought a middle ground between the traditionalists and the radical analysts, and he maintained this position of compromise: thus in the 1850s he argued for curricular emphasis on mixed mathematics, the maintenance of the older intuitive approach, and the suppression of excessive abstract analytics.

Peacock, like the French-based mathematician J. L. Lagrange, and like an older Cambridge reformer, Robert Woodhouse, urged founding the calculus by algebraically developing the successive derivatives of a function as the successive coefficients of the function's expansion in a Taylor series. He rejected limit theory-based calculus, be it that of Newton, of Lacroix in the textbook that he helped translate, or of Augustin Cauchy, the French mathematician who inspired the 'rigorous' foundations for the calculus as it would develop on the continent. He urged the Taylor series foundation, not because he thought it more rigorous--he thought all foundations could be made rigorous--but, rather, because he believed it to be more intuitively clear than limit-based formulations. In an 1833 report on analysis to the British Association for the Advancement of Science, Peacock noted Cauchy's insistence that only convergent series were legitimate and reviewed numerous convergency tests, but he rejected the necessity for these limit-based concerns in pure analysis. In his 1830 Treatise on Algebra (enlarged and revised edn, 1842-5), which he dedicated to Tate, Peacock provided his vision of analysis as formal algebra, a vision which reflected ideas of Woodhouse, Babbage, and other Cambridge mathematicians. Although this work earned Peacock renown as one of the founders of abstract algebra, here, as in his pedagogical predilections, he did not elude the intuitive, as recognized by his contemporaries and by modern historians.

Underlying Peacock's stake in intuitive mathematics was his interest in physical science. From 1816 to 1824, he was the primary mover in the building of the university observatory in opposition to some of the oligarchy. In 1819 he partook in the founding of the Cambridge Philosophical Society and became its vice-president (1831 and 1840) and president (1841-2). In 1830 he declined to sign a petition in support of John Herschel's candidacy for the presidency of the Royal Society during a campaign for the professionalization of British science organized by Charles Babbage. Moreover, as a member of the society's council, he worked closely with the duke of Sussex, the whig brother of the king, after the duke defeated Herschel in the presidential election.

In 1829 Peacock was the leading member of a syndicate charged with planning a university complex which included a substantial science centre. Although by February 1831 the senate had authorized financing for one half of the structure, including most of the science complex, a feud broke out between Peacock and another advocate for the structure, William Whewell. The feud lead to a scurrilous pamphlet war and caused the senate to question the proposals. The result was a decades-long delay in building the complex. None the less, upon being appointed to the Lowndean professorship by a whig government, Peacock gave well-attended lectures on practical astronomy in contrast to his predecessors in the chair who had given no lectures in the previous sixty-seven years. He also tendered lectures on pure mathematics, but these attracted no audience.

In 1843, five years into serving as a member of the commissions for restoring the standards of weight and measures which had been destroyed in the burning of the parliament building, and four years after having been appointed dean of Ely (1839) by a whig government, Peacock turned the astronomy lectures over to the Plumian professor of astronomy and experimental philosophy. He retained the Lowndean chair as a sinecure for the rest of his life. However, he sustained his interest in science, as witnessed by the fact that he continued writing a biography of Thomas Young, the natural philosopher who promoted the wave theory of light. Peacock published the biography and two volumes of Young's works in 1855.

In 1841 Peacock published Observations on the Statutes of the University of Cambridge, an advocacy of academic and political reform of the university and colleges based upon a whig interpretation of history. However, Peacock's ability to effect reform diminished when, later in 1841, a tory government appointed the Conservative Whewell to the mastership of Trinity, arguably the most powerful post in Cambridge and, not surprisingly, a position which Peacock, like Whewell, considered the summit of his ambition. Peacock gained the co-operation of Whewell in establishing a board of mathematical studies to rein in the anarchy of successive moderators and examiners expanding the tripos without approval of the senate, and he used his membership on the board, a consequence of his being Lowndean professor, to implement this restraint, but he had not the leverage within Cambridge to force political reform. However, whig governments appointed Peacock, Sedgwick, and Herschel to a royal commission of inquiry at Cambridge in 1850, and Peacock to a royal statutory commission for Cambridge in 1855. Although he died before the latter commission finished its work, through these commissions Peacock was able to initiate many reforms in the university and colleges, despite the vehement opposition of Whewell and other conservatives.

As dean of Ely, Peacock threw himself into the restoration of Ely Cathedral, both in directing the restoration and in raising funds. He was a prolocutor of the lower house of the convocation of Canterbury from 1841 to 1847 and from 1852 until 1857, when failing health prompted his resignation. He also brought about improvements in the city of Ely's drainage system and fostered the education of the middle and lower classes. In addition to his other ecclesiastical appointments, from 1847 onwards he was rector of Wentworth, near Ely.

In 1847 Peacock married Frances Elizabeth, daughter of William Selwyn, a QC and Cambridge graduate from Trinity. He suffered declining health over the ensuing decade, and he died, childless, on 8 November 1858 at 16 Suffolk Street, Pall Mall, London. He was buried in the Ely cemetery. In 1866, his widow married W. H. Thompson, whose tutor Peacock had been; Thompson had led the agitation for reform from within Trinity during the time of the parliamentary commissions, and a whig government, upon Whewell's death, appointed him master of Trinity shortly before the marriage.

HARVEY W. BECHER

Sources  
H. W. Becher, 'Radicals, whigs and conservatives: the middle and lower classes in the analytical revolution at Cambridge in the age of aristocracy', British Journal for the History of Science, 28 (1995), 405-26
H. Becher, 'Woodhouse, Babbage, Peacock, and modern algebra', Historia Mathematica, 7 (1980), 389-400
H. Becher, 'Voluntary science in nineteenth century Cambridge University to the 1850's', British Journal for the History of Science, 19 (1986), 57-87
Trinity Cam., Peacock MSS
RS, Herschel papers
PRS, 9 (1857-9), 536-43
Venn, Alum. Cant.
Trinity Cam., Whewell MSS
H. Becher, 'William Whewell and Cambridge mathematics', Historical Studies in the Physical Sciences, 11 (1980-81), 1-48
G. Peacock, Observations on the statutes of the University of Cambridge (1841)
H. Pycior, 'George Peacock and the British origins of symbolical algebra', Historia Mathematica, 8 (1981), 23-45
J. Richards, 'The art and science of British algebra: a study in the perception of mathematical truth', Historia Mathematica, 7 (1980), 342-65

Archives  
JRL, Methodist Archives and Research Centre, MS hymnbooks
JRL
Trinity Cam., corresp. |  BL, letters to Charles Babbage, Add. MSS 37182-37201, passim
CUL, letters to Sir George Stokes
CUL, corresp. with Sir George Airy
Norfolk RO, letters relating to Ely Cathedral glass
Ransom HRC, letters to Sir John Herschel
RS, corresp. with Sir John Herschel
RS, letters to Sir John Lubbock
Trinity Cam., corresp. with William Whewell

Likenesses  
S. Lane, oils, exh. RA 1843; Christies, 12 July 1990, lot 123 [see illus.]
S. Lane, photograph, 1853 (after unknown portrait), Trinity Cam., Peacock MSS
D. Y. Blakiston, oils, RS
print (after D. Y. Blakiston), RS
woodcut, BM

Wealth at death  
under £10,000: probate, 15 Jan 1859, CGPLA Eng. & Wales


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