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A Mysterious Copy of Lacroix’s Traité Élémentaire de Calcul Différentiel et de Calcul Intégral: De Morgan and Sylvester at the University of London

Adrian Rice (Randolph-Macon College)


Engraving of main building at University of London, 1828
Figure 3. Engraving of University College London’s main building (1828). Wikimedia Commons.

The University of London's first professor of mathematics was Augustus De Morgan (1806–1871), who was appointed in 1828, scarcely a year after graduating from Cambridge [Rice 1997]. Not surprisingly, the level of mathematics taught by De Morgan in those early years was very different, bearing a closer resemblance to high school mathematics than today’s undergraduate courses [Rice 1999]. His students were divided into ‘junior’ and ‘senior’ classes, with each group of students having a ‘higher’ and ‘lower’ division, based on ability. While the lower junior class worked on basic algebra and the first book of Euclid’s Elements, it was not until the higher senior class that students would be exposed to rigorous differential and integral calculus. When the University of London opened for its first lectures in November 1828, De Morgan’s higher senior class consisted of only three or four students—but it included one of the most talented mathematicians De Morgan would ever teach.

Portrait of Arthur Cayley. Portrait of J. J. Sylvester.
Figure 4. (Left) Augustus De Morgan. Convergence Portrait Gallery. (Right) James Joseph Sylvester.
Image of 1841 oil painting by George Patten, in private possession, courtesy of Alain Enthoven.

James Joseph Sylvester (1814-1897) would eventually become one of the foremost British mathematicians of the 19th century and was to contribute to the advancement of the subject in several areas, particularly linear algebra [Parshall 2006]. Born in London to a prosperous middle class Jewish family, he was admitted as a student of the university in November 1828, aged just fourteen. He immediately entered the higher division of De Morgan's senior class “and became by far the first pupil in it” [Anonymous 1837, f.3], distinguishing himself “by the facility with which he acquired a knowledge of the higher branches of Mathematics & the singularity of his power to apply them” [De Morgan 1841]. Indeed, so impressed was De Morgan by his remarkable young student that he later went on record to say “that he never, before or since, saw mathematical talent so strongly marked in a boy of that age” [Anonymous 1837, f.3].

However, outstanding though his mathematical talents undoubtedly were, Sylvester's general demeanor left much to be desired. Reports sent to his sister (in whose care he was at the time) concerning his conduct and attendance complained “of his inattention to his duties” [E. J. Sylvester, 9 Feb. 1829]. He was also apparently “of a most impetuous and irritable disposition, and his extreme youth, together with his religion, reputation for talent, and the disposition above-mentioned, made him, it is supposed, a mark for the practical jokes of his fellow students” [Anonymous 1837, f.4]. A consequence of this taunting, combined with the boy's volatile temper, led to the display of “so great a disposition to an act of violence that his friends were advised by the authorities of the College to remove him: which was accordingly done” [Anonymous 1837, f.4].

A clue to what form this violent behavior took lies in an extract from a letter, formerly in the archives of UCL, which stated that: “The accompanying knife has just been taken from young Sylvester, who had brought it from the Refreshment rooms for the purpose of stabbing Mr. Tulk.”[1] This event led to the myth that Sylvester was one of the first students to be expelled from the university. But a letter from his sister, written at the end of February 1829, reveals Sylvester's family had already concluded that “owing to the extreme youth of my Brother and the fact of his requiring constant control and attention they deem it advisable that he should for the present withdraw from the London University” [E. J. Sylvester, 25 Feb. 1829]. He was to return eight years later under very different circumstances, as UCL’s Professor of Natural Philosophy. But despite the brevity of his studies in London, he remained proud of the four months he had spent under the tutelage of De Morgan, “whose pupil,” he later recalled, “I may boast to have been” [J. J. Sylvester 1840, 43].


[1] This letter is now missing from the archives, but the card catalogue preserves this extract.


Adrian Rice (Randolph-Macon College), "A Mysterious Copy of Lacroix’s Traité Élémentaire de Calcul Différentiel et de Calcul Intégral: De Morgan and Sylvester at the University of London," Convergence (March 2023)