Todhunter, Isaac

(1820-1884), mathematician and historian of mathematics

by J. B. Mullinger, rev. Adrian Rice

© Oxford University Press 2004 All rights reserved

Todhunter, Isaac (1820-1884), mathematician and historian of mathematics, was born on 23 November 1820 in Rye, Sussex, the second son of George Todhunter (c.1792-1825), Congregationalist minister, and his wife, Mary Hume (c.1790-1860). His father's death in 1825 left the family in reduced financial circumstances, and his mother opened a school for girls at Hastings. Todhunter, who as a child was 'unusually backward' (Macfarlane, 134), was sent to a school in the same town kept by Robert Carr, and subsequently to one newly opened by a Mr J. B. Austin from London, by whose influence Todhunter's career was largely determined. About 1835 Todhunter moved with Austin to a school in Peckham where he became assistant master. While thus occupied, he managed to attend evening classes at University College, London, where he had for his instructors Thomas Hewitt Key, Henry Malden, George Long, James Joseph Sylvester, and Augustus De Morgan. He always held himself greatly indebted to all of them, but especially to the last, for whom his admiration was 'unbounded'. It was from this 'venerated master and friend' (Macfarlane, 142) he derived 'that interest in the history and bibliography of science, in moral philosophy and logic, which determined the course of his riper studies' (Mayor, 3). In 1842 Todhunter graduated BA, obtained a mathematical scholarship in the University of London, and, on proceeding MA two years later, obtained the gold medal awarded for that examination, as well as prizes for Greek and Hebrew. Concurrently with these studies, from 1841 he filled the post of mathematical master in a large school at Wimbledon.

On 4 May 1844, acting on De Morgan's advice, Todhunter entered St John's College, Cambridge. In 1848 he gained the senior wranglership and the first Smith's prize, as well as the Burney prize. In the following year he was elected fellow of his college (the delay probably being due to his nonconformist background). From this time he was mainly occupied as college lecturer and private tutor, and in the compilation of the numerous mathematical treatises, chiefly educational, by which he became widely known. Of these, his Euclid (1st edn, 1862) attained an enormous circulation and several editions, while his expositions of algebra (1858), trigonometry, plane and spherical (1859), mechanics (1867), and mensuration (1869), all became standard textbooks, remaining so until the beginning of the twentieth century. They secured a vast readership, were adopted by the Indian government, and were translated into Urdu and other oriental languages.

Todhunter was elected FRS on 5 June 1862, was a candidate for the Sadleirian professorship (to which Arthur Cayley was elected) in 1863, and became a member of the London Mathematical Society on 18 June 1866, in the second year of its existence. In 1864 he resigned his fellowship on his marriage, on 13 August, to Louisa Anna Maria (1832/3-1918), eldest daughter of Captain George Davies RN (at that time head of the Cambridge county constabulary force). In 1871 he won the Adams prize for his 'Researches on the calculus of variations'. Perhaps his most original work, it deals with the abstruse question of discontinuity in solution. In the same year he was elected a member of the council of the Royal Society, on which he served for two years. The Conflict of Studies and other Essays appeared in 1873, containing his views on many issues concerning education. In 1874 he was elected an honorary fellow of his college.

Todhunter's life was mainly that of a studious recluse, and his publications were the outcome of great research and industry which enabled him to acquire a wide acquaintance with general and foreign literature. Besides being a sound Latin and Greek scholar, he was also familiar with French, German, Spanish, Italian, Russian, Hebrew, Arabic, Persian, and Sanskrit. He was well versed in the history of philosophy, and was one of the chief founders of the moral science examination at Cambridge, acting as examiner in 1863-5. He was also responsible for editing posthumous works by two other prominent scientific figures: in 1865, the second edition of Boole's Treatise on Differential Equations and, eleven years later, the literary and scientific correspondence of William Whewell.

Todhunter is also remembered for his many valuable contributions to the history of mathematics. These were lengthy histories of the calculus of variations (1861), probability (1865), the theories of attraction and the figure of the earth (2 vols., 1873) and elasticity (2 vols., 1886-93), a posthumous publication completed by Karl Pearson. They remain valuable reference books to this day, although Todhunter's literary style hardly makes them light reading.

Todhunter's habits and tastes were singularly simple, and to a gentle, kindly disposition he added a high sense of honour, a warm sympathy with all that was calculated to advance the cause of genuinely scientific study in the university, and a love of animals, especially birds and cats. However, he had little love for art and no ear for music: 'He used to say he knew two tunes; one was "God save the Queen", the other wasn't; the former he recognized by the people standing up' (Macfarlane, 137). An affection of the eyes in 1880 proved the forerunner of an attack of paralysis which eventually prostrated him. He died on 1 March 1884, at his home, 6 Brookside, Trumpington Road, Cambridge. His widow, four sons, and a daughter survived him.

J. B. MULLINGER, rev. ADRIAN RICE

Sources  
J. E. B. M. [J. E. B. Mayor], 'In memoriam: Dr Todhunter', Cambridge Review, 5 (1883-4), 228-30, 245-7, 260-65; pubd separately (1884)
The Eagle, 13 (1885), 94-8
E. J. R., PRS, 37 (1884), xxvii-xxxii
A. Macfarlane, Lectures on ten British mathematicians of the nineteenth century (1916), 134-46
Venn, Alum. Cant.
W. Johnson, 'Isaac Todhunter, 1820-1884: textbook writer, scholar, coach and historian of science', International Journal of Mechanical Sciences, 38 (1996), 1231-70

Archives  
St John Cam., papers |  CUL, letters to Sir George Stokes
RAS, letters to Royal Astronomical Society
RS, corresp. with Sir John Herschel
Trinity Cam., letters to J. I. Hammond
Trinity Cam., notebooks relating to W. Whewell
UCL, college corresp.

Likenesses  
E. R. Mullins, marble bust, St John Cam.
G. J. Stodart, print (after photograph), St John Cam.
T. C. Wageman, watercolour drawing, Trinity Cam.
four photographs, St John Cam.
medallion portrait, St John Cam.

Wealth at death  
£81,330 7s. 0d.: probate, 21 April 1884, CGPLA Eng. & Wales


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