# Robert Leslie Ellis

### Quick Info

Bath, England

Trumpington, England

**Leslie Ellis**was a brilliant man with broad interests and abilities who suffered from ill health all his short life. Senior Wrangler in the Mathematical tripos at Cambridge in 1840, he became a fellow of Trinity College and was interested in areas of mathematics which involved philosophical ideas.

### Biography

**Robert Leslie Ellis**was the son of Francis Ellis (1772-1842) and Mary Hilber. Francis and Mary Ellis were married on 12 October 1803 at St Mary the Virgin, Bathwick, Somerset. On official documents, Francis Ellis gives his occupation as "esquire" meaning he was of independent means. Francis and Mary Ellis had six children: Everina Frances Ellis (born 4 December 1806); Henry William Ellis (born 9 May 1808); Penelope Sarah Ellis (born 11 March 1811); Francis Ellis (born 23 January 1813); Mary Jane Ellis (born 5 August 1815); and Robert Leslie Ellis, the subject of this biography, born 25 August 1817 and baptised in St Mary's Chapel, Walcot, St Swithin, Somerset on 17 September 1817. We note here that Robert Leslie Ellis was known by his friends as 'Leslie Ellis' and wrote papers under the name 'R Leslie Ellis'.

Harvey Goodwin, then Dean of Ely and later Bishop of Carlisle, writes about the influence of Ellis's parents [6]:-

His mother's health was not good, and from her he appears to have inherited that highly nervous constitution, which became, during a considerable portion of his life, as we shall see hereafter, the medium of great suffering. His father was a man of cheerful disposition, of active and well cultivated intellect, fond of speculative inquiry, and in worldly circumstances independent. His character and his mode of dealing with Robert, as a child, had a great influence upon him throughout his life: he became his father's companion from a very early age, and the affection with which he referred in later life to his father's care and to the happy days of his boyhood, could not fail to strike those who had the pleasure of knowing him intimately.We give a complete version of Harvey Goodwin's obituary of Ellis at THIS LINK.

Leslie Ellis was home educated by his father and two tutors, one for mathematics and the other for classics. His mathematics tutor was Thomas Stephens Davies (1795-1851) who was elected to the Royal Society of Edinburgh in 1831, then became a mathematics master at the Royal Military Academy in Woolwich in 1834. His classical tutor was H A S Johnstone. Being home educated, there are few records of his achievements as a child but what is known shows that he was reading adult works when still a young child. He made use of his father's library and also the library of the Bath Literary and Scientific Society which had officially opened in 1824. His progress in mathematics, for example, shows that he was studying the differential and integral calculus when 13 years old.

On 10 July 1834 he was admitted as a pensioner to Trinity College, Cambridge but he had no intention of matriculating in that year but intended to begin studying the mathematical tripos at Cambridge in 1835. In October 1834 he went to Papworth Everard in Cambridgeshire to study with James Challis. Challis had studied at Trinity College, Cambridge, being Senior Wrangler in the 1825 mathematical tripos. He was also First Smith's Prizeman and elected a fellow of Trinity College. He was ordained in 1830 and given the benefice of Papworth Everard by the College. He resigned his fellowship before Ellis began studying with him but later, in 1836, Challis became director of the Cambridge Observatory and Plumian Professor of Astronomy. A year studying with Challis would have been a wonderful experience for Ellis but sadly his health collapsed and, after six weeks residence at Papworth Everard, he had to return home. In fact his health was so poor that he was not sufficiently recovered to be able to matriculate at Trinity College in 1835 as he had intended and had to delay for one further year.

Ellis matriculated at Trinity College in the Michaelmas Term (October) 1836 and began his study of the mathematical tripos. His tutor was George Peacock and his coach was William Hopkins. Harvey Goodwin was studying the mathematical tripos at the same time as Ellis but seldom saw him [6]:-

Ellis never read with the class of which I was one; in fact, he did not need the kind of lecture which was adapted to myself and others; he required only that his reading should be arranged, and put in a form suitable for the Cambridge examinations. The only occasion upon which I was brought into contact with him as a fellow-student was in attending Professor Peacock's lectures on Plane Astronomy. I remember well the astonishment with which I witnessed his demeanour during the lectures: he made no note, he asked no question; but he quietly remarked as we left the lecture-room together one day, "It saves one the trouble of reading these things up."He seems to have had a very limited social life at Cambridge, attended few lectures and sought little support from his coach Hopkins [20]:-

Ellis's private journal reveals that, like Airy, having stolen a substantial lead on his peers, he was able to read a great deal of advanced mathematics by himself as an undergraduate. ... Ellis was considered remarkable precisely because he did not read with a private tutor in his second year and that, notwithstanding his remarkable mathematical ability, he did go to Hopkins in his final year in order that his "reading should be arranged, and put in a form suitable for the Cambridge examinations."A description of Ellis by Hopkins does, however, paint a clear picture of his student [6]:-

On one point he [Ellis] always seemed to puzzle me. The extent and definiteness of his acquirement, and his maturity of thought, were so great, so entirely pertaining to the man, that I could hardly conceive when he could have been a boy.Of course the poor health from which Ellis continued to suffer must have had a marked influence on how he behaved. His fellow students knew that nobody could compete with him for the position of Senior Wrangler provided his health allowed him to sit all the tripos examinations. Ellis, however, disliked the tripos system intensely [20]:-

Although exceptionally well-prepared in mathematics before entering Cambridge, Ellis had been warned by J D Forbes that his delicate health would make the Mathematical Tripos a risky venture. And, despite his head start, Ellis did indeed suffer appallingly as an undergraduate, especially during his final year of hard coaching with Hopkins. He recorded in his journal how early success in college examinations had marked him out as a potential senior wrangler, and how his subsequent attempts to live up to these expectations had gradually replaced his "freshness and purity of mind" with "vulgar and trivial ambition." Ellis privately expressed his sense of apprehension and despondency upon returning to Cambridge in February of his final undergraduate year: "And so here I am again, with a little of that sickening feeling. which comes over me from time to time, and which I can but ill describe, and with some degree of, harness bitter dislike of Cambridge and of my own repugnance to the wrangler making process." ... Ellis longed for the Tripos to be over. He confided despairingly to his journal, "this must and will pass away - if not before - when I leave this place and shake the dust off my shoes for a testament against the system."The examiners made some allowances in that he was allowed to sit the papers in a separate room. His health did allow him to sit all the papers and be became Senior Wrangler in the Mathematical tripos of 1840. Andrew Warwick provides a description of Ellis being presented to the Vice Chancellor which is based on Ellis's own notes [20]:-

Having attended a special celebratory breakfast at Trinity College, Ellis made his way, in hood, gown, and bands, to the Senate House. There he was congratulated by people waiting for the ceremony to begin, until William Whewell came up and "hinted at the impropriety" of the Senior Wrangler mingling with the crowd. Once everyone was seated in their proper places and the galleries filled with students, Ellis was led the full length of the Senate House by Thomas Burcham to thunderous applause ... [Ellis writes] "When all was ready William Hopkins and the other esquire bedell made a line with their maces. Burcham led me up the Senate House. Instantly my good friends of Trinity and elsewhere, two or three hundred men, began cheering most vehemently, and I reached the Vice Chancellor's chair surrounded by waving handkerchiefs and most head rending shouts. Burcham nervous. I felt his hand tremble as he pronounced the customary words, vobis praesento hunc juvenum." Having knelt before the Vice Chancellor to have his degree conferred, Ellis walked slowly to the back of the Senate House - to further loud cheers - where, overcome with emotion, he was sat down and revived with a bottle of smelling salts provided by a young woman from the crowd.Also in [20] we see the following:-

As Robert Ellis walked the length of a packed Senate House to tumultuous applause to receive his degree in 1840, William Walton was awed by the way his "pale and ill" countenance enhanced his "intellectual beauty." Even more strikingly, another onlooker remarked to Walton "pithily" that had he seen Ellis before the examination he would have known him to be unbeatable.Not only was Ellis Senior Wrangler, but he was also First Smith's prizeman and, soon after that, he was elected a fellow of Trinity College. Despite his remarkable mathematical abilities he considered a career in law and was admitted to the Inner Temple in 1838 and called to the bar in 1840. His circumstances, however, changed over the next few years. In 1841 his brother Henry William Ellis died, in the following year his father died, then on 27 August 1843 his brother Francis Ellis died. The result of the death of his father and elder brothers was that Leslie Ellis now inherited the bulk of the family fortune. He had no need to practice law, but this did not mean that his interest stopped [9]:-

... he devoted much time to the study of the civil law, leaving behind him several volumes of notes, but his ultimate ambition to be appointed professor of civil law remained unfulfilled.Ellis was most interested in areas of mathematics which involved philosophical ideas. We illustrate this by quoting the introduction to two of his papers, one on probability, the other on least squares. His paper

*On the Foundations of the Theory of Probabilities*was submitted to the Cambridge Philosophical Society and read on 14 February 1842. It begins:-

The Theory of Probabilities is at once a metaphysical and a mathematical science. The mathematical part of it has been fully developed, while, generally speaking, its metaphysical tendencies have not received much attention.Our second example is

This is the more remarkable, as they are in direct opposition to the views of the nature of knowledge, generally adopted at present.

The theory received its present form during the ascendancy of the school of Condillac. It rejects all reference to à priori truths as such, and attempts to establish them as mathematical deductions from the simple notion of probability. Are we prepared to admit, that our confidence in the regularity of nature is merely a corollary from Bernouilli's theorem? That until this theorem was published, mankind could give no account of convictions they had always held, and on which they had always acted? If we are not, what refutation have we to give? For these views are entitled to refutation, from the general reception they have met with, from the authority of the great writers by whom they were propounded, and even from the imposing form of the mathematical demonstration in which they are invested.

I shall be satisfied if the present essay does no more than call attention to the inconsistency of the theory of probabilities with any other than a sensational philosophy.

*On the Method of Least Squares*also submitted to the Cambridge Philosophical Society and read on 4 March 1844. It begins:-

The importance attached to the method of least squares is evident from the attention it has received from some of the most distinguished mathematicians of the present century, and from the variety of ways in which it has been discussed.While holding his fellowship, Ellis edited two volumes of the

Something, however, remains to be done namely, to bring the different modes in which the subject has been presented into juxta-position, so that the relations which they bear to one another may be clearly apprehended. For there is an essential difference between the way in which the rule of least squares has been demonstrated by Gauss, and that which was pursued by Laplace. The former of these mathematicians has in fact given two different demonstrations of the method, founded on quite distinct principles. The first of these demonstrations is contained in the 'Theoria Motûs', and is that which is followed by Encke in a paper of which a translation appeared in the Scientific Memoirs. At a later period Gauss returned to the subject, and subsequently to the publication of Laplace's investigation gave his second demonstration in the 'Theoria Combinationis Observationum'.

The subject has been also discussed by Poisson in the 'Connaissance des Tems' for 1827, and by several other French writers. Poisson's analysis is founded on the same principle as Laplace's: it is more general, and perhaps simpler. It is not, however, my intention to dwell upon mere differences in the mathematical part of the enquiry.

The consequence of the variety of principles which have been made use of by different writers has naturally been to produce some perplexity as to the true foundation of the method. As the results of all the investigations coincided, it was natural to suppose that the principles on which they were founded were essentially the same. Thus Mr Ivory conceived that if Laplace arrived at the same result as Gauss, it was because in the process of approximation he had introduced an assumption which reduced his hypothesis to that on which Gauss proceeded. In this I think Mr Ivory was certainly mistaken; it is at any rate not difficult to show that he had misunderstood some part at least of Laplace's reasoning: but that so good a mathematician could have come to the conclusion to which he was led, shows at once both the difficulty of the analytical part of the inquiry, and also the obscurity of the principles on which it rests. Again, a recent writer on the Theory of Probabilities has adopted Poisson's investigation, which, as I have said, is the development of Laplace's, and which proves in the most general manner the superiority of the rule of least squares, whatever be the law of probability of error, provided equal positive and negative errors are equally probable. But in a subsequent chapter we find that he coincides in Mr Ivory's conclusion, that the method of least squares is not established by the theory of probabilities, unless we assume one particular law of probability of error.

These two results are irreconcilable; either Poisson or Mr Ivory must be wrong. The latter indeed expressed his dissent from all that had been done by the French mathematicians on the subject, and in a series of papers in the Philosophical Magazine gave several demonstrations of the method of least squares, which he conceived ought not to be derived from the theory of probabilities. In this conclusion I cannot coincide; nor do I think Mr Ivory's reasoning at all satisfactory.

*Cambridge Mathematical Journal*. In one of these he published his obituary of D F Gregory. You can read a version of this obituary at THIS LINK.

He served as moderator of the mathematical tripos examinations in 1844 and examiner in the following year when he examined William Thomson. Although Thomson was Second Wrangler (a great disappointment to him), Ellis remarked to a friend [3]:-

... we are just about fit to mend his pens.Also in 1845, the British Association asked Ellis to write a report on recent progress in analysis. Alex Craik writes [2]:-

Ellis's most substantial piece is his 85-page "Report on the Recent Progress of Analysis (Theory of the Comparison of transcendentals)" commissioned for the sixteenth meeting of the British Association for the Advancement of Science in 1846. This is both a comprehensive historical survey and an up-to-date review of the literature, mainly from continental journals then little-known in Britain. The theory of elliptic functions, together with its extension and related work by Legendre, Hermite, Jacobi, Abel, Liouville and many others, are expertly summarised. Although it contains no new results, Ellis's convenient account must have been of great value to the British mathematical community, still struggling to catch up with continental scholars.One further work he undertook was [9]:-

... in conjunction with D D Heath and J Spedding, the edition of Francis Bacon's works published between 1857 and 1874. His wide reading and intellectual labour are nowhere as evident as in the general prefaces to Bacon's philosophical writings, which were allotted to him. The deterioration of his health in 1847 prevented him from completing his project, a fact that caused him great sorrow.Ellis's fellowship at Trinity College ended in 1849 and, hoping to improve his health, he travelled to the south of France and north Italy. He became ill in Mentone, where he believed he had slept in a damp bed, and then his health completely collapsed in San Remo which he reached on the following day. He developed rheumatic fever [6]:-

A physician, who was called in, seems to have exerted himself with great kindness and to the utmost of his skill, to do all that could be done. Ellis always retained an affectionate remembrance of him. He ordered his patient to be bled extensively, and after a few days the imminent danger was passed. Rheumatism however remained fixed hopelessly upon him; he was ever after in constant pain, with very little use of any part of his body; and the rest of his life, ten years, may be described as a long process of gradual dissolution.He remained in San Remo for three months, then was brought back to England in easy stages. On his return, he had a notion to enter politics as a candidate for Bath but the state of his health meant that he gave up that idea. He visited many doctors in an attempt to find a cure but to no avail. In 1853 he settled in Anstey Hall in Trumpington, a village two miles from Cambridge, where he hoped to be able to meet up with his university friends. Slow deterioration in his health meant that soon he was confined to his home, then later he was confined to bed. Although physically disabled, his remarkable mind continued to be extremely active. He dictated a paper on bees' cells, one on a Chinese Dictionary, he corresponded about the Romance language, Gothic, and Sanskrit among many other topics. He continued to think about mathematics which in many ways he considered a recreation.

You can read much more about this final part of Ellis's life in Harvey Goodwin's obituary of Ellis at THIS LINK.

Let us end with a couple of quotes. From [12] we have:-

Ellis was much admired by his Victorian contemporaries. George Boole, in an 1857 prize-essay about applications of probability theory, wrote that "there is no living mathematician for whose intellectual character I entertain a more sincere respect than I do for that of Mr Ellis." A decade later, Francis Galton expressed a similar sentiment when describing Ellis as one "whose name is familiar to generations of Cambridge men as a prodigy of universal genius."Harvey Goodwin writes [6]:-

I have no wish to indulge in any extravagant eulogy of my friend, but I should leave a sad blank in this brief memorial of him if I did not say that his moral qualities were not below his intellectual. His manner might be accounted by some persons cold, and he was certainly not one with whom familiar intercourse and the thorough freedom of friendship were attained rapidly; but those who knew him well knew that he possessed one of the most gentle of hearts, with a delicate consideration for the feelings of others, and a most grateful sense of any kindness shown to himself. Above all his sense of honour and propriety was perfect; nothing shabby or mean could exist in the same place with Leslie Ellis.

### References (show)

- A man of no ordinary attainments: the life and work of Robert Leslie Ellis (1817-1859),
*British Society for the History of Mathematics*(2018).

https://www.bshm.ac.uk/events/man-no-ordinary-attainments-life-and-work-robert-leslie-ellis-1817-1859 - A D D Craik,
*Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century*(Springer Verlag, 2008). - T Crilly, The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age,
*Historia Mathematica***31**(4) (2004), 455-497. - S E Despeaux, 'Very full of symbols': Duncan F Gregory, the calculus of operations, and the Cambridge Mathematical Journal, in
*J J Gray and K H Parshall (eds.), Episodes in the History of Modern Algebra (1800-1950)*(American Mathematical Society, Ann Arbor, 2007), 49-72. - J R Gibbins, Robert Leslie Ellis,
*The Athenaeum***1686**(1860), 205-206. - H Goodwin, Biographical Memoir of Robert Leslie Ellis, M.A., Late Fellow of Trinity College, Cambridge, in
*Robert L Ellis, The Mathematical and Other Writings of Robert Leslie Ellis*(Deighton, Bell, Cambridge - B Kilinç, Robert Leslie Ellis and John Stuart Mill on the One and the Many of Frequentism,
*British Journal for the History of Philosophy***8**(2) (2000), 251-274. - L Krüger, The slow rise of probabilism: philosophical arguments in the nineteenth century, in
*The probabilistic revolution***1**(Bradford Book, MIT Press, Cambridge, MA, 1987), 59-89. - M Panteki, Ellis, Robert Leslie (1817-1859), mathematician and classical scholar,
*Oxford Dictionary of National Biography*(Oxford University Press, Oxford, 2004). - W C Salmon, Robert Leslie Ellis and the frequency theory, in
*Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science, Pisa, 1978***II**(Reidel, Dordrecht-Boston, Mass., 1981), 139-143. - J Venn and J A Venn (eds.), Ellis, Robert Leslie, in
*Alumni Cantabrigienses: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900*Volume**2**: From 1752 to 1900 (Cambridge University Press, 2011).

https://venn.lib.cam.ac.uk/cgi-bin/search-2018.pl?sur=&suro=w&fir=&firo=c&cit=&cito=c&c=all&z=all&tex=ELS834RL&sye=&eye=&col=all&maxcount=50 - L M Verburgt, A letter of Robert Leslie Ellis to William Walton on probability,
*British Society for the History of Mathematics Bulletin***33**(2) (2018), 96-108. - L M Verburgt, Robert Leslie Ellis, William Whewell and Kant: the role of Rev H F C Logan,
*British Society for the History of Mathematics Bulletin***31**(1) (2016), 47-51. - L M Verburgt, Remarks on the idealist and empiricist interpretation of frequentism: Robert Leslie Ellis versus John Venn,
*British Society for the History of Mathematics Bulletin***29**(3) (2014), 184-195. - L M Verburgt, Robert Leslie Ellis's work on philosophy of science and the foundations of probability theory,
*Historia Mathematica***40**(4) (2013), 423-454. - L M Verburgt, Duncan F. Gregory and Robert Leslie Ellis: second-generation reformers of British mathematics,
*Intellectual History Review***28**(3) (2018), 369-397. - L M Verburgt, The objective and the subjective in mid-nineteenth-century British probability theory,
*Historia Mathematica***42**(4) (2015), 468-487. - L M Verburgt,
*"A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth- and early twentieth-century probability theory, mathematics and logic*(Ph.D. thesis, University of Amsterdam, 2015).

https://pure.uva.nl/ws/files/2685349/166217ProefschriftLukasMVerburgt2015completer.pdf - 7. W Walton (ed.),
*Robert L Ellis, The Mathematical and Other Writings of Robert Leslie Ellis*(Deighton, Bell, Cambridge, 1863).

https://archive.org/details/mathematicalothe00ellirich/page/n3/mode/2up - A Warwick,
*Masters of Theory. Cambridge and the Rise of Mathematical Physics*(The University of Chicago Press, Chicago-London, 2003). - S L Zabell, Ramsey, truth, and probability. The philosophy of Frank P Ramsey, Bologna, 1990,
*Theoria***57**(3) (1991), 211-238.

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Written by J J O'Connor and E F Robertson

Last Update June 2021

Last Update June 2021