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THURSDAY, SEPTEMBER 20, 1883 



SCIENCE WORTHIES 

 XXII.— Arthur Cayley 



IT is natural that the public in general should wish to 

 know something of the life and work of one whom 

 the British Association for the Advancement of Science 

 has honoured by placing him this year at its head, an 

 honour indeed which could not much longer have been 

 withheld, considering the foremost place which our new 

 President occupies among English mathematicians. But 

 when asked to tell the story I am tempted to exclaim 

 with the needy knifegrinder — 



" Story, God bless you, there is none to tell, Sir." 

 The quiet life of a student is not likely to be rich in sen- 

 sational incidents, and of the nature of the work done by 

 a labourer in the field of pure mathematics it is not 

 possible to give more than a vague idea to the outside 

 world. Some slight sketch I must attempt to give, and 

 in doing so I must express my obligations to Mr. J. W. L. 

 Glaisher, without the help of whose greater knowledge of 

 Cambridge matters and of the recent progress of mnhe- 

 matics I could not have undertaken this task. 



Arthur Cayley was born August 16, 1821. His father, 

 a grandson of Cornelius Cayley — who was Recorder of 

 Kingston-on-Hull from 1725 to 1771 — was settled at St. 

 Petersburg as partner in the firm of Russian merchants — 

 Thornton, Melville, and Cayley. It was during a short 

 visit of his parents to England that their second son, 

 Arthur, was born at Richmond, Surrey. An elder brother 

 had died in infancy ; a younger brother has since become 

 well known as an Italian scholar and a translator of 

 Dante. In 1829 the family returned permanently to 

 England, and after a while fixed their residence at Black- 

 heath. At a very early age Arthur gave the usual indica- 

 tion by which mathematical ability is wont first to show 

 itself, namely, great liking and aptitude f r arithmetical 

 calculations. A lady, who was one of his first instructors, 

 has told that he used to ask for sums in Long Division to 

 do while the other little bjys were at play. After four 

 years' teaching at a private school at Blackheath he was 

 sent at the age of fourteen to King's College School, 

 London, the principal of which (Hugh Rose), being struck 

 by the indications of mathematical genius which he gave, 

 prevailed on his father to abandon his intention of bring- 

 ing the boy up to his own business and induced him to 

 send him instead to Cambridge, where he entered Trinity 

 College at the rather unusually early age of seventeen. 

 At his college examinations Cayley was first by an 

 enormous interval ; but it was fortunate for him that the 

 wares in which I12 dealt were those which fetched the 

 highest price ; for, if classics had been given the prefer- 

 ence over mathematics instead of vice versa, he had in 

 his class at Trinity College two most formidable com- 

 petitors, namely, Mr. Munro, the well known scholar and 

 editor of Lucretius, and Mr. Justice Denman, who after- 

 wards came out as Senior Classic at the same time that 

 Cayley came out as Senior Wrangler and first Smith's 

 Prizeman. 

 This was in 1S42. In University as in other harvests, 

 Vol. xxviii. — No. 725 



there sometimes comes a run of unusually good years, 

 and this certainly appears to have been the case at the 

 period in question. The Senior Wrangler in 1840 was 

 Leslie Ellis, in 1841 Stokes, in 1842 Cayley, in 1S43 

 Adams ; the last three of whom have, for now over twenty 

 years, given lustre to the Cambridge mathematical school, 

 of which they have formed part of the working staff. I 

 do not know whether Cayley's success at the Tripos Ex- 

 amination was as little a surprise to himself as it was to 

 others. Stories were current in Cambridge at the time 

 of the equanimity with which he received the news of 

 his success. The best authenticated one is that he 

 was on the top of the coach on a night journey from 

 London to Cambridge when the tripos list was put into 

 his hands ; he quietly put it into his pocket, resigning 

 himself very contentedly to the necessity of waiting till 

 the morning light for a knowledge of its contents. 

 Caylev's name cannot be added to the list of those who 

 have combined distinction in the boats or on the cricket 

 field with high University honours. He was, however, an 

 active pedestrian, and was a member of the Alpine Club 

 in its comparatively early days. 



While still an undergraduate, Cayley commenced his 

 career of mathematical publications by a paper in the 

 Cambridge Mathematical Journal tot 1841. This periodi- 

 cal had been founded a little time before by Leslie Ellis, 

 who has been just mentioned, in conjunction with his 

 friend, Mr. Gregory, who thereby rendere 1 a service to 

 English mathematics that it would be difficult to estimate. 

 One who devotes himself to original mathematical re- 

 search must make up his mind to forego the pecuniary 

 rewards which attend other forms of successful literary 

 labour. The public which he addresses is so limited that, 

 instead of expecting to be paid for what he writes, he has 

 to think how he can give it to the world without too 

 severe pecuniary loss. If it were not for the help given 

 by learned societies and by mathematical periodicals, 

 every mathematician who was not rich would be forced 

 to keep his discoveries to himself, and on such terms few 

 would have spirit to persevere in research. At the time 

 of which I speak mathematical periodicals open to young 

 students scarcely existed, so that to young mathematicians 

 doubtful of the value of their own speculations, and 

 whose modesty would hardly permit them to ask for 

 publication from the Royal Society, an immense stimulus 

 was given by the foundation of the periodical just men- 

 tioned, the Cambridge Mathematical Journal, afterwards 

 continued under the names of the Cambridge and Dublin 

 Mathematical Journal and the Quarterly Journal oj 

 Mathematics. This journal roused the energies of the 

 younger members of the University by making known to 

 them that others of no higher standing than themselves 

 were engaged in original research and by promising them 

 the means of publishing whatever they might discover ; 

 and certainly it is no small thing that it can boast to have 

 given Cayley his first opportunity of coming before the 

 world. 



His prodigious activity however could not long be 

 content with a single outlet, and there were few organs 

 of mathematical publication at home or abroad which 

 did not receive communications from him. If his memoirs 

 were now collected, they would form a mass exhibiting a 

 spectacle of enormous literary industry. It appears, 



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