BIOGRAPHICAL NOTICE OF ARTHUR CAYLEY. 
XVII 
re Mathematics: the 
>f pure mathematics, 
roposal was approved 
nctioned by an Order 
elapse before certain 
til after three years 
he held the chair for 
ras modest, though it 
tnges, however, could 
he had no hesitation 
3vote his life to the 
having neglected the 
n to his University; 
s life in Cambridge, 
; in his life. Hence- 
by; yet it was by no 
. claims a part (often 
duty. But he was 
and he was directed 
fact, his ideal in life, 
il the charge of the 
out as the obvious 
}, he married Susan, 
e to dwell upon his 
ence to its singular 
another. Friends and 
uess and the gracious 
*ace into which they 
often in the drawing- 
d watchful, frequently 
deism or paradox in 
dgment was tolerated 
b there; in all things 
nd their two children, 
se of lectures in the 
'actice was maintained 
butes, which in 1882 
ntments. After that 
¡lmas term, the other 
3ws that he chose his 
subjects by preference from analytical geometry, dynamics (in his view, theoretical 
dynamics is a portion of pure mathematics), differential equations, theory of equations,. 
Abelian functions, elliptic functions, and modern algebra. The titles of the lectures, 
as announced, were sometimes vague, nor were they intended to limit his range; in 
all cases he went far beyond the boundary that so frequently limits Cambridge studies. 
Thus a course of lectures on differential equations, announced for the Michaelmas term 
in 1879, was chiefly concerned with conformal representation, polyhedral functions, and 
Schwarz’s investigations on the hypergeometric series. 
For many years he dispensed with the use of blackboard and chalk in his class 
room ; this was possible because his class usually was small. He brought his work 
written out upon the blue draft-paper,* which was regularly used by him in all his 
writing of mathematics; the exposition consisted partly of verbal explanations made 
as he showed the manuscript, partly of details written out at the moment. A change 
came in 1881, when his class amounted to fifteen or sixteen: he was then obliged 
to use the blackboard, and he subsequently maintained the new practice. Occasionally 
his older habit of explaining his manuscript recurred—he then placed it uj)on the 
board. This was especially the case when he brought carefully prepared diagrams, 
such as those used in the modular-function division of the plane: these diagrams 
were made much clearer by the use of water-colours to distinguish different sets of 
regions, and their preparation evidently gave him pleasure. 
But, as may be surmised, his influence as a teacher was overshadowed by his 
influence as an investigator. Those whom he affected by his lectures belonged for the 
most part to the mathematical teachers in Cambridge: the number of undergraduates 
whom he influenced was small, though, when any one of them did come under his 
influence, the effect was well marked. His starting point in any subject was usually 
beyond the range of all other than quite advanced students; but to any able under 
graduate who was willing to devote time, not merely to the comprehension of the 
matter in the lectures but also to collateral reading, the lectures were stimulating and 
inspiring. This effect was partly due to the easy strength with which he worked, 
partly to the spirit in which he approached old and new subjects alike; an independent 
suggestiveness and a singular freshness marked his views, and gave an added interest 
to his exposition even of a well-known theory. One reason of this freshness may be 
found in the fact that his lectures consisted of the current researches upon which he 
was engaged at the time; sometimes, even, a lecture would be devoted to results 
which he had obtained since the preceding lecture. Though the titles of the courses 
occasionally recur from one year to another, the same course was never given twice. 
The new matter in any course, once given, was usually incorporated in a paper or 
memoir; and when the same subject was nominally lectured upon again, it was a 
distinct part of the subject—old notes were never used a second time. 
It was not alone by his lectures that he acted as professor. Students, seeking 
help or desiring to interest him in their work, found him always willing to give them 
the benefit of his advice, his criticism, and his knowledge. Nor was it merely mathe 
maticians in Cambridge whom he helped in this way. He was continually consulted by 
* It was the customary “ scribbling paper ” of his undergraduate days. 
c 2