things that attracted and fascinated him were of two kinds, which may be called opposite to each other. On the one hand, he revelled in any new and prolific method; the feeling of creation, of abounding productiveness, was to him as the breath of his nostrils. It was largely this that made the Theory of Invariants so congenial to him. To see a whole new world, full of unexpected and harmonious relations, expanding before him, was to fill him with an absorbing and exuberant enthusiasm. In the case of invariants, it may be said that his joy in this sense of creation was not even confined to the discovery of theorems; the algebraic forms themselves were to him as living beings, and the processes, invented largely by himself, for causing these creatures of the mathematical intellect to generate their kind, were to him a source of genuine delight.

Alongside of this love of prolific creation, another intellectual bent, on the surface at least of quite the opposite character, was equally strongly marked in Sylvester. Any crucial problem, especially one that was associated with the name of one of the great masters, if once it attracted Sylvester's attention, fastened itself upon his mind with a grip that seemed never to slacken its tenacity. It kept coming up again and again for years, and as long as it remained unsolved seemed to become periodically a source of unrest and discomfort to his mind. He had not the serenity which belonged to many other great mathematicians, and notably to Cayley, and which in a great measure permitted them to choose among the possible subjects of thought such as they deemed most profitable to pursue. With Sylvester

such tranquil and deliberate choice was entirely out of the question. His temperament was essentially poetic, and it would have been as impossible for him to concentrate the powers of his mind on one subject when the current of his thought was setting toward another, as it would have been for Burns to decide in cold blood to write a poem like Highland Mary or The Daisy when the inspiration of Tam O'Shanter was upon him.

It was the mention of Sylvester's demonstration of Newton's rule that suggested these reflections. We who knew him well in later years can find no difficulty in understanding the hold this problem had upon him. It was the good fortune of his early hearers in this University to be present when he came into the lecture-room flushed with the achievement of a somewhat similar task. A certain fundamental theorem in the Theory of Invariants which had formed the basis of an important section of Cayley's work had never been completely demonstrated. The lack of this demonstration had always been to Sylvester's mind a most serious blemish in the structure. He had however, he told us, years ago given up the attempt to find the proof as hopeless. But upon coming fresh to the subject in connection with his Baltimore lectures, he again. grappled with the problem and by a fortunate inspiration succeeding in solving it. It was with a thrill of sympathetic pleasure that his young hearers thus found themselves in some measure associated with an intellectual feat by which had been overcome a difficulty that had successfully resisted assault for a quarter of a century. Nor was this the only

instance in which we had an opportunity of observing the tenacious hold upon his intellect of any problem that had come to assume in his mind the aspect of a challenge to the powers of mathematicians.

I have said that Sylvester's powers were set in motion by two opposite kinds of stimulus; that of abundantly rewarding results, and that of the stubborn resistance of concentrated difficulty. In both these kinds of endeavor he achieved many and signal triumphs. That intermediate kind of effort which slowly and patiently builds up and improves and perfects one's own work, and which gives minute. and prolonged study to the work of others, he did not command in any notable degree. He seemed incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it could not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the Theory of Functions and in allied disciplines he never became acquainted with. No one who witnessed the flaming up of his energies. when at the age of 62 in Baltimore he felt himself for the first time among a band of enthusiastic young workers pursuing pure mathematics for its own sake can doubt what the effect would have been if in the prime of his powers he had been surrounded by the influences which prevail in Berlin or in Göttingen. It may be confidently taken for granted that he would have done splendid work in those domains

of analysis which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.

Cambridge, his natural intellectual home, would have been far less helpful, since it was examinations and not research that gave tone to the mathematical life there. But Cambridge would of course have been immeasurably better than the situations. in which he actually found himself for forty years after his winning of the Second Wranglership. From a career at Cambridge, to the great loss of that University, of himself, and of mathematics, he was debarred by the religious tests then obtaining in the old English Universities. Professor Halsted in his account of Sylvester's work already referred to points out how the vicissitudes of his career were reflected in the richness or the meagreness of his mathematical production from period to period.

The life and work of Sylvester illustrate in a striking way the futility of the dispute as to the relative importance of native qualities and of external circumstances in determining the achievements of great men. If any man was ever an original genius, with consuming ardor for one intellectual pursuit, with love and devotion to it burning in youth and undiminished in age, Sylvester was such a man. If any province of thought is open to every worker in it, to work in as he pleases, uninfluenced by the doings of those who happen to be in his neighborhood, in his university, in his country, one would say that mathematics is that province. Yet no one could know Sylvester without feeling that, great and original as was his genius, environ

ment must in his case exercise an extraordinary influence on its activity. He was sensitive, passionate, fiery; the glowing language in which he habitually indulged in the midst of his mathematical memoirs was but a reflection of his ardent and excitable temper. Such a man must needs be keenly subject to depression and exaltation, to fits of apathy and ardor, according to the nature of his surroundings and experiences. Those who knew him cannot fail to be convinced that eminent as were his actual achievements they do not afford a true measure of his mathematical powers, in comparison with those of his great contemporaries. For he was at once less advantageously circumstanced then they, and in an exceptional degree subject to the influence of his surroundings.

Of his work as a teacher I can speak only upon the basis of his activity in this University. The one thing which constantly marked his lectures was enthusiastic love of the thing he was doing. He had in the fullest possible degree, to use the French phrase, the defect of this quality; for as he almost always spoke with enthusiastic ardor, so it was almost never possible for him to speak on matters incapable of evoking this ardor. In other words, the substance of his lectures had to consist largely of his own work, and, as a rule, of work hot from the forge. The consequence was that a continuous and systematic presentation of any extensive body of doctrine already completed was not to be expected from him. Any unsolved difficulty, any suggested extension, such as would have been passed by with a mention by other lecturers, became with him