[9]. Il cessa de calculer et de vivre.—Condorcet.
Of the scientific character of Euler it is impossible to speak in detail, since even the resumé of M. Condorcet, which is much longer than any account we can here insert, is meagre in the extreme; and we imagine that the reader would form no idea whatsoever of the man we are describing, from any brief enumeration of discoveries for which we should be able to allow room. In more than fifty years of incessant thought, Euler wrote thirty separate works and more than seven hundred memoirs: which could not altogether be contained in forty large quarto volumes. These writings embrace every existing branch of mathematics, and almost every conceivable application of them, to such an extent, that there is no one among mathematicians, past or present, who can be placed near to Euler in the enormous variety of the subjects which he treated. And the contents of these volumes are without exception the original fruit of his own brain; seeing that he left no subject as he found it. He is not a diffuse writer, except in giving a large number of examples, and this renders him in some respects the most instructive of all writers. His works are full of the most original thoughts developed in the most original manner; so that they have been a mine of information for his successors, which is even now far from being exhausted. Let a student be employed upon any subject connected with mathematics, however remotely, and he has discovered but little if he has not found out that Euler was there before him.
Of all mathematical writers, Euler is one of the most simple, and this in a manner which renders his writings not by any means a sound preparation for future investigations. Difficulties seem to have disappeared in the progress, or never to have been encountered; and the student is rather made to feel that Euler could take him anywhere, than furnished with the means of providing for himself, when his guide shall have left him. Hence the writings of others, in every way inferior to Euler in elegance and simplicity, are to be preferred, and have been preferred, for the formation of mathematical power.
Euler is to be measured by the assistance which he gave to his immediate successors, and here it is well known that he paved the way for the research of others in a more effectual manner than any of his contemporaries. The incessant repetition of his name in later authors is sufficient authority for this assertion. His writings are the first in which the modern analysis is uniformly the instrument of investigation. His predecessors, James and John Bernouilli, had perhaps the largest share in bringing the infinitesimal analysis of Newton and Leibnitz to the state of power required for extensive application. To Euler (besides important extensions) belongs the distinct merit of showing how to apply it to physical investigations, in conjunction with D’Alembert, who ran a splendid and contemporary career of a similar character in this respect. But though it would be perhaps admitted that there are individual results of the latter which exceed anything done by the former, in generality of application, there is no comparison whatsoever between the extent of the labours of the two.
Euler was a man of a simple, reserved, and benevolent mind; with a strong sense of devotion, and a decided religious habit, according to the Calvinism of the Established Church of his country. At the court of Frederic, he himself conducted the devotions of his family every evening; a practice which then and there implied much moral courage, and insensibility to ridicule. But he possessed humour, for when he was asked to calculate the horoscope of one of the Russian princes, he quietly suggested that it was the official duty of the astronomer, and imposed the duty upon a colleague, who doubtless did not feel very much flattered by the application.
There are few men whom the usual biographical formulæ as to moral character and habits would better fit than Euler, according to every account which has appeared of him. But such praises are no distinction; and it will be more to the purpose to state that the only occasion in which he was betrayed into printing a word which his eulogists have regretted, was in the dispute between Maupertuis and himself against others on the principle known by the name of least action, one of the warmest and most angry discussions which ever took place.
Perhaps it is to the quiet abstraction of his life that he owed the perpetuity of his tenure of investigation. Many eminent mathematical discoverers have run the brilliant part of their career while comparatively young. Euler “ceased to calculate and to live” at once. But it may be that this was a part of his natural constitution, and a distinct feature of his mind. The nature of his writings rather confirms the latter supposition. There is the same difference between them and those of others, that there is between conversation and oratory. He seems to be moving in his natural element, where others are swimming for their lives.
The best works of Euler for a young mathematician to read, in order to get an idea of his style and methods, are the ‘Analysis Infinitorum,’ and the ‘Treatise on the Integral Calculus.’
