Essay on the Powers of the Human Mind (Edinburgh, 1812), Vol. 2, p. 368.
[956]. It is the invaluable merit of the great Basle mathematician Leonhard Euler, to have freed the analytical calculus from all geometrical bonds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.—Hankel, H.
Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 12.
[957]. We may safely say, that the whole form of modern mathematical thinking was created by Euler. It is only with the greatest difficulty that one is able to follow the writings of any author immediately preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first one to teach.—Rudio, F.
Quoted by Ahrens W.: Scherz und Ernst in der Mathematik (Leipzig, 1904), p. 251.
[958]. The general knowledge of our author [Leonhard Euler] was more extensive than could well be expected, in one who had pursued, with such unremitting ardor, mathematics and astronomy as his favorite studies. He had made a very considerable progress in medical, botanical, and chemical science. What was still more extraordinary, he was an excellent scholar, and possessed in a high degree what is generally called erudition. He had attentively read the most eminent writers of ancient Rome; the civil and literary history of all ages and all nations was familiar to him; and foreigners, who were only acquainted with his works, were astonished to find in the conversation of a man, whose long life seemed solely occupied in mathematical and physical researches and discoveries, such an extensive acquaintance with the most interesting branches of literature. In this respect, no doubt, he was much indebted to an uncommon memory, which seemed to retain every idea that was conveyed to it, either from reading or from meditation.—Hutton, Charles.
Philosophical and Mathematical Dictionary (London, 1815), pp. 493-494.
[959]. Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid[6] gave him the first idea.—Brewster, David.
Letters of Euler (New York, 1872), Vol. 1, p. 24.