Geometer Quotes
You well know ... for which reason I began searching for a number of demonstrations proving a statement due to the ancient Greeks ... and which passion I felt for the subject ... so that you reproached me my preoccupation with these chapters of geometry, not knowing the true essence of these subjects, which consists precisely in going in each matter beyond what is necessary. ... Whatever way he [the geometer] may go, through exercise will he be lifted from the physical to the divine teachings, which are little accessible because of the difficulty to understand their meaning ... and because the circumstance that not everybody is able to have a conception of them, especially not the one who turns away from the art of demonstration.
Al-Biruni
J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid "deeper than e'er plummet sounded" out of the schoolboy's reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson's Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson's additions and keeping strictly to the original treatise.
Florian Cajori
On the 15th of April 1744, I described the principle upon which the following work is based, in the public assembly of the Royal Academy of Sciences of Paris, as reported in the Acts of that academy.
At the end of the same year, Professor Euler published his excellent book Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. In a supplement to his book, this illustrious geometer showed that, in the trajectory of a particle acted on by a central force, the velocity multiplied by the line element of the trajectory is minimized.
This observation gave me great pleasure, as a beautiful application of my principle to the motion of the planets, which is determined by this principle.
From the same principle, I will now try to derive higher and more important truths.
Pierre Louis Maupertuis
It has been said that to appreciate what virtue and morals mean, men must live virtuous and moral lives. It is equally true, that a knowledge of the objects of science is not to be attained by any scheme of definitions, however carefully contrived. He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer.
James Joseph Sylvester
The Key! it is of wonderful construction, with its infinity of combination, and its unlimited capacity to fit every lock. ... it is the great master-key which unlocks every door of knowledge and without which no discovery which deserves the name - which is law, and not isolated fact - has been or ever can be made. Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications; he may have exalted it into his idol and worshipped it; he may have degraded it into his toy . . . when he should have been hard at work with it, using it for the benefit of mankind and the glory of his Creator.
Benjamin Peirce
I will add that I have recently received from Hungary a little paper on non-Euclidean geometry in which I rediscover all my own ideas and results worked out with great elegance... The writer is a very young Austrian officer, the son of one of my early friends, with whom I often discussed the subject in 1798, although my ideas were at that time far removed from the development and maturity which they have received through the original reflections of this young man. I consider the young geometer J. Bolyai a genius of the first rank.
Carl Friedrich Gauss
Because certain elements of geometry have for a long time been included in the general course of education, every educated man is able to distinguish between the practical task of the land surveyor and the theoretical investigation of the geometer. The corresponding distinction between the theory of probability and statistics has yet to be recognized.
Richard von Mises
Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. Santaló, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety.
Shiing-Shen Chern
![The geometrical spirit is not so tied to geometry that it cannot be detached from it and transported to other branches of knowledge. A work of morals or politics or criticism, perhaps even of eloquence, would be better (other things being equal) if it were done in the style of a geometer. The order, clarity, precision and exactitude which have been apparent in good books for some time might well have their source in this geometric spirit. ...Sometimes one great man gives the tone to a whole century; [Descartes], to whom one might legitimately be accorded the glory of having established a new art of reasoning, was an excellent geometer. (Bernard Le Bovier de Fontenelle)](https://cdn.quotesdtb.com/img/quotes_images_webp/12/bernard-le-bovier-de-fontenelle-519812.webp)
It would be an error... to suppose that science makes the artist; yet it lends to him the most powerful assistance. In general, it is difficult to keep it within due limits; and I shall even freely admit that Albert Durer, in his work upon the proportions of the human frame, has imparted to it a certain scientific dryness, which lessens its utility. One finds there more of the geometer than the artist, and the geometer, moreover, such as he was at a time when it had not yet been discovered how much the rules of style enhance the value of scientific works, and, above all, of those which appertain at the same time to the domain of the fine arts.
Adolphe Quetelet