A Quote by John Stuart Mill
The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
Quote Topics
Quote Author
Related Quotes
As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
The greatest progress is in the sciences that study the simplest systems. So take, say, physics - greatest progress there. But one of the reasons is that the physicists have an advantage that no other branch of sciences has. If something gets too complicated, they hand it to someone else.
Algebra is but written geometry and geometry is but figured algebra.
The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions.
There is no need to express art in terms of nature. It can perfectly well be expressed in terms of geometry and the exact sciences.
Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
Algebra is nothing more than geometry, in words;
geometry is nothing more than algebra, in pictures.
Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?
Progress-progress is the dirtiest word in the language-who ever told us- And made us believe it-that to take a step forward was necessarily, was always A good idea?
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
Mass application of technological innovations, which constitutes much of the distinctive substance of modern economic growth, is closely connected with the further progress of science, in its turn the basis for additional advance in technology.
Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.
Laws are important and valuable in the exact natural sciences, in the measure that those sciences are universally valid.
The greatest progress we have made, and the greatest progress we have yet to make, is in the human heart. In the end, all the world's wealth and a thousand armies are no match for the strength and decency of the human spirit.
Related Authors
Alan Watts Quotes
English
Philosopher
Albert Camus Quotes
French
Philosopher
Aristotle Quotes
Greek
Philosopher
Arthur Schopenhauer Quotes
German
Philosopher
Blaise Pascal Quotes
French
Philosopher
Confucius Quotes
Chinese
Philosopher
Francis Bacon Quotes
English
Philosopher
Friedrich Nietzsche Quotes
German
Philosopher
Jiddu Krishnamurti Quotes
Indian
Philosopher
Laozi Quotes
Chinese
Philosopher
Michel de Montaigne Quotes
French
Philosopher
Plato Quotes
Greek
Philosopher
Ralph Waldo Emerson Quotes
American
Philosopher
Seneca the Younger Quotes
Roman
Philosopher
Thomas Carlyle Quotes
Scottish
Philosopher
William James Quotes
American
Philosopher