A Quote by Richard Courant
With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.
Related Quotes
With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method
You'll remember Newton was furious at Leibniz, because he developed calculus at the same time. And he went to his death believing that he had copied him. And no, it's because all the elements were there, so it's almost inevitable that the next discovery - as long as people are free and allowed to experiment and try new things.
I was trying to run something to ground that had come to my attention when I was working on the Baroque Cycle. That series, of course, was about the conflict between Newton and Leibniz. Leibniz developed a system of metaphysics called monadology, which looked pretty weird at the time and was promptly buried by Newtonian-style physics.
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.
Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Newton, of course, was the inventor of differential calculus so his place in the tale is quite special.
[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?
Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
Ultimately, Leibniz argued, there are only two absolutely simple concepts, God and Nothingness. From these, all other concepts may be constructed, the world, and everything within it, arising from some primordial argument between the deity and nothing whatsoever. And then, by some inscrutable incandescent insight, Leibniz came to see that what is crucial in what he had written is the alternation between God and Nothingness. And for this, the numbers 0 and 1 suffice.
Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
There are certainly lots of jobs in computer coding, but coding doesn't really require advanced mathematics. And engineering jobs, they vary widely in the amount of demand that we actually need. So, you know, the number of people for whom the job description includes Newton's calculus is not perhaps that high.
Virtue is the habit of acting according to wisdom. GOTTFRIED WILHELM LEIBNIZ, "Felicity", Leibniz: Political Writings Virtue is harder to be got than knowledge of the world; and, if lost in a young man, is seldom recovered. JOHN LOCKE, Some Thoughts Concerning Education However wicked men may be, they do not dare openly to appear the enemies of virtue, and when they desire to persecute her they either pretend to believe her false or attribute crimes to her.
When I was about thirteen, the library was going to get 'Calculus for the Practical Man.' By this time I knew, from reading the encyclopedia, that calculus was an important and interesting subject, and I ought to learn it.
Related Authors
Ada Lovelace Quotes
English
Mathematician
Alfred North Whitehead Quotes
English
Mathematician
Benoit Mandelbrot Quotes
French
Mathematician
Carl Friedrich Gauss Quotes
German
Mathematician
Charles Babbage Quotes
English
Mathematician
David Hilbert Quotes
German
Mathematician
G. H. Hardy Quotes
British
Mathematician
George Polya Quotes
Hungarian
Mathematician
Hannah Fry Quotes
English
Mathematician
Henri Poincare Quotes
French
Mathematician
Isaac Barrow Quotes
English
Mathematician
Isaac Newton Quotes
English
Mathematician
Norbert Wiener Quotes
American
Mathematician
Pythagoras Quotes
Greek
Mathematician
Rene Descartes Quotes
French
Mathematician
Seymour Papert Quotes
American
Mathematician