Quotes & Sayings About Applied Mathematics

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics. — G.H. Hardy

The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. — Henry David Thoreau

I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto. — Walter Kohn

My decision to leave applied mathematics for economics was in part tied to the widely-held popular belief in the 1960s that macroeconomics had made fundamental inroads into controlling business cycles and stopping dysfunctional unemployment and inflation. — Robert C. Merton

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers. — G.H. Hardy

There are those who believe that mathematics can sustain itself and grow without any further contact with anything outside itself, and those who believe that nature is still and always will be one of the main (if not the main) sources of mathematical inspiration. The first group is identified as "pure mathematicians" (though "purist" would be more adequate) while the second is, with equal inadequacy, referred to as "applied". — Mark Kac

It was all so very businesslike that one watched it fascinated. It was pork-making by machinery, pork-making by applied mathematics. And yet somehow the most matter-of-fact person could not help thinking of the hogs; they were so innocent, they came so very trustingly; and they were so very human in their protests - and so perfectly within their rights! They had done nothing to deserve it; and it was adding insult to injury, as the thing was done here, swinging them up in this cold-blooded, impersonal way, without pretence at apology, without the homage of a tear. — Upton Sinclair

You are from alone in the community of scientists, and here is a professional secret to encourage you: many of the most successful scientists in the world today are mathematically no more than semiliterate. A metaphor will clarify the paradox in this statement. Where elite mathematicians often serve as architects of theory in the expanding realm of science, the remaining large majority of basic and applied scientists map the terrain, scout the frontier, cut the pathways, and raise the first buildings along the way. They define the problems that mathematicians, on occasion, may help solve. They think primarily in images and facts, and only marginally in mathematics. — Edward O. Wilson

Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians. — Edsger Dijkstra

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. — G.H. Hardy

To be an engineer, and build a marvelous machine, and to see the beauty of its operation is as valid an experience of beauty as a mathematician's absorption in a wondrous theorem. One is not "more" beautiful than the other. To see a space shuttle standing on the launch pad, the vented gases escaping, and witness the thunderous blast-off as it climbs heavenward on a pillar of flame - this is beauty. Yet it is a prime example of applied mathematics. — Calvin C. Clawson

As an undergraduate at Columbia, I went to the engineering school. I had a great deal of training in engineering and mathematics as well as subdiversified training. And then I went to the California Institute of Technology to do my Ph.D. in applied math. — Robert C. Merton

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes. — Alfred Tarski

Pure concepts of the understanding. So the Humean problem is completely solved, though in a way that would have surprised its inventor. The solution secures an a priori origin for the pure concepts of the understanding, and for the universal laws of nature it secures a status as valid laws of the understanding; but it does this in such a way as to limit the use of these concepts to experience only, and it grounds them in a relation between the understanding and experience that is the complete reverse of anything that Hume envisaged - instead of the concepts being derived from experience, that experience is derived from them. My line of argument yields the following result: All synthetic a priori principles are simply principles of possible experience; they can never be applied to things in themselves, but only to appearances as objects of experience. Hence pure mathematics as well as pure natural science can never bear on anything except appearances — Anonymous

It is in the world of things and places, times and troubles and turbid
processes, that mathematics is not so much applied as illustrated. — David Berlinski

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications. — James R Newman

There is one thing only which a Muslim can profitably learn from the west, the exact sciences in their pure and applied form. Only natural sciences and mathematics should be taught in Muslim schools, while tuition of European philosophy, literature and history should lose the position of primacy which today it holds on the curriculum. — Muhammad Asad

Before creation, God did just pure mathematics. Then He thought it would be a pleasant change to do some applied. — John Edensor Littlewood

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics. — Balfour Stewart

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer ... — Oliver Heaviside

Although in principle we know the equations that govern the whole of biology, we have not been able to reduce the study of human behavior to a branch of applied mathematics. — Stephen Hawking

You will perceive that economy, scientifically speaking, is a very contracted science; it is in fact a sort of vague mathematics which calculates the causes and effects of man's industry, and shows how it may be best applied. — William Stanley Jevons

Physicists traced the failure to the jitters of quantum uncertainty. Mathematical techniques had been developed for analyzing the jitters of the strong, weak, and electromagnetic fields, but when the same methods were applied to the gravitational field-a field that governs the curvature of spacetime itself-they proved ineffective. This left the mathematics saturated with inconsistencies such as infinite probabilities. — Brian Greene

Applied mathematics will always need pure mathematics just as anteaters will always need ants. — Paul Halmos

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover. — Edward Frenkel

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. — Clifford A. Pickover

Game theory is a branch of, originally, applied mathematics, used mostly in economics and political science, a little bit in biology, that gives us a mathematical taxonomy of social life, and it predicts what people are likely to do and believe others will do in cases where everyone's actions affect everyone else. — Colin Camerer

He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical. — Henry David Thoreau

Winfree came from a family in which no one had gone to college. He got started, he would say, by not having proper education. His father, rising from the bottom of the life insurance business to the level of vice president, moved family almost yearly up and down the East Coast, and Winfree attended than a dozen schools before finishing high school. He developed a feeling that the interesting things in the world had to do with biology and mathematics and a companion feeling that no standard combination of the two subjects did justice to what was interesting. So he decided not to take a standard approach. He took a five-year course in engineering physics at Cornell University, learning applied mathematics and a full range of hands-on laboratory styles. Prepared to be hired into military-industrial complex, he got a doctorate in biology, striving to combine experiment with theory in new ways. — James Gleick

meantime, here is a list of degrees for five of the nerdiest writers: J. STEWART BURNS BS Mathematics, Harvard University MS Mathematics, UC Berkeley DAVID S. COHEN BS Physics, Harvard University MS Computer Science, UC Berkeley AL JEAN BS Mathematics, Harvard University KEN KEELER BS Applied Mathematics, Harvard University PhD Applied Mathematics, Harvard University JEFF WESTBROOK BS Physics, Harvard University PhD Computer Science, Princeton University — Simon Singh

Very few people can communicate with one another. The only language that's not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture. But other than that, many systems today are subject to interpretation. — Jacque Fresco

A famous Japanese Zen master, Hakuun Yasutani Roshi, said that unless you can explain Zen in words that a fisherman will comprehend, you don't know what you're talking about. Some fifty years ago a UCLA professor told me the same thing about applied mathematics. We like to hide from the truth behind foreign-sounding words or mathematical lingo. There's a saying: The truth is always encountered but rarely perceived. If we don't perceive it, we can't help ourselves and we can't much help anyone else. — Jeff Bridges

Newton was asked as a mathematician, not as a moralist. He replied 'Gentlemen, in applied mathematics, you must describe your unit. — Isabel Paterson

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. — Nikolai Lobachevsky

Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success. — Marcus Tullius Cicero