Quotes & Sayings About Differential Equations

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school - roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply. — Carl Sagan

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future). — Benoit Mandelbrot

If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success. — Max Born

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations. — Felix Klein

I thought of computers as very low class. I thought of myself as a pure mathematician and was interested in partial differential equations and topology and things like that. — Whitfield Diffie

We have the only cookbook in the world that has partial differential equations in it. — Nathan Myhrvold

Knowing what is big and what is small is more important than being able to solve partial differential equations. — Stanislaw Ulam

What is the origin of the urge, the fascincation that drives physicists, mathematicians, and presumably other scientists as well? Psychoanalysis suggests that it is sexual curiosity. You start by asking where little babies come from, one thing leads to another, and you find yourself preparing nitroglycerine or solving differential equations. This explanation is somewhat irritating, and therefore probably basically correct. — David Ruelle

The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way. — Henri Poincare

A major triumph of mathematical imagination: the use of visual imagery to condense a large quantity of information into a single comprehensible picture ... Mathematicians are just beginning to understand these basic building blocks of change and to analyze how they combine. The methodology involved has a very different spirit from traditional modeling with differential equations: it is more like chemistry than calculus, requiring careful counterpoint between analysis and synthesis. — Ian Stewart

I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that. — Francis Collins

Among all of the mathematical disciplines the theory of differential equations is the most important ... It furnishes the explanation of all those elementary manifestations of nature which involve time. — Sophus Lie

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics. — John Von Neumann

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon ... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms. — Joseph Fourier

Differential equations won't help you much in the design of aeroplanes - not yet, anyhow. — Nevil Shute

An essential pedagogic step here is to relegate the teaching of mathematical methods in economics to mathematics departments. Any mathematical training in economics, if it occurs at all, should come after students have at the very least completed course work in basic calculus, algebra and differential equations (the last being one about which most economists are woefully ignorant). This simultaneously explains why neoclassical economists obsess too much about proofs and why non-neoclassical economists, like those in the Circuit School, experience such difficulties in translating excellent verbal ideas about credit creation into coherent dynamic models of a monetary production economy. — Steve Keen

Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential equations which govern the flight of the ball. They just catch it. — Paul Ormerod

"Do you know," the Devil confided, "not even the best mathematicians on other planets - all far ahead of yours - have solved it? Why, there is a chap on Saturn - he looks something like a mushroom on stilts - who solves partial differential equations mentally; and even he's given up." — Arthur Porges

Man's destiny is to know, if only because societies with knowledge culturally dominate societies that lack it. Luddites and anti-intellectuals do not master the differential equations of thermodynamics or the biochemical cures of illness. They stay in thatched huts and die young. — E. O. Wilson

The difficulty involved in the proper and adequate means of describing changes in continuous deformable bodies is the method of differential equations ... They express mathematically the physical concept of contiguous action.
Einstein's Theory of Relativity — Max Born

Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing. — Vladimir Arnold

The ultimate goal of a meteorologist is to set up differential equations of the movements of the air and to obtain, as their integral, the general atmospheric circulation, and as particular integrals the cyclones, anticyclones, tornados, and thunderstorms. — Andrija Maurovic

Consider paint a film of light reflecting/absorbing material, and a colored paint a material which gives a particular, characteristic transmission of light via differential absorption and reflection. Call this reflected quality 'luminance' and measure it in millilamberts. This measure is as real and present as height, breadth, depth; and I find the phenomenon equally sumptuous and convincing ... Painted light, not color, not form, not perspective, or line, not image, or words, or equations, is painting. I make paintings which do not represent light, they are light. — Jo Baer

Now, I like to think that I'm of reasonable intelligence, but ordinary differential equations and myself...we don't really hang in the same comprehension circles. So, try as I might to follow my teacher's logic in how he got 3f"(x) + 5xf(x) to equal eleven, I never quite understood. His answer in no way, shape, or form resembled mine, and this misalignment -this complete confusion of how point A got to point B- is kind of where I'm at right now. "Dreaming?" I repeat dubiously. — E.J. Mellow

2:40AM - 2:41AM (erotic_performance.exe): The curtain opened to reveal a Gateway 2000 computer and monitor running a Fenestra 98 operating system. The display booted up and opened a program on its desktop. The computer then began to rapidly recite a multitude of differential equations as well as their respective 3D graphical representations for 20 seconds. At the end of the program, the monitor displayed the word "INSERT" in the form of a screensaver. D-6744 and D-3432 both inserted $5 into its floppy drive. The curtain then closed at the end of the show. — Anonymous

The arts and humanities are not mere entertainment, to be turned to for relaxation after a busy day spent solving differential equations; they are our templates for living, for governing ourselves and our societies. Nor can science offer any help with the knottier problems besetting the human race. It can remedy bad smells, bad pains, and bad roads, but not bad behavior, bad government, or bad ideas. — John Derbyshire

While researching this answer, I managed to lock up my copy of Mathematica several times on balloon-related differential equations, and subsequently got my IP address banned from Wolfram|Alpha for making too many requests. The ban-appeal form asked me to explain what task I was performing that necessitated so many queries. I wrote, "Calculating how many rental helium tanks you'd have to carry with you in order to inflate a balloon large enough to act as a parachute and slow your fall from a jet aircraft." Sorry, Wolfram. — Randall Munroe