Top 265 Differential Equations Quotes & Sayings

Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.

...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.

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

But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.

When, in school, they were teaching algebra, I was studying differential equations at home.

Everything, however complicated - breaking waves, migrating birds, and tropical forests - is made of atoms and obeys the equations of quantum physics. But even if those equations could be solved, they wouldn't offer the enlightenment that scientists seek. Each science has its own autonomous concepts and laws.

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.

Even in relativity theory even though you can analyze space - time in terms of this four-dimensional geometrical structure one of the dimensions is different. And this shows up in the equations. It has a different sign - rather than plus it shows up as a negative minus. So even in relativity theory time is distinct from space in terms of the way in which these dimensions manifest themselves in the equations.

In order to solve this differential equation you look at it until a solution occurs to you.

The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.

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).

In my free time I do differential and integral calculus.

I do believe that everyone growing up faces differential opportunities. With me, it was books and travel and some good teachers.

Basically, we try to buy value expressed in the differential between its price and what we think its worth.

Profits are not made by differential cleverness, but by differential stupidity.

Science is a differential equation. Religion is a boundary condition.

Tom and I didn't have a problem with the height differential but Paramount did, so we tried to hide it.

Do not be afraid to skip equations (I do this frequently myself).

The standard high school curriculum traditionally has been focused towards physics and engineering. So calculus, differential equations, and linear algebra have always been the most emphasized, and for good reason - these are very important.

Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. LIke a work of art or a haunting poem, equations have a beauty and rhythm all their own.

If you don't read poetry how the hell can you solve equations?

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.

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.

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

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

Yes, we now have to divide up our time like that, between politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.

"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."

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.

Global equations undergo changes, this is their nature.

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.

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?

All life evolves by the differential survival of replicating entities.

But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony.

If you look at Einstein's equations and put in low speeds and low gravity, they become Newton's equations.

As Darwin himself was at pains to point out, natural selection is all about differential survival within species, not between them.

I've not been in a live-in relationship. But I've been exposed to various kinds of equations that can exist between people. When I came from Bangalore, it was black and white. Over the years, I've realised that there's more to what we see on a day-to-day basis. There are all kinds of relationships, all kinds of equations.

What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations.

Love can reach the same level of talent, and even genius, as the discovery of differential calculus.

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

Natural selection is all about the differential success of rival DNA in getting itself transmitted vertically in the species archives.

Words are a pretty fuzzy substitute for mathematical equations.

To actually play a game, where you are in the World Cup, there is significance to it, the point differential matters, all these things kind of add up.

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

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

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.

Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.

Who ... is not familiar with Maxwell's memoirs on his dynamical theory of gases? ... from one side enter the equations of state; from the other side, the equations of motion in a central field. Ever higher soars the chaos of formulae. Suddenly we hear, as from kettle drums, the four beats 'put n=5.' The evil spirit v vanishes; and ... that which had seemed insuperable has been overcome as if by a stroke of magic ... One result after another follows in quick succession till at last ... we arrive at the conditions for thermal equilibrium together with expressions for the transport coefficients.

Newton, of course, was the inventor of differential calculus so his place in the tale is quite special.

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.

The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity... the rigid electron is no working hypothesis, but a working hindrance. Approaching Maxwell's equations with the concept of the rigid electron seems to me the same thing as going to a concert with your ears stopped up with cotton wool. We must admire the courage and the power of the school of the rigid electron which leaps across the widest mathematical hurdles with fabulous hypotheses, with the hope to land safely over there on experimental-physical ground.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

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.

I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.

God is not described in equations.

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

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.

Equations are the devil's sentences.

If there are four equations and only three variables, and no one of the equations is derivable from the others by algebraic manipulation then there is another variable missing.

I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.