Top 204 Equations Quotes & Sayings - Page 3

My algebra was relatively poor. I found it very difficult to use equations that substituted numbers - to which I had a synesthetic and emotional response - for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.

What counts, I found, is not what you cover, but what you uncover. Covering subjects in a class can be a boring exercise, and students feel it. Uncovering the laws of physics and making them see through the equations, on the other hand, demonstrates the process of discovery, with all its newness and excitement, and students love being part of it.

"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."

A robber who justified his theft by saying that he really helped his victims, by his spending giving a boost to retail trade, would find few converts; but when this theory is clothed in Keynesian equations and impressive references to the 'multiplier effect,' it unfortunately carries more conviction.

Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.

I think you can fan the flames, but I think in the same way that a mathematician is a mathematician - He's not taught to be a mathematician. He either has a feeling for equations and an understanding and delight in it, not only in the purity of it, but in its beauty as well.

A common misconception about how things such as space shuttles come to be is that engineers simply apply the theories and equations of science. But this cannot be done until the new thing-to-be is conceived in the engineer's mind's eye. Rather than following from science, engineered things lead it.

Because for me, equations and symbols aren't just a thing. They're a voice that speaks out about the incredible richness of nature and the startling simplicity in the patterns that twist and turn and warp and evolve all around us, from how the world works to how we behave.

It was basic research in the photoelectric field-in the photoelectric effect that would one day lead to solar panels. It was basic research in physics that would eventually produce the CAT scan. The calculations of today's GPS satellites are based on the equations that Einstein put to paper more than a century ago.

The complicated, ambiguous milieu of human contact is being replaced with simple, scalable equations. We maintain thousands more friends than any human being in history, but at the cost of complexity and depth. Every minute spent online is a minute of face-to-face time lost.

Any schemes - such as 'think of symmetry laws', or 'put the information in mathematical form', or 'guess equations'- are known to everybody now, and they are all tried all the time. When you are stuck, the answer cannot be one of these, because you will have tried these right away...The next scheme, the new discovery, is going to be made in a completely different way.

I have made the most important discovery of my career, the most important discovery of my life: It is only in the mysterious equations of love that any logic or reasons can be found.

It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

The truth shall set you free. When you hear the truth, it sets you free. So mathematics is truth. It adds up. There's no error. Only time there's an error is when man miscalculates his own problems or his own equations.

As with Randall Terry and other anti-abortion leaders, women simply did not figure into [Roeder's] equations. If all the abortion providers were dead, the problem would be solved, and he'd never have to think about those who sought to end their pregnancies through illegal or dangerous means.

...the computer models are very good at solving equations of fluid dynamics but very bad at describing the real world. The real world is full of things like clouds and vegetation and soil and dust which the models describe very poorly.

The relativity principle in connection with the basic Maxwellian equations demands that the mass should be a direct measure of the energy contained in a body; light transfers mass. With radium there should be a noticeable diminution of mass. The idea is amusing and enticing; but whether the Almighty is laughing at it and is leading me up the garden path -- that I cannot know.

It required unusual inquisitiveness to pursue the development of scientific curiosities such as charged pith balls, the voltaic cell, and the electrostatic machine. Without such endeavors and the evolution of associated instrumentation, initially of purely scientific interest, most of the investigations that lead to the basic equations of electromagnetism would have been missed. ... We would have been deprived of electromagnetic machinery as well as knowledge of electromagnetic waves.

People think six is a great many, when it's children. ...they don't mind six pairs of boots, or six pounds of apples, or six oranges, especially in equations, but they seem to think that you ought not to have five brothers and sisters.

Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge.

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.

Technologies evolve in the strangest ways. Computers were created to calculate ballistics equations, and now we use them to create amusing illusions. Creating amusing illusions is a big business if you play it right.

In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

Symmetry does mean something different for physicists than for members of the public. It means that an object or a theory does not change when you make some transformation - either rotating or moving it or doing something to the equations.

We seem to forget that innovation doesn't just come from equations or new kinds of chemicals, it comes from a human place. Innovation in the sciences is always linked in some way, either directly or indirectly, to a human experience.

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.

The aim ... is to provide a clear and rigorous basis for determining when a causal ordering can be said to hold between two variables or groups of variables in a model . . . . The concepts refer to a model-a system of equations-and not to the 'real' world the model purports to describe.

The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?

Evidence in support of general relativity came quickly. Astronomers had long known that Mercury’s orbital motion around the sun deviated slightly from what Newton’s mathematics predicted. In 1915, Einstein used his new equations to recalculate Mercury’s trajectory and was able to explain the discrepancy, a realization he later described to his colleague Adrian Fokker as so thrilling that for some hours it gave him heart palpitations.

It's a spectacular signal. It's a signal many of us have wanted to observe since the time LIGO was proposed. It shows the dynamics of objects in the strongest gravitational fields imaginable, a domain where Newton's gravity doesn't work at all, and one needs the fully non-linear Einstein field equations to explain the phenomena.

Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.

The real truth that dare not speak itself, is that no one is in control, absolutely no one... Nobody is in control. This stuff is ruled by the equations of dynamics and chaos. Now, there may be entities seeking control - the World Bank, the Communist Party, the rich, the somebody-or-others - but to seek control is to take enormous aggravation upon yourself... It's like trying to control a dream.

Extra dimensional theories are sometimes considered science fiction with equations. I think that's a wrong attitude. I think extra dimensions are with us, they are with us to stay, and they entered physics a long time ago. They are not going to go away.

To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.

What is it with science these days? Everyone is so quick to believe in it, in all these new scientific discoveries, new pills for this, new pills for that. Get thinner, grow hair, yada, yada, yada, but when it requires a little faith in something you all go crazy.' He shook his head, 'If miracles had chemical equations then everyone would believe.

We can summarize electricity, magnetism and gravity into equations one inch long, and that's the power of field theory. And so I said to myself: I will create a field theory of strings. And when I did it one day, it was incredible, realizing that on a sheet of paper I can write down an equation which summarized almost all physical knowledge.

My mother was the nicest person in the world. I still have people coming to me to say how she was so warm, generous, and kind-hearted. She never washed her dirty linen in public. She always maintained her equations with people.

I have found that when calculating what no one has calculated before, like my observing sessions on the mountain, my mental acuity peaks. Ironically, these are the times that I would flunk the reality check normally reserved for mental patients and dazed boxers: What is your name? What day is it? Who is the president of the United States?... I do not know, and I do not care. I am at peace with my equations as I connect to the cosmic engines that drive our universe.

Concern for man himself and his fate must always form the chief interest of all technical endeavors, concern for the great unsolved problems of the organization of labor and the distribution of goods-in order that the creations of our mind shall be a blessing and not a curse to mankind. Never forget this in the midst of your diagrams and equations.

Mathematicians are proud of the fact that, generally, they do their work with a piece of chalk and a blackboard. They value hand-done proofs above all else. A big question in mathematics today is whether or not computational proofs are legitimate. Some mathematicians won't accept computational proofs and insist that a real proof must be done by the human hand and mind, using equations.

I now want to tell three stories about advances in twentieth-century physics. A curious fact emerges in these tales: time and again physicists have been guided by their sense of beauty not only in developing new theories but even in judging the validity of physical theories once they are developed. Simplicity is part of what I mean by beauty, but it is a simplicity of ideas, not simplicity of a mechanical sort that can be measured by counting equations or symbols.

This is often the way it is in physics - our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort.

There is something so mysterious that it is almost like God. God is in the equations. God is in the fundamental constants. And that's fine. I mean, that's just redefinition of that which we find mysterious at the basis of the universe.

…Our sunsets have been reduced to wavelengths and frequencies. The complexities of the universe have been shredded into mathematical equations. Even our self-worth as human beings has been destroyed.

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.

There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense.

In our travels, we have come across many equations--math for understanding the universe, for making music, for mapping stars, and also for tipping, which is important. Here is our favorite equation: Us plus Them equals All of Us. It is very simple math. Try it sometime. You probably won’t even need a pencil.

'Scientific' computer simulations predict global warming based on increased greenhouse gas emissions over time. However, without water's contribution taken into account they omit the largest greenhouse gas from their equations. How can such egregious calculation errors be so blatantly ignored? This is why man-made global warming is 'junk' science.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

What is quite worrisome is the absence of analysis and reflection. Take the word "terrorism." It has become synonymous now with anti-Americanism, which, in turn, has become synonymous with being critical of the United States, which, in turn, has become synonymous with being unpatriotic. That's an unacceptable series of equations.

I understood Stephen's point of view because if you had been given a death sentence at the age of 21, would you find it easy to believe in a loving God? Also, Stephen's work was taking him into the depths of the universe, and it was, I thought, fairly understandable that there wasn't much room for God in his equations.

I deliberately and consciously give preference to a dramatic, mythological way of thinking and speaking, because this is not only more expressive but also more exact than an abstract scientific terminology, which is wont to toy with the notion that its theoretic formulations may one fine day be resolved into algebraic equations.

My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.

I do not personally want to believe that we already know the equations that determine the evolution and fate of the universe; it would make life too dull for me as a scientist. ... I hope, and believe, that the Space Telescope might make the Big Bang cosmology appear incorrect to future generations, perhaps somewhat analogous to the way that Galileo's telescope showed that the earth-centered, Ptolemaic system was inadequate.

In the abstract world of American economists, equations run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.

While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women.

...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.

India was China's teacher in religion and imaginative literature, and the world's teacher in trignometry, quandratic equations, grammar, phonetics, Arabian Nights, animal fables, chess, as well as in philosophy, and that she inspired Boccaccio, Goethe, Herder, Schopenhauer, Emerson, and probably also old Aesop.

A mathematician either has a feeling for equations and an understanding and delight in it, not only in the purity of it, but in its beauty as well. I don't think that's something that you learn at school. I think you can get better in mathematics on a school level, but when you're talking about being a mathematician, I think that's definitely a gift of genes or whatever, you know? Whatever your pool is.