Quotes & Sayings About Mathematical 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

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? — Stephen Wolfram

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

... 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. — Dan Brown

One of the ideas of this book is to give the reader a possibility to develop
problem-solving skills using both systems, to solve various nonlinear
PDEs in both systems. To achieve equal results in both systems, it is not sufficient simply "to translate" one code to another code. There are numerous examples, where there exists some predefined function in one system and does not exist in another. Therefore, to get equal results
in both systems, it is necessary to define new functions knowing the method or algorithm of calculation. — Inna K. Shingareva

Yes, we have to divide up our time like that, between our 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. — Albert Einstein

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. — Hermann Minkowski

Words are a pretty fuzzy substitute for mathematical equations. — Isaac Asimov

In the one real, time-drenched universe, everything has a particular history precisely because it is finite, and not part of an infinite array. Moreover, the cosmological use of the infinite serves to mask the failure of a physical theory taken beyond the boundaries of its proper domain of application. The most notable instance is the inference in contemporary cosmology of an infinite initial singularity from the field equations of general relativity. Finally, the admission of the mathematical infinite into natural science effaces the difference, which we emphasize, between nature and mathematics. Nature works in time, with which mathematics has trouble. Mathematics offers, among other things, the infinite, which nature abhors. — Lee Smolin

It is more important to have beauty in one's equations than to have them fit experiment. — Paul Dirac

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. — Paul Dirac

You have a roommate."
"Yeah." He sounds confused.
"The, um, picture on your door surprised me."
"NO. No. I prefer my women with ... fewer carnivorous beasts and less weaponry." He pauses and smiles. "Naked is okay. What she needs are a golden retriever and a telescope. Maybe then it would do it for me."
I laugh.
"A squirrel and a laboratory beaker?"
"A bunny rabbit and a flip chart," I say.
"Only if the flip chart has mathematical equations on it."
I fake swoon onto his bed. "Too much, too much! — Stephanie Perkins

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. — Kenneth E. Boulding

Under the federal reserve act, panics are scientifically created. The present panic is the first scientifically created one, worked out as we figured, a mathematical equation. — Charles Lindbergh

If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries. — Carl Friedrich Gauss

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 think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don't have any physical meaning at all. Sometimes they do.
At age 60. — Paul Dirac

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

I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation. — Friedrich August Von Hayek

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? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? — Stephen Hawking

If it's art or literature you're interested in, I suggest you read the Greeks. Pure art exists only in slave-owning societies. The Greeks had slaves to till their fields, prepare their meals, and row their galleys while they lay about on sun-splashed Mediterranean beaches, composing poems and grappling with mathematical equations. That's what art is. If you're the sort of guy who raids the refrigerators of silent kitchens at three o'clock in the morning, you can only write accordingly. That's who I am. — Haruki Murakami

The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. — Paul Dirac

I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen's, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell's equations. — Kenneth E. Iverson

A mathematician believes that describing the speed of Mercury with equations amounts to science. — Bill Gaede

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. — Clifford Truesdell

No physicist started out impatient with common-sense notions, eager to replace them with some mathematical abstraction that could be understood only by rarified theoretical physics. Instead, they began, as we all do, with comfortable, standard, common-sense notions. The trouble is that Nature does not comply. If we no longer insist on our notions of how Nature ought to behave, but instead stand before Nature with an open and receptive mind, we find that common sense often doesn't work. Why not? Because our notions, both hereditary and learned, of how Nature works were forged in the millions of years our ancestors were hunters and gatherers. In this case common sense is a faithless guide because no hunter-gatherer's life ever depended on understanding time-variable electric and magnetic fields. There were no evolutionary penalties for ignorance of Maxwell's equations. In our time it's different. — Carl Sagan

Music, like the visual arts, is rooted in our experience of the natural world," said Schwartz. "It emulates our sound environment in the way that visual arts emulate the visual environment." In music we hear the echo of our basic sound making instrument-the vocal tract. This explanation for human music is simpler still than Pythagoras's mathematical equations: we like the sounds that are familiar to us-specifically, we like sounds that remind us of us. — Christine Kenneally

These electric and magnetic fields can be elegantly unified into what's known as the electromagnetic field, represented by six numbers at each point in spacetime. As we discussed in Chapter 7, light is simply a wave rippling through the electromagnetic field, so if our physical world is a mathematical structure, then all the light in our Universe (which feels quite physical) corresponds to six numbers at each point in spacetime (which feels quite mathematical). These numbers obey the mathematical relations that we know as Maxwell's equations, shown in Figure 10.4. — Max Tegmark

This means that, where appropriate, we will dive into mathematical equations, mathematical intuition, mathematical axioms, and cartoon versions of big mathematical ideas. — Joel Grus

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 most important use to which he had put his memory was that he had stuffed an unprecedented number of mathematical constants and equations into it. Most of us have very few mathematical constants in our mind, perhaps only the up-to-twelve-times multiplication table. Johnny had put in his mind layers and layers of algebraic verities. These were the explanation of his extraordinary powers of mental calculation. — Norman Macrae

One nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. — Douglas Adams

We are mathematical equations where your life is the sum of all choices you've made until now. The good news is you can change the equation so that you start making a difference in your life. — Steve Maraboli

Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as elegance of description really reflects the interconnectedness of Nature's laws at different levels. — Murray Gell-Mann

The 'Muse' is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first awake. — Roman Payne

Real life issues are not mathematical equations. We're not calculators crunching numbers. We're humans sorting through complex, multi-layered issues, and we're doing so while enduring the (sometimes profound) personal effects of our conclusions. While we want to be reasonable, we are inexorably pulled in the direction of our oldest mental habits and by our deepest life-impacting needs. We're repelled by those ideas which can jeopardize our comfort, safety, and happiness. We can try to be fair, but all the while we are fighting against our needs and fears. There are things we don't want to be true (or false). Our lives are built on certain beliefs which, if disproved, could wreck us. These are the truths that we 'can't handle'. — Daniel Ionson

It took me 1057 pages to describe the hundreds of mathematical equations, algorithms and programming techniques that I invented and used. — Philip Emeagwali

Modern economics is a set of formal models and equations purporting to fully determine human behaviour, at least in the economic realm. And there is no way that uncertainty can be compressed into determinate mathematical models. — Murray Rothbard

I'm trying to justify it somehow, he thought, meaning it not in the moral sense but rather in the mathematical one. Buildings are built by observing certain natural laws; natural laws may be expressed by equations; equations must be justified. Where was the justification in what had happened less than half an hour ago? — Stephen King

The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself. — Ralph Waldo Emerson

In other words, the idea is the there's a fourth level of parallel universes that's vastly larger than the three we've encountered so far, corresponding to different mathematical structures. The first three levels correspond to noncommunicating parallel universes within the same mathematical structure: Level I simply means distant regions from which light hasn't yet had time to reach us, Level II covers regions that are forever unreachable because of the cosmological inflation of intervening space, and Level III, Everett's "Many Worlds," involves noncommunicating parts of the Hilbert space of quantum mechanics. Whereas all the parallel universes at Levels I, II and III obey the same fundamental mathematical equations (describing quantum mechanics, inflation, etc.), Level IV parallel universes dance to the tunes of different equations, corresponding to different mathematical structures. Figure 12.2 illustrates this four-level multiverse hierarchy, one of the core ideas of this book. — Max Tegmark

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. — Richard P. Feynman

All the standard equations of mathematical physics can be separated and solved in Kerr geometry. — Subrahmanyan Chandrasekhar

Investment success cannot be captured in a mathematical equation or a computer program. — Seth Klarman

You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations. — Stephen Wolfram

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. — Paul Dirac

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

All of the patterns we've discussed of course exist in four dimensions rather than three, and the metaphors about braids, cables and trees, shouldn't be taken too literally. The key point is simply that you can be an unchanging pattern in spacetime-the specific details of this pattern are less important for the points we're making. This pattern is part of the mathematical structure that is our Universe, and the relations between different parts of the pattern are encoded in mathematical equations. As we saw in Chapter 8, Everett's quantum mechanics endows you with an even more interesting-but no less mathematical-structure, since a single you (the tree trunk) can split into many branches, each feeling that they're the one and only you
we'll return to this later. — Max Tegmark

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. — Celia Green

It [the depression] was not accidental. It was a carefully contrived occurrence worked out as one works out a mathematical equation. The international bankers sought to bring about a condition of despair here so that they might emerge as the rulers of us all. — Louis Thomas McFadden

There are many ways to generate numerical falsehoods from data, many ways to create proofiness from even valid meaurements. Causuistry distorts the relationships between two sets of numbers. Randumbness creates patterns where none are to be found. Regression to the moon disguises nonsense in mathematical-looking lines or equations or formulae, making even the silliest ideas seem respectable. Such as the one described by this formula:
Callipygianness=(S+C)x(B+F)/T-V)
Where S is shape, C is circularity, B is bounciness, F ir firmness, T is texture, and V is waist-to-hip ratio. This formula was devised by a team of academic psychologists after many hours of serious research into the female derriere. Yes, indeed. This is supposed to be the formula for the perfect butt.

It fact, it's merely a formula for a perfect ass — Charles Seife

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation. — Anthony Scopatz

Psychohistory was the quintessence of sociology; it was the science of human behavior reduced to mathematical equations. The individual human being is unpredictable, but the reactions of human mobs, Seldon found, could be treated statistically. — Isaac Asimov

Some psychologists and philosophers are distrustful of the concept of self. They argue against it because they do not like separating man from the continuum with animals, and they believe the concept of the self gets in the way of scientific experimentation. But rejecting the concept of "self" as "unscientific" because it cannot be reduced to mathematical equations is roughly the same as the argument two and three decades ago that Freud's theories and the concept of "unconscious" motivation were "unscientific." It is a defensive and dogmatic science - and therefore not true science - which uses a particular scientific method as a Procrustean bed and rejects all forms of human experience which don't fit. — Rollo May

For S, the first piece of information in a list was always, and without fail, inextricably linked to the second piece of information, which could only be followed by the third. It didn't matter whether he was memorizing Dante's Divine Comedy or mathematical equations; his memories were always stored in linear chains. Which is why he could recite poems just as easily backward as forward. — Joshua Foer