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...

**Ian Stewart**

the-power-equations-lies-in-philosophically-difficult-correspondence-between-mathematics-collective-creation-human-minds-external-physical-ian-stewart

The reason Dick's physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans and Oppy and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.

**Freeman Dyson**

the-reason-dicks-physics-was-hard-for-ordinary-people-to-grasp-was-that-he-did-not-use-equations-the-usual-theoretical-physics-was-done-since-time-newton-was-to-begin-by-writing-

We have written the equations of water flow. From experiment, we find a set of concepts and approximations to use to discuss the solution-vortex streets, turbulent wakes, boundary layers. When we have similar equations in a less familiar situation, and one for which we cannot yet experiment, we try to solve the equations in a primitive, halting, and confused way to try to determine what new qualitatitive features may come out, or what new qualitative forms are a consequence of the equations. Our equations for the sun, for example, as a ball of hydrogen gas, describe a sun without sunspots, without the rice-grain structure of the surface, without prominences, without coronas. Yet, all of these are really in the equations; we just haven't found the way to get them out... The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colourful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets-those eight or ten balls, each agglomerated from the same dust clouds and each obeying exactly the same laws of physics. The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrodinger's equation contains frogs, musical composers, or morality-or whether it does not. We cannot say whether something beyond it like God is needed, or not. And so we can all hold strong opinions either way.

**Richard Feynman**

we-have-written-equations-water-flow-from-experiment-we-find-set-concepts-approximations-to-use-to-discuss-solutionvortex-streets-turbulent-wakes-boundary-layers-when-we-have-sim

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.

**Michio Kaku**

like-music-art-mathematical-equations-can-have-natural-progression-logic-that-can-evoke-rare-passions-in-scientist-although-lay-public-considers-michio-kaku

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.

**Ezra Pound**

poetry-is-sort-inspired-mathematics-which-gives-us-equations-not-for-abstract-figures-triangles-squares-like-but-for-human-emotions-if-one-has-ezra-pound

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.

**Martin Rees**

everything-however-complicated-breaking-waves-migrating-birds-tropical-forests-is-made-atoms-obeys-equations-quantum-physics-but-even-if-those-equations-could-be-solved-they-woul

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**

what-appear-to-be-most-valuable-aspects-theoretical-physics-we-have-are-mathematical-descriptions-which-enable-us-to-predict-events-these-celia-green

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.

**Deepika Padukone**

ive-not-been-in-live-in-relationship-but-ive-been-exposed-to-various-kinds-equations-that-can-exist-between-people-when-i-came-from-bangalore-it-was-black-white-over-years-ive-re

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.

**Paul Dirac**

it-is-more-important-to-have-beauty-in-ones-equations-than-to-have-them-fit-experiment-it-seems-that-if-one-is-working-from-point-view-getting-paul-dirac

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**

even-if-there-is-only-one-possible-unified-theory-it-is-just-set-rules-equations-what-is-it-that-breathes-fire-into-equations-makes-universe-for-them-to-describe-the-usual-approa

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.

**Ludwig Boltzmann**

who-is-not-familiar-with-maxwells-memoirs-on-his-dynamical-theory-gases-from-one-side-enter-equations-state-from-other-side-equations-motion-ludwig-boltzmann

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**

the-rigid-electron-is-in-my-view-monster-in-relation-to-maxwells-equations-whose-innermost-harmony-is-principle-relativity-rigid-electron-is-no-hermann-minkowski

I understand the mechanism of my own thinking. I know precisely how I know, and my understanding is recursive. I understand the infinite regress of this self-knowing, not by proceeding step by step endlessly, but by apprehending the limit. The nature of recursive cognition is clear to me. A new meaning of the term "self-aware." Fiat logos. I know my mind in terms of a language more expressive than any I'd previously imagined. Like God creating order from chaos with an utterance, I make myself anew with this language. It is meta-self-descriptive and self-editing; not only can it describe thought, it can describe and modify its own operations as well, at all levels. What Ge¶del would have given to see this language, where modifying a statement causes the entire grammar to be adjusted. With this language, I can see how my mind is operating. I don't pretend to see my own neurons firing; such claims belong to John Lilly and his LSD experiments of the sixties. What I can do is perceive the gestalts; I see the mental structures forming, interacting. I see myself thinking, and I see the equations that describe my thinking, and I see myself comprehending the equations, and I see how the equations describe their being comprehended. I know how they make up my thoughts. These thoughts.

**Ted Chiang**

i-understand-mechanism-my-own-thinking-i-know-precisely-how-i-know-my-understanding-is-recursive-i-understand-infinite-regress-this-selfknowing-not-by-proceeding-step-by-step-end

it-is-more-important-to-have-beauty-in-ones-equations-than-to-have-them-fit-experiment-paul-dirac

many-physicists-these-days-sound-like-delphic-oracle-with-equations-john-twelve-hawks

those-who-think-science-is-measurement-should-search-darwins-works-for-numbers-equations-david-h-hubel

when-in-school-they-were-teaching-algebra-i-was-studying-differential-equations-at-home

playing-threehour-rush-show-is-like-running-marathon-while-solving-equations-neil-peart

maxwells-equations-have-had-greater-impact-on-human-history-than-any-ten-presidents-carl-sagan

the-true-will-is-thus-both-determined-by-its-equations-free-because-those-equation-are-simply-its-own-name-spelt-out-fully-aleister-crowley

knowing-what-is-big-what-is-small-is-more-important-than-being-able-to-solve-partial-differential-equations-stanislaw-ulam

a-mathematician-believes-that-describing-speed-mercury-with-equations-amounts-to-science-bill-gaede

the-special-theory-relativity-owes-its-origins-to-maxwells-equations-electromagnetic-field-albert-einstein

in-2056-i-think-youll-be-able-to-buy-tshirts-on-which-are-printed-equations-describing-unified-laws-our-universe-max-tegmark

economists-others-who-are-satisfied-with-naturefree-equations-develop-dangerous-hubris-about-potency-our-species-garrett-hardin

the-simple-equations-that-generate-convoluted-mandelbrot-fractal-have-been-called-wittiest-remarks-ever-made-john-allen-paulos

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**

any-schemes-such-as-think-symmetry-laws-put-information-in-mathematical-form-guess-equations-are-known-to-everybody-now-they-are-all-tried-all-richard-p-feynman

the-universe-is-governed-by-science-but-science-tells-us-that-we-cant-solve-the-equations-directly-in-the-abstract

the-behavior-economy-as-whole-at-aggregate-macrolevel-is-built-up-from-individual-equations-at-microlevel-paul-ormerod

the-quantum-hypothesis-will-eventually-find-its-exact-expression-in-certain-equations-which-will-be-more-exact-formulation-law-causality-max-planck

One of the pleasing things about science is that we do all climb towards the heavens on the shoulders of our predecessors. Economics, like physics, has its heroes, and the letter 'H' that I used in my mathematical equations was not there to honor Sir William Hamilton, but rather Harold Hotelling.

**Paul Samuelson**

one-pleasing-things-about-science-is-that-we-do-all-climb-towards-heavens-on-shoulders-our-predecessors-economics-like-physics-has-its-heroes-letter-h-that-i-used-in-my-mathemati

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**

perhaps-we-see-equations-as-simple-because-they-are-easily-expressed-in-terms-mathematical-notation-already-invented-at-earlier-stage-development-murray-gellmann

Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.

**Isaac Newton**

through-algebra-you-easily-arrive-at-equations-but-always-to-pass-therefrom-to-elegant-constructions-demonstrations-which-usually-result-by-means-isaac-newton

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

**Stephen Singular**

as-with-randall-terry-other-antiabortion-leaders-women-simplydid-not-figure-into-roeders-equations-if-all-abortionproviders-were-dead-problem-would-stephen-singular

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.

**Daniel Tammet**

my-algebra-was-relatively-poor-i-found-it-difficult-to-use-equations-that-substituted-numbers-to-which-i-had-synesthetic-emotional-response-for-daniel-tammet

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.

**Libba Bray**

in-our-travels-we-have-come-across-many-equationsmath-for-understanding-universe-for-making-music-for-mapping-stars-also-for-tipping-which-is-libba-bray

See, the thing is, I had a little misunderstanding with Trent Gibson in Pre-Calculus earlier. I dropped my textbook on his face-accidentally, while we were discussing some... equations-and he thought I was trying to brain him. So of course, he narked to Shoemaker, and apparently accidents are grounds for disciplinary action these days.

**Isobel Irons**

see-thing-is-i-had-little-misunderstanding-with-trent-gibson-in-precalculus-earlier-i-dropped-my-textbook-on-his-faceaccidentally-while-we-were-discussing-some-equations-he-thoug

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.

**Carl Jung**

i-deliberately-consciously-give-preference-to-dramatic-mythological-way-thinking-speaking-because-this-is-not-only-more-expressive-but-also-more-carl-jung

Grandad taught me that the alien signs and symbols of algebraic equations were not just marks on paper. They were not flat. They were three-dimensional, and you could approach them from different directions, look at them from different ways, stand them on their heads. You could take them apart and put them back together in a variety of shapes, like Legos. I stopped being scared of them.

**Mal Peet**

grandad-taught-me-that-alien-signs-symbols-algebraic-equations-were-not-just-marks-on-paper-they-were-not-flat-they-were-threedimensional-you-mal-peet

I don't create my images as visual equations to be solved, but rather, i create them as internal landscapes that the viewer can explore. I enjoy sharing the why behind the what, of my creations... but my way, isn't the only way, to experience them. There is no correct way to interpret them. Perception is reality and yours may be different from mine and that's okay.

**Jaeda DeWalt**

i-dont-create-my-images-as-visual-equations-to-be-solved-but-rather-i-create-them-as-internal-landscapes-that-viewer-can-explore-i-enjoy-sharing-why-behind-what-my-creations-but-