Quotes & Sayings About Mathematical Beauty

Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty. — Ian Stewart

A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. — Paul Dirac

Theoretical physicists accept the need for mathematical beauty as an act of faith ... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty. — Paul Dirac

No salvation comes from exhumed gods; we must penetrate deeper into substance. If I take a fossil, say, a trilobite, in my hand (marvelously preserved specimens are found in the quarries at the foot of the Casbah), I am transfixed by the impact of mathematical harmony. Purpose and beauty, as fresh as on the first day, are still seamlessly united in a medal engraved by a master's hand. The bios must have discovered the secret of tripartition in this primordial crab. Tripartition then frequently recurs, even without any natural kinship; figures, in transversal symmetry, dwell in the triptych.
How many millions of years ago might this creature have animated an ocean that no longer exists? I hold its impression, a seal of imperishable beauty, in my hand. Some day, this seal, too, will decay or else burn out in cosmic conflagrations of the future. The matrix that formed it remains concealed in and operative from the law, untouched by death or fire. — Ernst Junger

Two moral forces shaped how we think and live in this shining twentieth century: the Virgin, and the Dynamo. The Dynamo represents the desire to know; the Virgin represents the freedom not to know.

What's the Virgin made of? Things that we think are silly, mostly. The peculiar logic of dreams, or the inexplicable stirring we feel when we look on someone that's beautiful not in a way that we all agree is beautiful, but the unique way in which a single person is. The Virgin is faith and mysticism; miracle and instinct; art and randomness.

On the other hand, you have the Dynamo: the unstoppable engine. It finds the logic behind a seeming miracle and explains that miracle away; it finds the order in randomness to which we're blind; it takes the caliper to a young woman's head and quantifies her beauty in terms of pleasing mathematical ratios; it accounts for the secret stirring you felt by discoursing at length on the nervous systems of animals. — Dexter Palmer

To me, it is far nobler to create my own meaning derived from that around me, using my critical faculties, than to accept unquestioningly the meaning that a superdeity has enforced upon me. The same with beauty and the universe around us. There is something worth dwelling on in that notion that we don't need for a god to cause and define that universe - that beauty, that spectacle - when we are appreciating it. Whether it be an incredibly complex yet symmetrical mathematical equation, a butterfly's wings or the expansive Hubble space telescope pictures of nebulae and clouds of space dust and gases, there is much to marvel at in the universe. It's even more marvelous that there is no painter at nature's easel. — Jonathan MS Pearce

If nature leads us to mathematical forms of great simplicity and beauty - by forms, I am referring to coherent systems of hypotheses, axioms, etc. - to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature ... . You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared. — Werner Heisenberg

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. — D'Arcy Wentworth Thompson

Wherever there is number, there is beauty. — Proclus

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence. — Paul Dirac

The feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know — Henri Poincare

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

Music can have wonderful, formal, quasi-mathematical perfection, and it can have heartbreaking tenderness, poignancy, and beauty. But it does not have to have any 'meaning' whatever. One may recall music, give it the life of imagination simply because one likes it - this is reason enough. Or perhaps there may be no reason at all, as Rodolfo Llinas points out. — Oliver Sacks

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

There is no such thing as beauty, especially in the human face ... what we call the physiognomy. It's all a mathematical and imagined alignment of features. Like, if the nose doesn't stick out too much, the sides are in fashion, if the earlobes aren't too large, if the hair is long ... It's kind of a mirage of generalization. People think of certain faces as beautiful, but, truly, in the final measure, they are not. It's a mathematical equation of zero. "True beauty" comes, of course, of character. Not through how the eyebrows are shaped. So many women that I'm told are beautiful ... hell, it's like looking into a soup bowl. — Charles Bukowski

All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true. — Georg C. Lichtenberg

A businessman is someone who buys at ten and is happy to get out at twelve. The other kind of man buys at ten, sees it rise to eighteen and does nothing. He is waiting for it to get to twenty. The beauty of numbers. When it drops to ten again he waits for it to get back to eighteen. When it drops to two he waits for it to get back to ten. Well, it gets back there. But he has wasted a quarter of his life. And all he's got out of his money is a little mathematical excitement. — V.S. Naipaul

It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on ... But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time. — Paul Dirac

The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, mathematical order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers. — Kenneth Clark

You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us. — Werner Heisenberg

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony. — Hermann Weyl

There is indeed a fundamental beauty in mathematical abstractions. They so attracted the Greek philosopher Plato that he declared that all those things that we can see and touch are, in fact, mere shadows of the true reality and that the real things of this universe can be found only through the use of pure reason. Plato's knowledge of mathematics was relatively naive, and many of the cherished purities of Greek mathematics have been shown to be flawed. — David Salsburg

It is almost possible to say that there is a mathematical relationship between the beauty of his surroundings and the activity of the child; he will make discoveries rather more voluntarily in a gracious setting than in an ugly one. — Maria Montessori

If theory is the role of the architect, then such beautiful proofs are the role of the craftsman. Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales. — Michael Atiyah

Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there. — Marcus Du Sautoy

Mathematical solutions are selected by the subliminal self on the basis of "mathematical beauty," of the harmony of numbers and forms, of geometric elegance. — Robert M. Pirsig

The perfection of mathematical beauty is such ... that whatsoever is most beautiful and regular is also found to be most useful and excellent. — D'Arcy Wentworth Thompson

The Golden Proportion, sometimes called the Divine Proportion, has come down to us from the beginning of creation. The harmony of this ancient proportion, built into the very structure of creation, can be unlocked with the 'key' ... 528, opening to us its marvelous beauty. Plato called it the most binding of all mathematical relations, and the key to the physics of the cosmos. — Bonnie Gaunt

There is a certain tyranny about perfection, a certain exhaustion about it even, something that denies the viewer a role in its creation and that asserts itself with all the dogmatism of an unambiguous statement. True beauty cannot be measured because it is fluctuating, it has only a few angles from which it may be seen, and then not in all lights and at all times. It flirts dangerously with ugliness, it takes risks with itself, it does not side comfortably with mathematical rules of proportion, it draws its appeal from precisely those areas that will also lend themselves to ugliness. Nothing can be beautiful that does not take a calculated risk with ugliness. — Alain De Botton

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events. — Morris Kline

The detective story, as created by Poe, is something as specialised and as intellectual as a chess problem, whereas the best English detective fiction has relied less on the beauty of the mathematical problem and much more on the intangible human element. [ ... ] In The Moonstone the mystery is finally solved, not altogether by human ingenuity, but largely by accident. Since Collins, the best heroes of English detective fiction have been, like Sergeant Cuff, fallible. — T. S. Eliot

When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity. — Vladimir Kramnik

As for everything else, so for a mathematical theory: beauty can be perceived but not explained. — Arthur Cayley

Sense of beauty, perception, and the mathematical universe are all part of the same texture. — Neeti Sinha

Mathemagical mathematics combines the beauty of mathematical structure with the entertainment value of a trick. — Martin Gardner

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence
a duty and a duty alone
and no hint of magic or beauty of the subject might be allowed to come through. — Roger Penrose

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree. — Aristotle.

As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry. — Blaise Pascal

We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both. — Henry David Thoreau

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. — Paul Dirac