Mathematics Beauty Quotes

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

Once upon a time, there was a girl who talked to the moon. And she was mysterious and she was perfect, in that way that girls who talk to moons are. In the house next door, there lived a boy. And the boy watched the girl grow more and more perfect, more and more beautiful with each passing year. He watched her watch the moon. And he began to wonder if the moon would help him unravel the mystery of the beautiful girl. So the boy looked into the sky. But he couldn't concentrate on the moon. He was too distracted by the stars. And it didn't matter how many songs or poems had already been written about them, because whenever he thought about the girl, the stars shone brighter. As if she were the one keeping them illuminated. One day, the boy had to move away. He couldn't bring the girl with him, so he brought the stars. When he'd look out his window at night, he would start with one. One star. And the boy would make a wish on it, and the wish would be her name. At the sound of her name, a second star would appear. And then he'd wish her name again, and the stars would double into four. And four became eight, and eight became sixteen, and so on, in the greatest mathematical equation the universe had ever seen. And by the time an hour had passed, the sky would be filled with so many stars that it would wake the neighbors. People wondered who'd turned on the floodlights. The boy did. By thinking about the girl.

The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. It was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated.

This most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being... This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont, to be called Lord God παντοκρατωρ or Universal Ruler.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

Maybe that is what beauty was, for humans. Accidents, imperfections, placed inside a pretty pattern. Asymmetry. The defiance of mathematics.

[When asked why are numbers beautiful?] It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

Mathematics rightly viewed possesses not only truth but supreme beauty.

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

[Grief] is everything. It is the fabric of selfhood, and beautifully chaotic. It shares mathematical characteristics with many natural forms.

It's possible to understand the world from studying a leaf. You can comprehend the laws of aerodynamics, mathematics, poetry and biology through the complex beauty of such a perfect structure. It's also possible to travel the whole globe and learn nothing.

Beauty is startling. She wears a gold shawl in the summer and sells seven kinds of honey at the flea market. She is young and old at once, my daughter and my grandmother. In school she excelled in mathematics and poetry. . . Beauty will dance with anyone who is brave enough to ask her.

[The Old Astronomer to His Pupil] Reach me down my Tycho Brahe, I would know him when we meet, When I share my later science, sitting humbly at his feet; He may know the law of all things, yet be ignorant of how We are working to completion, working on from then to now. Pray remember that I leave you all my theory complete, Lacking only certain data for your adding, as is meet, And remember men will scorn it, 'tis original and true, And the obloquy of newness may fall bitterly on you. But, my pupil, as my pupil you have learned the worth of scorn, You have laughed with me at pity, we have joyed to be forlorn, What for us are all distractions of men's fellowship and smiles; What for us the Goddess Pleasure with her meretricious smiles. You may tell that German College that their honor comes too late, But they must not waste repentance on the grizzly savant's fate. Though my soul may set in darkness, it will rise in perfect light; I have loved the stars too fondly to be fearful of the night. What, my boy, you are not weeping? You should save your eyes for sight; You will need them, mine observer, yet for many another night. I leave none but you, my pupil, unto whom my plans are known. You 'have none but me,' you murmur, and I 'leave you quite alone'? Well then, kiss me, -- since my mother left her blessing on my brow, There has been a something wanting in my nature until now; I can dimly comprehend it, -- that I might have been more kind, Might have cherished you more wisely, as the one I leave behind. I 'have never failed in kindness'? No, we lived too high for strife,-- Calmest coldness was the error which has crept into our life; But your spirit is untainted, I can dedicate you still To the service of our science: you will further it? you will! There are certain calculations I should like to make with you, To be sure that your deductions will be logical and true; And remember, 'Patience, Patience,' is the watchword of a sage, Not to-day nor yet to-morrow can complete a perfect age. I have sown, like Tycho Brahe, that a greater man may reap; But if none should do my reaping, 'twill disturb me in my sleep So be careful and be faithful, though, like me, you leave no name; See, my boy, that nothing turn you to the mere pursuit of fame. I must say Good-bye, my pupil, for I cannot longer speak; Draw the curtain back for Venus, ere my vision grows too weak: It is strange the pearly planet should look red as fiery Mars,-- God will mercifully guide me on my way amongst the stars.

My beautiful proof lies all in ruins.

Séverin crossed his arms. “Zofia, tell him he’s pretty.” Zofia didn’t look up from her tea. “I am personally undecided, but if we’re assessing based on objectivity, then according to the principles of the golden ratio, also known as phi, which is approximately 1.618, your facial beauty is mathematically pleasing.

It is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case.

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

If one is working from the point of view of getting beauty into one's equation, ... one is on a sure line of progress.

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.

The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.

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.

Beauty in mathematics is seeing the truth without effort.

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there's a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run "behind the scenes" by the same organization, the same physical laws. It's an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It's a feeling of awe — of scientific awe — which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe.

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.

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.

We love men because they can never fake orgasms, even if they wanted to. Because they write poems, songs, and books in our honor. Because they never understand us, but they never give up. Because they can see beauty in women when women have long ceased to see any beauty in themselves. Because they come from little boys. Because they can churn out long, intricate, Machiavellian, or incredibly complex mathematics and physics equations, but they can be comparably clueless when it comes to women. Because they are incredible lovers and never rest until we’re happy. Because they elevate sports to religion. Because they’re never afraid of the dark. Because they don’t care how they look or if they age. Because they persevere in making and repairing things beyond their abilities, with the naïve self-assurance of the teenage boy who knew everything. Because they never wear or dream of wearing high heels. Because they’re always ready for sex. Because they’re like pomegranates: lots of inedible parts, but the juicy seeds are incredibly tasty and succulent and usually exceed your expectations. Because they’re afraid to go bald. Because you always know what they think and they always mean what they say. Because they love machines, tools, and implements with the same ferocity women love jewelry. Because they go to great lengths to hide, unsuccessfully, that they are frail and human. Because they either speak too much or not at all to that end. Because they always finish the food on their plate. Because they are brave in front of insects and mice. Because a well-spoken four-year old girl can reduce them to silence, and a beautiful 25-year old can reduce them to slobbering idiots. Because they want to be either omnivorous or ascetic, warriors or lovers, artists or generals, but nothing in-between. Because for them there’s no such thing as too much adrenaline. Because when all is said and done, they can’t live without us, no matter how hard they try. Because they’re truly as simple as they claim to be. Because they love extremes and when they go to extremes, we’re there to catch them. Because they are tender they when they cry, and how seldom they do it. Because what they lack in talk, they tend to make up for in action. Because they make excellent companions when driving through rough neighborhoods or walking past dark alleys. Because they really love their moms, and they remind us of our dads. Because they never care what their horoscope, their mother-in-law, nor the neighbors say. Because they don’t lie about their age, their weight, or their clothing size. Because they have an uncanny ability to look deeply into our eyes and connect with our heart, even when we don’t want them to. Because when we say “I love you” they ask for an explanation.

Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work.

Last time I asked: 'What does mathematics mean to you?', and some people answered: "The manipulation of numbers, the manipulation of structures.' And if I had asked what music means to you, would you have answered: 'The manipulation of notes?

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.

Mathematics and poetry are the two ways to drink the beauty of truth.

This most beautiful system [The Universe] could only proceed from the dominion of an intelligent and powerful Being.

The greatest mathematics has the simplicity and inevitableness of supreme poetry and music, standing on the borderland of all that is wonderful in Science, and all that is beautiful in Art.

For the most part, physicists and mathematicians have settled on a fine division of labour in which the former complain about the finickiness of the latter, and the latter complain about the sloppiness of the former.

Tom felt his darkness. His father was beautiful and clever, his mother was short and mathematically sure. Each of his brothers and sisters had looks or gifts or fortune. Tom loved all of them passionately, but he felt heavy and earth-bound. He climbed ecstatic mountains and floundered in the rocky darkness between the peaks. He had spurts of bravery but they were bracketed in battens of cowardice.

It is convenient for the old men to blame Eve. To insist we are damned because a country girl talked to the snake one afternoon long ago. Children must starve in Somalia for that, and old women be abandoned in our greatest cities. It’s why we will finally be thrown into the lakes of molten lead. Because she was confused by happiness that first time anyone said she was beautiful. Nevertheless, she must be the issue, so people won’t notice that rocks and galaxies, mathematics and rust are also created in His image.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty— a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

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.

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone.

We especially need imagination in science. It is not all logic, nor all mathematics, but is somewhat beauty and poetry.

Perfection. That's what it's about. It's those moments. When you can feel the perfection of creation. The beauty the physics you know the wonder of mathematics. The elations of action and reaction and that is the kind of perfection that I want to be connected to.

As he soars, he thinks, suddenly, of Dr. Kashen. Or not of Dr. Kashen, necessarily, but the question he had asked him when he was applying to be his advisee: What's your favorite axiom? (The nerd pickup line, CM had once called it.) "The axiom of equality," he'd said, and Kashen had nodded, approvingly. "That's a good one," he'd said. The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. I was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated. And in that microsecond that he finds himself suspended in the air, between ecstasy of being aloft and the anticipation of his landing, which he knows will be terrible, he knows that x will always equal x, no matter what he does, or how many years he moves away from the monastery, from Brother Luke, no matter how much he earns or how hard he tries to forget. It is the last thing he thinks as his shoulder cracks down upon the concrete, and the world, for an instant, jerks blessedly away from beneath him: x = x, he thinks. x = x, x = x.

All nature has come to expect from God a sense of orderliness. Whatever God does carries with it His fingerprint. And in the world around us His fingerprint of orderliness is evident to anybody who is honest with the facts. If you look at nature, you will discover a mathematical exactness. Without this precision, the entire world would be in utter confusion. One plus one always equals two no matter what part of the universe you happen to be in. And the laws of nature operate in beautiful harmony, a harmony that is ordered by God Himself.

Going back to the basis, the phrase ‘Fight Like A Girl’, and we’ve all heard that growing up. And by that they mean that you’re some kind of weakling and have no skills as a male. It’s said to little boys when they can’t fight yet, and it ridicules us. By the time we were born, the most of us hear things which program you to accept and know that you are less than your male counter part. It comes apparent in the way you’re paid for your job, it comes apparent when yóu are not allowed to go outside after a certain hour because you stand a good chance of getting raped while no one says that to your boyfriend. While women, anywhere, live in some kind of fear, there is no equality and that is mathematically impossible. We cannot see that change or solved in our lifetimes, but we have to do everything that we can. We should remind ourselves that we are fifty-one percent. Everyone should know that fighting like a girl is a positive thing and that there is not inherently anything wrong with us by the fact that we are born like ladies. That is a beautiful thing that we should never be put down because of. Being compared to a woman should only make a man feel stronger. It should be a compliment. In this world we’re creating it actually is. I remember this one guy who came to our show in Texas or something and he had painted his shirt “real men fight like a girl”, and I cried, because he was going away in the army next day. He bought my book because he wanted something he could read over there. I just hoped that this men, fully straight and fully male can maintain and retain all of those things that make him understand us, and what makes him so beautiful. A lot of military training is step one: you take all those guys and put them in front of bunch of hardcore videogames where you kill a bunch of people and become desensitised. But that is NOT power! I will not do that. I will not become less of a human being and I refuse to give up my femininity because that’s bullshit. I’m not going to have to shave my head and become all buff and all that to be able to say “now I’m powerful” because that’s bullshit. All of this, all of us, we are power. You don’t have to change anything to be strong.

This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centers of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One.

The mathematical order is beautiful precisely because it has no effect on the real world. Life isn't going to be easier, not is anyone going to make a fortune, just because they know something about prime numbers.

If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

In that moment, the future - uncontainable by any Theorem mathematical or otherwise - stretched out before Colin: infinite and unknowable and beautiful.

We see that music, like the world, is formed from unchanging mathematical principles deployed in time, creating complexity, variety and beauty.

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.

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.

It struck me at some point that the whole basis of education was memory. A list of names, a column of numbers, a mathematical formula, a beautiful poem—to learn it you had to upload it to the part of the brain that stored stuff, but that was the same part of my brain I was resisting. My memory had been spotty since Mummy disappeared, by design, and I didn’t want to fix it, because memory equaled grief. Not remembering was balm.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains.

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 sense tried by the present-day kaleidoscope of events.

I knew that the languages which one learns there are necessary to understand the works of the ancients; and that the delicacy of fiction enlivens the mind; that famous deeds of history ennoble it and, if read with understanding, aid in maturing one's judgment; that the reading of all the great books is like conversing with the best people of earlier times; it is even studied conversation in which the authors show us only the best of their thoughts; that eloquence has incomparable powers and beauties; that poetry has enchanting delicacy and sweetness; that mathematics has very subtle processes which can serve as much to satisfy the inquiring mind as to aid all the arts and diminish man's labor; that treatises on morals contain very useful teachings and exhortations to virtue; that theology teaches us how to go to heaven; that philosophy teaches us to talk with appearance of truth about things, and to make ourselves admired by the less learned; that law, medicine, and the other sciences bring honors and wealth to those who pursue them; and finally, that it is desirable to have examined all of them, even to the most superstitious and false in order to recognize their real worth and avoid being deceived thereby

She was his comet, his shooting star. She sparkled like the heavens, and when she smiled it felt like mathematical equations sliding into place. The world in balance, each side properly weighted. She was everything that was beauty, and everything that was brilliant, and he was – He was not well.

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu. Reduced to general theories, mathematics would be a beautiful form without content.

Mathematical solutions are selected by the subliminal self on the basis of “mathematical beauty,” of the harmony of numbers and forms, of geometric elegance.

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

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.

Something else gets under your skin, keeps you working days and nights at the sacrifice of your sleeping and eating and attention to your family and friends, something beyond the love of puzzle solving. And that other force is the anticipation of understanding something about the world that no one has ever understood before you. Einstein wrote that when he first realized that gravity was equivalent to acceleration -- an idea that would underlie his new theory of gravity -- it was the "happiest thought of my life." On projects of far smaller weight, I have experienced that pleasure of discovering something new. It is an exquisite sensation, a feeling of power, a rush of the blood, a sense of living forever. To be the first vessel to hold this new thing. All of the scientists I've known have at least one more quality in common: they do what they do because they love it, and because they cannot imagine doing anything else. In a sense, this is the real reason a scientist does science. Because the scientist must. Such a compulsion is both blessing and burden. A blessing because the creative life, in any endeavor, is a gift filled with beauty and not given to everyone, a burden because the call is unrelenting and can drown out the rest of life. This mixed blessing and burden must be why the astrophysicist Chandrasekhar continued working until his mid-80's, why a visitor to Einstein's apartment in Bern found the young physicist rocking his infant with one hand while doing mathematical calculations with the other. This mixed blessing and burden must have been the "sweet hell" that Walt Whitman referred to when he realized at a young age that he was destined to be a poet. "Never more," he wrote, "shall I escape.

How can I number the worlds to which the eye gives me entry? - the world of light, of colour, of shape, of shadow: of mathematical precision in the snowflake, the ice formation, the quartz crystal, the patterns of stamen and petal: of rhythm in the fluid curve and plunging line of the mountain faces. Why some blocks of stone, hacked into violent and tortured shapes, should so profoundly tranquillise the mind I do not know. Perhaps the eye imposes its own rhythm on what is only a confusion: one has to look creatively to see this mass of rock as more than jag and pinnacle - as beauty. Else why did men for so many centuries think mountains repulsive? A certain kind of consciousness interacts with the mountain-forms to create this sense of beauty. Yet the forms must be there for the eye to see. And forms of a certain distinction: mere dollops won't do it. It is, as with all creation, matter impregnated with mind: but the resultant issue is a living spirit, a glow in the consciousness, that perishes when the glow is dead. It is something snatched from non-being, that shadow which creeps in on us continuously and can be held off by continuous creative act. So, simply to look on anything, such as a mountain, with the love that penetrates to its essence, is to widen the domain of being in the vastness of non-being. Man has no other reason for his existence.

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

But that would mean it was originally a sideways number eight. That makes no sense at all. Unless..." She paused as understanding dawned. "You think it was the symbol for infinity?" "Yes, but not the usual one. A special variant. Do you see how one line doesn't fully connect in the middle? That's Euler's infinity symbol. Absolutus infinitus." "How is it different from the usual one?" "Back in the eighteenth century, there were certain mathematical calculations no one could perform because they involved series of infinite numbers. The problem with infinity, of course, is that you can't come up with a final answer when the numbers keep increasing forever. But a mathematician named Leonhard Euler found a way to treat infinity as if it were a finite number- and that allowed him to do things in mathematical analysis that had never been done before." Tom inclined his head toward the date stone. "My guess is whoever chiseled that symbol was a mathematician or scientist." "If it were my date stone," Cassandra said dryly, "I'd prefer the entwined hearts. At least I would understand what it means." "No, this is much better than hearts," Tom exclaimed, his expression more earnest than any she'd seen from him before. "Linking their names with Euler's infinity symbol means..." He paused, considering how best to explain it. "The two of them formed a complete unit... a togetherness... that contained infinity. Their marriage had a beginning and end, but every day of it was filled with forever. It's a beautiful concept." He paused before adding awkwardly, "Mathematically speaking.

That's the big difference between [the BookWorld] and [the RealWorld]," said Plum. "When things happen after a randomly pointless event, all that follows is simply unintended consequences, not a coherent narrative thrust that propels the story forward." I rolled the idea of unintended consequences around in my head. "Nope, I said finally, "you've got me on that one." "It confuses me, too," admitted Plum, "but that's the RealWorld for you. A brutal and beautiful place, run for the most part on passion, fads, incentives, and mathematics. A lot of mathematics.

To be an engineer, and build a marvelous machine, and to see the beauty of its operation is as valid an experience of beauty as a mathematician's absorption in a wondrous theorem. One is not "more" beautiful than the other. To see a space shuttle standing on the launch pad, the vented gases escaping, and witness the thunderous blast-off as it climbs heavenward on a pillar of flame - this is beauty. Yet it is a prime example of applied mathematics.

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.

When will you ask for your post back?” he whispered in her ear. “I miss the smell of industrial-strength solvents.” She laughed softly. “Soon. And when will you have papers read at the mathematical society again? I rather like having my husband called a genius for reasons that are not clear to me.” My husband. The words rolled off her tongue, easy and beautiful. He kissed her fervently. “Soon. My brilliance quite overflowed on the way home. I have four notebooks to show for it.” “Good. We don’t want people to think I love you for your looks alone.” “In that case we should also put you in some rather revealing gowns once in a while, so that people don’t think I married you for your accomplishments alone.

Neither parents nor schools are very effective at teaching the young to find pleasure in the right things. Adults, themselves often deluded by infatuation with fatuous models, conspire in the deception. They make serious tasks seem dull and hard, and frivolous ones exciting and easy. Schools generally fial to teach how exciting, how mesmerizingly beautiful science or mathematics can be; they teach the routine of literature or history rather than the adventure.

The modern science of nature is significant for many other reasons, beyond the obvious setting of conservation priorities and actions. Foremost in my mind being the fact that it is beautiful. Its wondrous mathematical synchronicities, the specifics of its chemical analyses, the complexity of its physics are beyond both the practical and intuitive knowledge of most lay naturalists (or mystics), no matter how seasoned. When mingled with the wildness of the natural world and the creativity of the human mind, good science reveals its center, its story, its deeper teaching. The science has its own poetic force.

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.

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

Look you wanna know the truth? I don’t really care about the stats or the cup or the trophy or anything like that. In fact even the games aren’t that important to me. What matters to me is the perfect throw, making the perfect catch, the perfect step and block. Perfection. That's what it's about. It's those moments. When you can feel the perfection of creation. The beauty the physics you know the wonder of mathematics. The elations of action and reaction and that is the kind of perfection that I want to be connected to.

Thus far our meditation on quantum reality has revealed that the world of everyday matter, when properly understood, embodies concepts of extraordinary beauty. Indeed, ordinary matter is built up from atoms that are, in a rich and precise sense, tiny musical instruments. In their interplay with light, they realize a mathematical Music of the Spheres that surpasses the visions of Pythagoras, Plato, and Kepler. In molecules and ordered materials, those atomic instruments play together as harmonious ensembles and synchronized orchestras.

Nothing is more fecund, all the mathematicians know it, than those obscure analogies, the blurred reflections from one theory to another ... nothing gives more pleasure to the researcher. One day the illusion drifts away, the premonition changes to a certitude: the twin theories reveal their common source before disappearing; as the Gita teaches it, knowledge and indifference are reached at the same time. The metaphysics has become mathematics, ready to form the subject matter of a treatise, the cold beauty of which cannot move us anymore.

I stretched my arms towards the sky like blades of tall grass The sun beat between my shoulders like carnival drums I sat still in hopes that it would help my wings grow So then I could really be fly And then she arrived Like day break inside a railway tunnel Like the new moon, like a diamond in the mines Like high noon to a drunkard, sudden She made my heart beat in a now-now time signature Her skinny canvas for ultraviolet brushstrokes She was the sun's painting She was a deep cognac color Her eyes sparkled like lights along the new city She lips pursed as if her breath was too sweet And full for her mouth to hold I said, "You are the beautiful, the stress of mathematics." I said, "For you, I would peel open the clouds like new fruit And give you lightning and thunder as a dowry I would make the sky shed all of it's stars, light and rain And I would clasp the constellations across your waist And I would make the heavens your cape And they would be pleased to cover you They would be pleased to cover you May I please, cover you, please

Quantum mechanics. What a repository, a dump, of human aspiration it was, the borderland where mathematical rigor defeated common sense, and reason and fantasy irrationally merged. Here the mystically inclined could find whatever they required and claim science as their proof. And for these ingenious men in their spare time, what ghostly and beautiful music it must be--spectral asymmetry, resonances, entanglement, quantum harmonic oscillators--beguiling ancient airs, the harmony of the spheres that might transmute a lead wall into gold and bring into being the engine that ran on virtually nothing, on virtual particles, that emitted no harm and would power the human enterprise as well as save it. Beard was stirred by the yearnings of these lonely men. And why should he think they were lonely? It was not, or not only, condescension that made him think them so. They did not know enough, but they knew too much to have anyone to talk to. What mate waiting down the pub or in the British Legion, what hard-pressed wife with job and kids and housework, was going to follow them down these warped funnels in the space-time continuum, into the wormhole, the shortcut to a single, final answer to the global problem of energy?

Were he now still among the living, Dr. Incandenza would now describe tennis in the paradoxical terms of what’s now called ‘Extra-Linear Dynamics.’ And Schtitt, whose knowledge of formal math is probably about equivalent to that of a Taiwanese kindergartner, nevertheless seemed to know what Hopman and van der Meer and Bollettieri seemed not to know: that locating beauty and art and magic and improvement and keys to excellence and victory in the prolix flux of match play is not a fractal matter of reducing chaos to a pattern. Seemed intuitively to sense that it was a matter not of reduction at all, but — perversely — of expansion, the aleatory flutter of uncontrolled, metastatic growth — each well-shot ball admitting of n possible responses, n² responses to those responses, and on into what Incandenza would articulate to anyone who shared both his backgrounds as a Cantorian continuum of infinities of possible move and response, Cantorian and beautiful because infoliating, contained, this diagnate infinity of infinities of choice and execution, mathematically uncontrolled but humanly contained, bounded by the talent and imagination of self and opponent, bent in on itself by the containing boundaries of skill and imagination that brought one player finally down, that kept both from winning, that made it, finally, a game, these boundaries of self.

I must study politics and war," wrote John Adams, "that my sons may have the liberty to study mathematics, and philosophy, geography, natural history, and naval architecture, navigation, commerce, and agriculture, in order to give their children the right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain." Adams saw clearly that politics is the indispensable foundation for things elegant and beautiful. First and above all else, you must secure life, liberty and the right to pursue your own happiness.

This world is of a single piece; yet, we invent nets to trap it for our inspection. Then we mistake our nets for the reality of the piece. In these nets we catch the fishes of the intellect but the sea of wholeness forever eludes our grasp. So, we forget our original intent and then mistake the nets for the sea. Three of these nets we have named Nature, Mathematics, and Art. We conclude they are different because we call them by different names. Thus, they are apt to remain forever separated with nothing bonding them together. It is not the nets that are at fault but rather our misunderstanding of their function as nets. They do catch the fishes but never the sea, and it is the sea that we ultimately desire.

As always when he worked with this much concentration he began to feel a sense of introverting pressure. There was no way out once he was in, no genuine rest, no one to talk to who was capable of understanding the complexity (simplicity) of the problem or the approaches to a tentative solution. There came a time in every prolonged effort when he had a moment of near panic, or "terror in a lonely place," the original semantic content of the word. The lonely place was his own mind. As a mathematician he was free from subjection to reality, free to impose his ideas and designs on his own test environment. The only valid standard for his work, its critical point (zero or infinity), was the beauty it possessed, the deft strength of his mathematical reasoning. THe work's ultimate value was simply what it revealed about the nature of his intellect. What was at stake, in effect, was his own principle of intelligence or individual consciousness; his identity, in short. This was the infalling trap, the source of art's private involvement with obsession and despair, neither more nor less than the artist's self-containment, a mental state that led to storms of overwork and extended stretches of depression, that brought on indifference to life and at times the need to regurgitate it, to seek the level of expelled matter. Of course, the sense at the end of a serious effort, if the end is reached successfully, is one of lyrical exhilaration. There is air to breathe and a place to stand. The work gradually reveals its attachment to the charged particles of other minds, men now historical, the rediscovered dead; to the main structure of mathematical thought; perhaps even to reality itself, the so-called sum of things. It is possible to stand in time's pinewood dust and admire one's own veronicas and pavanes.

David watched Sol finish the can of beans. Sol always ate fast. He overate. Since he was eight. Sol leaned back in the wooden chair against the wall, under the window. Baby brother. Sol could have been anything he wanted to be. Nothing mathematical, nothing quantitative, of course, but anything else. A beautiful boy, a wonderful brother, they got along well. Then when Sol turned eight years old, age of a new beginning, their mother obsessed over him, ignoring David. Obsessed over Sol and his underwear. Over and over, a regeneration, a newness. Changed his clothes constantly, had him on her lap every minute possible. She put him in bed and tucked the covers in every night. She refused to let their father do it, so he always took care of David. But, of course, David needed no help and Sol always needed Ruth to take care of him. Sol was still being breast fed even when he finally went to kindergarten. Then Ruth slowly increased regular, solid food. But before bed, Sol had a nightcap, mother’s milk. Their special time. Their unique closeness took a turn from breastfeeding to something else. By the time Sol was in third grade, he was one of the fattest kids in class. Then the brothers became a real team. Now here he was. David and Sol still together, on a mission given by the Creator. It was perfect.

The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality - Dr. Li had once called it coy and twee, a fan dance of an axiom - but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. It was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life.

He was beautiful when he sat alone, he was like me, he had wide lapels, he was holding the mug in the hardest possible way so that his fingers were all twisted but still long and beautiful, he didn’t like to sit alone all the time, but this time, I swear, he didn’t care on way or the other. I’ll tell you why I like to sit alone, because I’m a sadist, that’s why we like to sit alone, because we’re the sadists who like to sit alone. He sat alone because he was beautifully dressed for the occasion and because he was not a civilian. We are the sadists you don’t have to worry about, you think, and we have no opinion on the matter of whether you have to worry about us, and we don’t even like to think about the matter because it baffles us. Maybe he doesn’t mean a thing to me any more but I think he was like me. You didn’t expect to fall in love, I said to myself and at the same time I answered gently, Do you think so? I heard you humming beautifully, your hum said that I can’t ignore you, that I’d finally come around for a number of delicious reasons that only you knew about, and here I am, Miss Blood. And you won’t come back, you won’t come back to where you left me, and that’s why you keep my number, so you don’t dial it by mistake when you’re fooling with the dial not even dialing numbers. You begin to bore us with your pain and we have decided to change your pain. You said you were happiest when you danced, you said you were happiest when you danced with me, now which do you mean? And so we changed his pain, we threw the idea of a body at him and we told him a joke, and then he thought a great deal about laughing and about the code. And he thought that she thought that he thought that she thought the worst thing a woman could do was to take a man away from his work because that made her what, ugly or beautiful? And now you’ve entered the mathematical section of your soul which you claimed you never had. I suppose that this, plus the broken heart, makes you believe that now you have a perfect right to go out and tame the sadists. He had the last line of each verse of the song but he didn’t have any of the other lines, the last line was always the same, Don’t call yourself a secret unless you mean to keep it. He thought he knew, or he actually did know too much about singing to be a singer; and if there is actually such a condition, is anybody in it, and are sadists born there? It is not a question mark, it is not an exclamation point, it is a full stop by the man who wrote Parasites of Heaven. Even if we stated our case very clearly and all those who held as we do came to our side, all of them, we would still be very few.

Of course, I’ve only brought up two examples. Other universal laws of physics have been used as weapons as well, though we don’t know all of them. It’s very possible that every law of physics has been weaponized. It’s possible that in some parts of the universe, even … Forget it, I don’t even believe that.” “What were you going to say?” “The foundation of mathematics.” Cheng Xin tried to imagine it, but it was simply impossible. “That’s … madness.” Then she asked, “Will the universe turn into a war ruin? Or, maybe it’s more accurate to ask: Will the laws of physics turn into war ruins?” “Maybe they already are.… The physicists and cosmologists of the new world are focused on trying to recover the original appearance of the universe before the wars more than ten billion years ago. They’ve already constructed a fairly clear theoretical model describing the pre-war universe. That was a really lovely time, when the universe itself was a Garden of Eden. Of course, the beauty could only be described mathematically. We can’t picture it: Our brains don’t have enough dimensions.” Cheng Xin thought back to the conversation with the Ring again. Did you build this four-dimensional fragment? You told me that you came from the sea. Did you build the sea? “You are saying that the universe of the Edenic Age was four-dimensional, and that the speed of light was much higher?” “No, not at all. The universe of the Edenic Age was ten-dimensional. The speed of light back then wasn’t only much higher—rather, it was close to infinity. Light back then was capable of action at a distance, and could go from one end of the cosmos to the other within a Planck time.… If you had been to four-dimensional space, you would have some vague hint of how beautiful that ten-dimensional Garden must have been.” “You’re saying—” “I’m not saying anything.” Yifan seemed to have awakened from a dream. “We’ve only seen small hints; everything else is just guessing. You should treat it as a guess, just a dark myth we’ve made up.” But Cheng Xin continued to follow the course of the discussion taken so far. “—that during the wars after the Edenic Age, one dimension after another was imprisoned from the macroscopic into the microscopic, and the speed of light was reduced again and again.…” “As I said, I’m not saying anything, just guessing.” Yifan’s voice grew softer. “But no one knows if the truth is even darker than our guesses.… We are certain of only one thing: The universe is dying.” The

Finding a taxi, she felt like a child pressing her nose to the window of a candy store as she watched the changing vista pass by while the twilight descended and the capital became bathed in a translucent misty lavender glow. Entering the city from that airport was truly unique. Charles de Gaulle, built nineteen miles north of the bustling metropolis, ensured that the final point of destination was veiled from the eyes of the traveller as they descended. No doubt, the officials scrupulously planned the airport’s location to prevent the incessant air traffic and roaring engines from visibly or audibly polluting the ambience of their beloved capital, and apparently, they succeeded. If one flew over during the summer months, the visitor would be visibly presented with beautifully managed quilt-like fields of alternating gold and green appearing as though they were tilled and clipped with the mathematical precision of a slide rule. The countryside was dotted with quaint villages and towns that were obviously under meticulous planning control. When the aircraft began to descend, this prevailing sense of exactitude and order made the visitor long for an aerial view of the capital city and its famous wonders, hoping they could see as many landmarks as they could before they touched ground, as was the usual case with other major international airports, but from this point of entry, one was denied a glimpse of the city below. Green fields, villages, more fields, the ground grew closer and closer, a runway appeared, a slight bump or two was felt as the craft landed, and they were surrounded by the steel and glass buildings of the airport. Slightly disappointed with this mysterious game of hide-and-seek, the voyager must continue on and collect their baggage, consoled by the reflection that they will see the metropolis as they make their way into town. For those travelling by road, the concrete motorway with its blue road signs, the underpasses and the typical traffic-logged hubbub of industrial areas were the first landmarks to greet the eye, without a doubt, it was a disheartening first impression. Then, the real introduction began. Quietly, and almost imperceptibly, the modern confusion of steel and asphalt was effaced little by little as the exquisite timelessness of Parisian heritage architecture was gradually unveiled. Popping up like mushrooms were cream sandstone edifices filigreed with curled, swirling carvings, gently sloping mansard roofs, elegant ironwork lanterns and wood doors that charmed the eye, until finally, the traveller was completely submerged in the glory of the Second Empire ala Baron Haussmann’s master plan of city design, the iconic grand mansions, tree-lined boulevards and avenues, the quaint gardens, the majestic churches with their towers and spires, the shops and cafés with their colourful awnings, all crowded and nestled together like jewels encrusted on a gold setting.

Why do I know I exist if I also know I will not? Why was I given access to logical space and the mathematical structure of the world? Just to lose them when my body is destroyed? Why do I wake up in the night with the thought that I will die, why do I sit up, drenched in sweat, and scream and slap myself and try to suppress the thought that I will disappear for all eternity, that I will never be again, to the end of time? Why will the world end with me? We age: we stand quietly in line with those condemned to death. We are executed one after the other in a sinister extermination camp. We are first stripped of our beauty, youth, and hope. We are next wrapped in the penitential robe of illness, weariness, and decay. Our grandparents die, our parents are executed in front of us, and suddenly time gets short, you suddenly see your reflection in the axeblade. And only then do you realize you are living in a slaughterhouse, that generations are butchered and swallowed by the earth, that billions are pushed down the throat of hell, that no one, absolutely no one escapes. That not one person that you see coming out of the factory gates in a Mélies film is still alive. That absolutely everyone in an eighty-year-old sepia photograph is dead. That we all come into this world from a frightening abyss without our memories, that we suffer unimaginably on a speck of dust, and that we then perish, all in a nanosecond, as though we had never lived, as though we had never been.

I grew up in Brooklyn, New York.. a city neighborhood that included houses, lampposts, walls, and bushes. But with an early bedtime in the winter, I could look out my window and see the stars, and the stars were not like anything else in my neighborhood. [At age 5] I didn’t know what they were. [At age 9] my mother … said to me, “You have a library card now, and you know how to read. Take the streetcar to the library and get a book on stars.” … I stepped up to the big librarian and asked for a book on stars. … I sat down and found out the answer, which was something really stunning. I found out that the stars are glowing balls of gas. I also found out that the Sun is a star but really close and that the stars are all suns except really far away I didn’t know any physics or mathematics at that time, but I could imagine how far you’d have to move the Sun away from us till it was only as bright as a star. It was in that library, reading that book, that the scale of the universe opened up to me. There was something beautiful about it. At that young age, I already knew that I’d be very happy if I could devote my life to finding out more about the stars and the planets that go around them. And it’s been my great good fortune to do just that.

Tom felt his darkness. His father was beautiful and clever, his mother was short and mathematically sure. Each of his brothers and sisters had looks or gifts or fortune. Tom loved all of them passionately, but he felt heavy and earth-bound. He climbed ecstatic mountains and floundered in the rocky darkness between the peaks. He had spurts of bravery but they were bracketed in battens of cowardice. Samuel said that Tom was quavering over greatness, trying to decide whether he could take the cold responsibility. Samuel knew his son’s quality and felt the potential of violence, and it frightened him, for Samuel had no violence—even when he hit Adam Trask with his fist he had no violence. And the books that came into the house, some of them secretly—well, Samuel rode lightly on top of a book and he balanced happily among ideas the way a man rides white rapids in a canoe. But Tom got into a book, crawled and groveled between the covers, tunneled like a mole among the thoughts, and came up with the book all over his face and hands. John Steinbeck. East of Eden (Kindle Locations 4766-4770). Viking.

Now we can see what makes mathematics unique. Only in mathematics is there no significant correction-only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day. Ptolemy may have developed an erroneous picture of the planetary system, but the system of trigonometry he worked out to help him with his calculations remains correct forever. Each great mathematician adds to what came previously, but nothing needs to be uprooted. Consequently, when we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago. Nothing pertaining to humanity becomes us so well as mathematics. There, and only there, do we touch the human mind at its peak.

It as mathematical, marriage, not, as one might expect, additional; it was exponential. This one man, nervous in a suite a size too small for his long, lean self, this woman, in a green lace dress cut to the upper thigh, with a white rose behind her ear. Christ, so young. The woman before them was a unitarian minister, and on her buzzed scalp, the grey hairs shone in a swab of sun through the lace in the window. Outside, Poughkeepsie was waking. Behind them, a man in a custodian's uniform cried softly beside a man in pajamas with a Dachshund, their witnesses, a shine in everyone's eye. One could taste the love on the air, or maybe that was sex, or maybe that was all the same then. 'I do,' she said. 'I do,' he said. They did. They would. Our children will be so fucking beautiful, he thought, looking at her. Home, she thought, looking at him. 'You may kiss,' said the officiant. They did, would. Now they thanked everyone and laughed, and papers were signed and congratulations offered, and all stood for a moment, unwilling to leave this gentile living room where there was such softness. The newlyweds thanked everyone again, shyly, and went out the door into the cool morning. They laughed, rosy. In they'd come integers, out they came, squared. Her life, in the window, the parakeet, scrap of blue midday in the London dusk, ages away from what had been most deeply lived. Day on a rocky beach, creatures in the tide pool. All those ordinary afternoons, listening to footsteps in the beams of the house, and knowing the feeling behind them. Because it was so true, more than the highlights and the bright events, it was in the daily where she'd found life. The hundreds of time she'd dug in her garden, each time the satisfying chew of spade through soil, so often that this action, the pressure and release and rich dirt smell delineated the warmth she'd felt in the cherry orchard. Or this, each day they woke in the same place, her husband waking her with a cup of coffee, the cream still swirling into the black. Almost unremarked upon this kindness, he would kiss her on the crown of her head before leaving, and she'd feel something in her rising in her body to meet him. These silent intimacies made their marriage, not the ceremonies or parties or opening nights or occasions, or spectacular fucks. Anyway, that part was finished. A pity...

At first all was well. In fact, all was terrific. The Takers were pedaling away and the wings of their craft were flapping beautifully. They felt wonderful, exhilarated. They were experiencing the freedom of the air: freedom from restraints that bind and limit the rest of the biological community. And with that freedom came marvels—all the things you mentioned the other day: urbanization, technology, literacy, mathematics, science. “Their flight could never end, it could only go on becoming more and more exciting. They couldn’t know, couldn’t even have guessed that, like our hapless airman, they were in the air but not in flight. They were in free fall, because their craft was simply not in compliance with the law that makes flight possible. But their disillusionment is far away in the future, and so they’re pedaling away and having a wonderful time. Like our airman, they see strange sights in the course of their fall. They see the remains of craft very like their own—not destroyed, merely abandoned—by the Maya, by the Hohokam, by the Anasazi, by the peoples of the Hopewell cult, to mention only a few of those found here in the New World. ‘Why,’ they wonder, ‘are these craft on the ground instead of in the air? Why would any people prefer to be earthbound when they could have the freedom of the air, as we do?’ It’s beyond comprehension, an unfathomable mystery.

Every culture has its own creation myth, its own cosmology. And in some respects every cosmology is true, even if I might flatter myself in assuming mine is somehow truer because it is scientific. But it seems to me that no culture, including scientific culture, has cornered the market on definitive answers when it comes to the ultimate questions. Science may couch its models in the language of mathematics and observational astronomy, while other cultures use poetry and sacrificial propitiations to defend theirs. But in the end, no one knows, at least not yet. The current flux in the state of scientific cosmology attests to this, as we watch physicists and astronomers argue over string theory and multiverses and the cosmic inflation hypothesis. Many of the postulates of modern cosmology lie beyond, or at least at the outer fringes, of what can be verified through observation. As a result, aesthetics—as reflected by the “elegance” of the mathematical models—has become as important as observation in assessing the validity of a cosmological theory. There is the assumption, sometimes explicit and sometimes not, that the universe is rationally constructed, that it has an inherent quality of beauty, and that any mathematical model that does not exemplify an underlying, unifying simplicity is to be considered dubious if not invalid on such criteria alone. This is really nothing more than an article of faith; and it is one of the few instances where science is faith-based, at least in its insistence that the universe can be understood, that it “makes sense.” It is not entirely a faith-based position, in that we can invoke the history of science to support the proposition that, so far, science has been able to make sense, in a limited way, of much of what it has scrutinized. (The psychedelic experience may prove to be an exception.)