Maths Life Quotes

Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

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

Lottery: A tax on people who are bad at math.

My name is Hazel. Augustus Waters was the great sat-crossed love of my life. Ours was an epic love story, and I won't be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because-like all real love stories-it will die with us, as it should. I'd hoped that he'd be eulogizing me, because there's no one I'd rather have..." I started crying. "Okay, how not to cry. How am I-okay. Okay." I took a few deep breaths and went back to the page. "I can't talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and infinite collection of others. Of course, there is a Bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful.

There was quite a lot of competitiveness about it, with everybody wanting to beat not only cancer itself, but also the other people in the room. Like, I realize that this is irrational, but when they tell you that you have, say, a 20 percent chance of living five years, the math kicks in and you figure that’s one in five . . . so you look around and think, as any healthy person would: I gotta outlast four of these bastards.

I really wondered why people were always doing what they didn't like doing. It seemed like life was a sort of narrowing tunnel. Right when you were born, the tunnel was huge. You could be anything. Then, like, the absolute second after you were born, the tunnel narrowed down to about half that size. You were a boy, and already it was certain you wouldn't be a mother and it was likely you wouldn't become a manicurist or a kindergarten teacher. Then you started to grow up and everything you did closed the tunnel in some more. You broke your arm climbing a tree and you ruled out being a baseball pitcher. You failed every math test you ever took and you canceled any hope of being a scientist. Like that. On and on through the years until you were stuck. You'd become a baker or a librarian or a bartender. Or an accountant. And there you were. I figured that on the day you died, the tunnel would be so narrow, you'd have squeezed yourself in with so many choices, that you just got squashed.

School literally doesn’t care about you unless you’re good at writing stuff down or you’re good at memorising or you can solve bloody maths equations. What about the other important things in life?

The best way to be appreciative for your life is to live it; don't die for any other reason but love. Dreams are what guide us, art is what defines us, math is makes it all possible, and love is what lights our way.

A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.

The point about zero is that we do not need to use it in the operation of daily life. No one goes out to buy zero fish.

[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.

only a handful of pregnant women are like Emily; that is, they go to the hospital with pain and get the surprise of their life by delivering a child. Using Emily’s least-favorite math term, decimals, the number would be 0.0004 percent of all U.S. births. About fifteen hundred surprise babies a year.

In life two negatives don't make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse.

The future isn’t written in the stars. There are no guarantees. So claim your adulthood. Be intentional. Get to work. Pick your family. Do the math. Make your own certainty. Don’t be defined by what you didn’t know or didn’t do. You are deciding your life right now.

My previous outlook could be summed up as follows: Life is shit. Math makes sense. Fictional characters are superior to real people because real people are equal parts pitiful and predictable.

I'd never had a mind for math. ... It was a logic that made little sense to me. In my perception, the world wasn't a graph or a formula or an equation. It was a story.

And what he meant was that maths wasn't like life because in life there are no straightforward answers in the end

Some things in life are not pleasant but they have to be done. For instance, German and maths.

My name is Hazel. Augustus Waters was the great star-crossed love of my life. Ours was an epic love story, and I won't be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because-like all real love stories-it will die with us, as it should. I'd hoped that he'd be eulogizing me, because there's no one I'd rather have..." I started crying. "Okay, how not to cry. How am I-okay. Okay." I took a few deep breaths and went back to the page. "I can't talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and infinite collection of others. Of course, there is a Bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I'm likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn't trade it for the world. You gave me a forever within the numbered days, and I'm grateful.

That is the inescapable math of tragedy and the multiplication of grief. Too many good people die a little when they lose someone they love. One death begets two or twenty or one hundred. It's the same all over the world.

Brilliant Muslim scholars applied Qur’anic insights to spark the medieval Islamic Golden Age filled with a mind-boggling outpouring of creativity in science, math, medicine, fashion, philosophy, economics, mental health therapy, architecture, art, and beyond.

When every other facet of my life was a mess, music stayed true as math.

But people aren’t math problems.” I gave a heavy shrug. “I can miss my dad and hate him at the same time. I can be worried about this book and torn up about my family and sick over the house I’m living in, and still look out at Lake Michigan and feel overwhelmed by how big it is. I spent all last summer thinking I’d never be happy again, and now, a year later, I still feel sick and worried and angry, but at moments, I’m also happy. Bad things don’t dig down through your life until the pit’s so deep that nothing good will ever be big enough to make you happy again. No matter how much shit, there will always be wildflowers. There will always be Petes and Maggies and rainstorms in forests and sun on waves.

Knowing you don’t have much time left changes things. You get kind of philosophical. And you figure things out—more like, they figure themselves out—and everything gets real clear. Your first kiss isn’t as important as your last. The math test really didn’t matter. The pie really did. The stuff you’re good at and the stuff you’re bad at are just different parts of the same thing. Same goes for the people you love and the people you don’t—and the people who love you and the people who don’t. The only thing that mattered was that you cared about a few people. Life is really, really short.

My “Best Woman” speech Good evening everyone, my name is Rosie and as you can see Alex has decided to go down the non-traditional route of asking me to be his best woman for the day. Except we all know that today that title does not belong to me. It belongs to Sally, for she is clearly his best woman. I could call myself the “best friend” but I think we all know that today that title no longer refers to me either. That title too belongs to Sally. But what doesn’t belong to Sally is a lifetime of memories of Alex the child, Alex the teenager, and Alex the almost-a-man that I’m sure he would rather forget but that I will now fill you all in on. (Hopefully they all will laugh.) I have known Alex since he was five years old. I arrived on my first day of school teary-eyed and red-nosed and a half an hour late. (I am almost sure Alex will shout out “What’s new?”) I was ordered to sit down at the back of the class beside a smelly, snotty-nosed, messy-haired little boy who had the biggest sulk on his face and who refused to look at me or talk to me. I hated this little boy. I know that he hated me too, him kicking me in the shins under the table and telling the teacher that I was copying his schoolwork was a telltale sign. We sat beside each other every day for twelve years moaning about school, moaning about girlfriends and boyfriends, wishing we were older and wiser and out of school, dreaming for a life where we wouldn’t have double maths on a Monday morning. Now Alex has that life and I’m so proud of him. I’m so happy that he’s found his best woman and his best friend in perfect little brainy and annoying Sally. I ask you all to raise your glasses and toast my best friend Alex and his new best friend, best woman, and wife, Sally, and to wish them luck and happiness and divorce in the future. To Alex and Sally!

This is life. It's messy and unpredictable, full of wonderful surprises and mind.numbing disappointment. the uncertainty of it all is why I hide, trying to avoid all the pain and the heartache.

Algorithms are not arbiters of objective truth and fairness simply because they're math.

I have some advice for the young generation who are wanting to become successful in life: become more grateful. Once you do that, Allah says, "If you are grateful, I will surely increase you (in everything)." If you're having a hard time in math, science, language and whatever else, become grateful to Allah and He will open doors for you. You'll even get better at basketball and become more athletic. I pray that Allah makes you grateful young people who are examples for others all over the world, ameen.

It's not the way they taught us. They didn't know the formula for love. One plus one actually equals one. 1+1=1.

I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

Picture a thirteen-year-old boy sitting in the living room of his family home doing his math assignment while wearing his Walkman headphones or watching MTV. He enjoys the liberties hard won over centuries by the alliance of philosophic genius and political heroism, consecrated by the blood of martyrs; he is provided with comfort and leisure by the most productive economy ever known to mankind; science has penetrated the secrets of nature in order to provide him with the marvelous, lifelike electronic sound and image reproduction he is enjoying. And in what does progress culminate? A pubescent child whose body throbs with orgasmic rhythms; whose feelings are made articulate in hymns to the joys of onanism or the killing of parents; whose ambition is to win fame and wealth in imitating the drag-queen who makes the music. In short, life is made into a nonstop, commercially prepackaged masturbational fantasy.

Half the time he felt entirely out of control. Half the time he threw up walls out of fear. And half the time he opted out of life before anyone had the chance to discard him. No matter that the math didn’t add up, it was just how he felt.

Maybe Lindsay and I are best friends and we hate each other, both. Maybe I’m only one math class away from being a slut like Anna Cartullo. Maybe I am like her, deep down. Maybe we all are: just one lunch period away from eating alone in the bathroom. I wonder if it’s ever really possible to know the truth about someone else, or if the best we can do is just stumble into each other, heads down, hoping to avoid collision.

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.

If you choose to try to make a life with another person, you will live by that choice. You'd find yourself having to choose again and again to remain rather than run. It helps if you enter into a committed relationship prepared to work, ready to be humbled and willing to accept and even enjoy living in that in-between space, bouncing between the poles of beautiful and horrible, sometimes in the span of a single conversation, sometimes over the course of years. And inside of that choice and those years you'll almost certainly come to see that there is no such thing as a 50-50 balance, instead it will be like beads on an abacus, sliding back and forth, the maths rarely tidy, the equation never quite solved....

Life is a linear equation in which you can't cross multiply! If you think you can do it, you can do it. If you think you can't do it, you can't do it. It's a simple formula!

Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.

We accept, reject, and discern through symbols. These are as important to our understanding of life, our understanding of existence and what has value, whats worthwhile, as math and science ... it's all part of how we work through things, how we make decisions.

There was a survey done a few years ago that affected me greatly. it was discovered that intelligent people either estimate their intelligence accurately or slightly underestimate themselves, but stupid people overestimate their intelligence and by huge margins. (And these were things like straight up math tests, not controversial IQ tests.)

It is all about numbers. It is all about sequence. It's the mathematical logic of being alive. If everything kept to its normal progression, we would live with the sadness--cry and then walk--but what really breaks us cleanest are the losses that happen out of order.

In all things in this life, we are told "It's okay if you don't make it the first time!", "It's fine if you don't get it right the first time, just try again and again!" We are told this in learning how to ride a bike, in learning how to bake a cake, in solving our math equations...in everything. Except marriage. Why are we all expected to get such an enormous and weighty thing right, the very first time, and if we don't we're considered as failures? I beg to differ! This is a stupidity!

When I was in high school, my math teacher Mr. Packwood used to say, "If you're stuck on a problem, don't sit there and think about it; just start working on it. Even if you don't know what you're doing, the simple act of working on it will eventually cause the right ideas to show up in your head".

Home is where heart is. Heart where cookie is. Math clear: Home is cookie.

My life depended on some math I’d done earlier. If I dropped a sign or added two numbers wrong, I might never wake up.

I'm not sure which is better-the chance to experience love and lose it, or to live my life without it.

I thought of the infinitely many points that can divide the space between two human hearts.

This thing we have, it hurts, he continued. But the pain is almost sweet because it means YOU happened. We happened. And I can't regret that, no matter how little or how long I get to tag along with you and pretend that I don't hate having people recognize me or take pictures or having people whisper about my record-- " Your record?" " My criminal record, Bonnie, Nothing platinum there. I'm an ex-con, and starting over and building a new life where I can put it behind me, I'm building a new life where it will never be behind me, and for you, its worth it. It's easy math.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

Why does it have to hurt? Why does it have to be hard?” Tish asked me. “You know how math is your hardest class right now, but it’s also where you’re learning the most?” I explained. “It’s like that. Life is about learning, and we learn best when things get hard.

Maybe more of us should have plots. Let's take them out of books and put them back in life where they belong.

Life is more than a job; jobs are more than a paycheck; and a country is more than its wealth. Education is more than the acquisition of marketable skills, and you are more than your ability to contribute to your employer’s bottom line or the nation’s GDP, no matter what the rhetoric of politicians or executives would have you think. To ask what college is for is to ask what life is for, what society is for—what people are for. Do students ever hear this? What they hear is a constant drumbeat, in the public discourse, that seeks to march them in the opposite direction. When policy makers talk about higher education, from the president all the way down, they talk exclusively in terms of math and science. Journalists and pundits—some of whom were humanities majors and none of whom are nurses or engineers—never tire of lecturing the young about the necessity of thinking prudently when choosing a course of study, the naïveté of wanting to learn things just because you’re curious about them.

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.

Jack stares at me blankly. ‘A what?’ he asks. I choke back the laugh. ‘A boy. You know? A Y-chromosome holder? You don’t seem to notice them as much as you do the X-carriers.’ ‘What are you talking about?’ Jack asks, ‘A boy? She’s just a kid.’ I hesitate, wondering how Jack is only just doing the maths on this one now. ‘She’s seventeen. She’s not a kid anymore.’ Jack looks like he’s about to go all Incredible Hulk and burst out of his clothes before rampaging through the bar. He jumps off the stool. ‘If any boy ever lays a finger on my sister, I’m going to kill him,’ he says. Again I stare at him in silence, thinking of all the girls Jack has laid fingers and much more of his anatomy on besides. Poor Lila. If she ever wants to have a shot at a normal life, as in one that doesn’t require a vow of celibacy, she needs to stay in London.

The best way to be appreciative for your life is to live it; don’t die for any other reason but love. Dreams are what guide us, art is what defines us, math is what makes it all possible, and love is what lights our way.” ~ Mike Norton

People who don't like math always accuse mathematicians of trying to make math complicated. (...) But anyone who does love math knows it's really the opposite: math rewards simplicity, and mathematicians value it above all else. So it's no surprise that Walter's favourite axiom was also the most simple in the realm of mathematics: the axiom of the empty set. The axiom of the empty set is the axiom of zero. it states that there must be a concept of nothingness, that there must be the concept of zero: zero value, zero items. Math assumes there's a concept of nothingness, but is it proven? No. But it must exist. And if we're being philosophical—which we today are—we can say that life itself is the axiom of the empty set. It begins in zero and ends in zero. We know that both states exist, but we will not be conscious of either experience: they are states that are necessary parts of life, even as they cannot be experienced as life. We assume the concept of nothingness, but we cannot prove it. But it must exist. So I prefer to think that Walter has not died but has instead proven for himself the axiom of the empty set, that he has proven the concept of zero. I know nothing else would have made him happier. An elegant mind wants elegant endings, and Walter had the most elegant mind. So I wish him goodbye; I wish him the answer to the axiom he so loved.

The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That's when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die.

I went outside. Tried taking in the billions of stars above, lingering long enough to allow each point of light the chance to scratch a deep hole in the back of my retina, so that when I finally did turn to face the dark surrounding forest I thought I saw the billion eyes of a billion cats blinking out, in the math of the living, the sum of the universe, the stories of history , a life older than anyone could have ever imagined. And even after they were gone--fading away together, as if they really were one--something still lingered in those sweet folds of black pine , sitting quietly, almost as if it too were waiting for something to wake.

Think of those fingers as abilities. A creative person may write, paint, sculpt, or think up math formulae; he or she might dance or sing or play a musical instrument. Those are the fingers, but creativity is the hand that gives them life. & just as all hands are basically the same - form follows function - all creative people are the same once you get down to the place where the fingers join.

Your first kiss isn’t as important as your last. The math test really didn’t matter. The pie really did. The stuff you’re good at and the stuff you’re bad at are just different parts of the same thing. Same goes for the people you love and the people you don’t—and the people who love you and the people who don’t. The only thing that mattered was that you cared about a few people. Life is really, really short.

Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future -- or better yet, reconstruct the past. I wish I could do that now.

Life is not a sport. Life is not math. There is no final end goal and there is no right answer. Just because your truth does not match someone else's truth does not make either of you wrong. Life is not a zero sum game. If I am right, that does not make you wrong. If you are right, that does not make me wrong either. A jar of vinegar can sit in a cupboard beside a box of baking soda peacefully, and we can allow those who disagree with us to exist alongside us without reacting to them. There is nothing to prove. There is enough room in the world for all of us.

So what were your favorite subjects in school?" "School?" He leaned back in his chair as though he needed the extra space to think about it. "Probably math. It always made sense. Unlike English, economics, and girls." "And exactly how do you plan on taking over the free world if you don't understand economics?" "I'll hire advisers. I'll hire you, in fact." "Okay. Let me know when your army of junior high zombies is ready.

I've written about 2,000 short stories; I've only published 300 and I feel I'm still learning. Any man who keeps working is not a failure. He may not be a great writer, but if he applies the old fashioned virtues of hard, constant labor, he'll eventually make some kind of career for himself as a writer. Ray Bradbury, 1967 interview (Doing the Math - that means for every story he sold, he wrote six "un-publishable" ones. Keep typing!)

I reached for his hand and he let me take it, his dark eyes soft and open. “When I first found out about my dad’s affair, I tried to do that kind of math,” I admitted. “How much lying and cheating could he have done and still have been a good father? How deep could he have gotten himself in with That Woman and still loved my mom? Still liked his life. I tried to figure out how happy he could’ve been, how much he could’ve missed us when he was away, and when I was feeling particularly bad, how much he must’ve hated us to be willing to do what he did. And I never got my answers.

His hand caresses my cheek. "Scarlett, I don't want to lose you by fucking up our friendship. I want you in my life, and if we do this, I will lose you. If that means showing some self-restraint for once in my goddamn life, then I will." Both his hands cup my cheeks. "You make me want to be a better person. This is me being a better person.

This was the math she ran every night, every moment. How much time to try to get the work done? How much time to rest? She could never quite make the numbers work. She was always just scraping by, stretching the budget, always coming up a little short, and the panic clung to her, dogging her steps.

Todd, trust math. As in Matics, Math E. First-order predicate logic. Never fail you. Quantities and their relation. Rates of change. The vital statistics of God or equivalent. When all else fails. When the boulder's slid all the way back to the bottom. When the headless are blaming. When you do not know your way about. You can fall back and regroup around math. Whose truth is deductive truth. Independent of sense or emotionality. The syllogism. The identity. Modus Tollens. Transitivity. Heaven's theme song. The night light on life's dark wall, late at night. Heaven's recipe book. The hydrogen spiral. The methane, ammonia, H2O. Nucleic acids. A and G, T and C. The creeping inevibatility. Caius is mortal. Math is not mortal. What it is is: listen: it's true.

A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn.

The future isn't written in the stars. There are no guarantees. So claim your adulthood. Be intentional. Get to work. Pick your family. Do the math. Make your own certainty. Don't be defined by what you didn't know or didn't do. You are deciding your life right now.

MR JEAVONS SAID THAT I liked maths because it was safe. He said I liked maths because it meant solving problems, and these problems were difficult and interesting, but there was always a straightforward answer at the end. And what he meant was that maths wasn’t like life because in life there are no straightforward answers at the end. I know he meant this because this is what he said. This is because Mr Jeavons doesn’t understand numbers. Here

Things will change more radically than you could ever imagine. Things will end up 300 miles north of your wildest predictions. Healthy people drop dead in supermarket queues. The future love of your life could be the man sitting next to you on the bus. Your secondary school math teacher and rugby coach might now go by the name of Susan. Everything will change. And it could happen any morning.

You can tell if a discipline is BS if the degree depends severely on the prestige of the school granting it. I remember when I applied to MBA programs being told that anything outside the top ten or twenty would be a waste of time. On the other hand a degree in mathematics is much less dependent on the school (conditional on being above a certain level, so the heuristic would apply to the difference between top ten and top two thousand schools). The same applies to research papers. In math and physics, a result posted on the repository site arXiv (with a minimum hurdle) is fine. In low-quality fields like academic finance (where papers are usually some form of complicated storytelling), the “prestige” of the journal is the sole criterion.

Well," he said, "in law, we talk about a beautiful summation, or a beautiful judgment: and what we mean by that, of course, is the loveliness of not only its logic but its expression. And similarly, in math, when we talk about a beautiful proof, what we’re recognizing is the simplicity of the proof, its … elementalness, I suppose: its inevitability.

I am sorry that I cannot make it okay. I am sorry that I cannot save you -- but not that sorry. Part of me thinks that your very vulnerability brings you closer to the meaning of life, just as for others, the quest to believe oneself white divides them from it. The fact is that despite their dreams, their lives are also not inviolable. When their own vulnerability becomes real -- when the police decide that tactics for the ghetto should enjoy wider usage, when their armed society shoots down their children, when nature sends hurricanes against their cities -- they are shocked in a way that those of us who were born and bred to understand cause and effect can never be. And I would not have you like them. You have been cast into a race in which the wind is always at your face and the hounds are always at your heels. And to varying degrees this is true of all life. The difference is that you do not have the privilege of living in ignorance of this essential fact. I am speaking to you as I always have -- as the sober and serious man I have always wanted you to be, who does not apologize for his human feelings, who does not make excuses for his height, his long arms, his beautiful smile. You are growing into consciousness, and my wish for you is that you feel no need to constrict yourself to make other people comfortable. None of that can change the math anyway. I never wanted you to be twice as good as them, so much as I have always wanted you to attack every day of your brief bright life in struggle. The people who must believe they are white can never be your measuring stick. I would not have you descend into your own dream. I would have you be a conscious citizen of this terrible and beautiful world.

We think there's a reason for everything, as if life was supposed to make sense. It's not exactly math. People aren't numbers. Everybody knows life doesn't make any sense at all, so we just better deal with the whole mess. Have a beer. Have a cup of coffee. Have a piece of cake. Go out to a movie. Enjoy the Popcorn.

. . . we come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and other latter-day cabalists will have numbers to tell them the truth or they will have nothing. . . . We must remember that Galileo merely said that the language of nature is written in mathematics. He did not say that everything is. And even the truth about nature need not be expressed in mathematics. For most of human history, the language of nature has been the language of myth and ritual. These forms, one might add, had the virtues of leaving nature unthreatened and of encouraging the belief that human beings are part of it. It hardly befits a people who stand ready to blow up the planet to praise themselves too vigorously for having found the true way to talk about nature.

You can be a rich person alone. You can be a smart person alone. But you cannot be a complete person alone. For that you must be part of, and rooted in, an olive grove. This truth was once beautifully conveyed by Rabbi Harold S. Kushner in his interpretation of a scene from Gabriel García Márquez’s classic novel One Hundred Years of Solitude: Márquez tells of a village where people were afflicted with a strange plague of forgetfulness, a kind of contagious amnesia. Starting with the oldest inhabitants and working its way through the population, the plague causes people to forget the names of even the most common everyday objects. One young man, still unaffected, tries to limit the damage by putting labels on everything. “This is a table,” “This is a window,” “This is a cow; it has to be milked every morning.” And at the entrance to the town, on the main road, he puts up two large signs. One reads “The name of our village is Macondo,” and the larger one reads “God exists.” The message I get from that story is that we can, and probably will, forget most of what we have learned in life—the math, the history, the chemical formulas, the address and phone number of the first house we lived in when we got married—and all that forgetting will do us no harm. But if we forget whom we belong to, and if we forget that there is a God, something profoundly human in us will be lost.

in law, we talk about a beautiful summation, or a beautiful judgment: and what we mean by that, of course, is the loveliness of not only its logic but its expression. And similarly, in math, when we talk about a beautiful proof, what we’re recognizing is the simplicity of the proof, its … elementalness, I suppose: its inevitability.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Why do any of us do what we don't want to do?" I don't respond, unsure what answer he's looking for. He smiles, but it's sad. "Because we're afraid of what will happen if we don't." I always considered fear to be a motivator or a reason not to do something, but I never considered it a reason to continue an ongoing behavior. This opens a vault full or questions about my own life. I've always assumed I'm afraid to engage in activities because I'm afraid of what might happen. But maybe I'm looking at it all wrong. Maybe I should be asking myself if I'm really afraid of leaving what makes me comfortable.

The primary math of the real world is one and one equals two. The layman (as, often, do I) swings that every day. He goes to the job, does his work, pays his bills and comes home. One plus one equals two. It keeps the world spinning. But artists, musicians, con men, poets, mystics and such are paid to turn that math on its head, to rub two sticks together and bring forth fire. Everybody performs this alchemy somewhere in their life, but it’s hard to hold on to and easy to forget. People don’t come to rock shows to learn something. They come to be reminded of something they already know and feel deep down in their gut. That when the world is at its best, when we are at our best, when life feels fullest, one and one equals three. It’s the essential equation of love, art, rock ’n’ roll and rock ’n’ roll bands. It’s the reason the universe will never be fully comprehensible, love will continue to be ecstatic, confounding, and true rock ’n’ roll will never die.

One day, you look in the mirror, and see gray hair. One day, you realize there is less of your life left than what you’ve already lived. And you think, How did this happen so fast? It was only yesterday when I was having my first legal drink, when I was diapering him, when I was young. When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space? Some

Physicist Freeman Dyson once explained that what’s often attributed to the supernatural, or magic, or miracles, is actually just basic math. In any normal person’s life, miracles should occur at the rate of roughly one per month: The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of one per second. So the total number of events that happen to us is about 30,000 per day, or about a million per month. If the chance of a “miracle” is one in a million, we should therefore experience one per month, on average.

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s 'The Mathematical Analysis of Logic'.

I have grown weary of talking about life as if it is deserved, or earned, or gifted, or wasted. I'm going to be honest about my scoreboard and just say that the math on me being here and the people who have kept me here doesn't add up when weighed against the person I've been and the person I can still be sometimes. But isn't that the entire point of gratitude? To have a relentless understanding of all the ways you could have vanished, but haven't? The possibilities for my exits have been endless, and so the gratitude for my staying must be equally endless. I am sorry that this one is not about movement, or history, or dance. But instead about stillness. About all of the frozen moments that I have been pulled back from, in service of attempting another day.

Every sentence I could think of has already been said a hundred times over, by people whose words come out perfect and beautifully formed, where mine die on the tongue or straggle out onto the page, mangled and imperfect. But my story isn’t perfect, because I’m not perfect. Nothing is perfect except maybe in math, in the line that extends forever in both directions. Math is beautiful, I have always known that, but so is life. And I have grown to accept imperfection.

Instructions for a Broken Heart I will find a bare patch of earth, somewhere where the ruins have fallen away, somewhere where I can fit both hands, and I will dig a hole. And into that hole, I will scream you, I will dump all the shadow places of my heart—the times you didn’t call when you said you’d call, the way you only half listened to my poems, your eyes on people coming through the swinging door of the café—not on me—your ears, not really turned toward me. For all those times I started to tell you about the fight with my dad or when my grandma died, and you said something about your car, something about the math test you flunked, as an answer. I will scream into that hole the silence of dark nights after you’d kissed me, how when I asked if something was wrong—and something was obviously so very wrong—how you said “nothing,” how you didn’t tell me until I had to see it in the dim light of a costume barn—so much wrong. I will scream all of it. Then I will fill it in with dark earth, leave it here in Italy, so there will be an ocean between the hole and me. Because then I can bring home a heart full of the light patches. A heart that sees the sunset you saw that night outside of Taco Bell, the way you pointed out that it made the trees seem on fire, a heart that holds the time your little brother fell on his bike at the fairgrounds and you had pockets full of bright colored Band-Aids and you kissed the bare skin of his knees. I will take that home with me. In my heart. I will take home your final Hamlet monologue on the dark stage when you cried closing night and it wasn’t really acting, you cried because you felt the words in you and on that bare stage you felt the way I feel every day of my life, every second, the way the words, the light and dark, the spotlight in your face, made you Hamlet for that brief hiccup of a moment, made you a poet, an artist at your core. I get to take Italy home with me, the Italy that showed me you and the Italy that showed me—me—the Italy that wrote me my very own instructions for a broken heart. And I get to leave the other heart in a hole. We are over. I know this. But we are not blank. We were a beautiful building made of stone, crumbled now and covered in vines. But not blank. Not forgotten. We are a history. We are beauty out of ruins.

IT WAS EASIER FOR PEOPLE to be good at something when more of us lived in small, rural communities. Someone could be homecoming queen. Someone else could be spelling-bee champ, math whiz or basketball star. There were only one or two mechanics and a couple of teachers. In each of their domains, these local heroes had the opportunity to enjoy the serotonin-fuelled confidence of the victor. It may be for that reason that people who were born in small towns are statistically overrepresented among the eminent.68 If

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.

What have I ever had to do in my life that really needed to be done? I always had a choice, and I always took the easy way out—we always took the easy way out. At our age the burden of double maths on a Monday morning and finding a spot the size of Pluto on my nose was as complicated as it ever got for me. This time round I’m having a baby. A baby. And that baby will be around on the Monday, on the Tuesday, on the Wednesday, Thursday, Friday, Saturday, and Sunday. I have no weekends off. No three-month holidays. I can’t take a day off, call in sick, or get Mum to write a note. I am going to be the mum now. I wish I could write myself a note. I’m scared, Alex. Rosie

I thought you people were supposed to be good at math." "Yes, my people all do math for fun, while simultaneously dry-cleaning our karate outfits and giving each other manicures and pedicures, all in between our numerous piano and violin recitals," I said, slamming his book shut. "Do you own freaking work. Although I guess that's a completely foreign concept to you, isn't it? Since you've been deep-throating a silver spoon your whole life." "That is so hot that you just said that," Camden said, lazily swiggin his Red Bull. "Besides, I'll work one of these days when I have to. I'll either go into real estate like my dad or find some rich old widow who wants...uh...services." "That doesn't sound like work," I said. "Of course it is, if she's old," he answered.

A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another. That’s why great art, poetry, music, and literature can be so compelling. When we grasp the chunk, it takes on a new life in our own minds—we form ideas that enhance and enlighten the neural patterns we already possess, allowing us to more readily see and develop other related patterns. Once we have created a chunk as a neural pattern, we can more easily pass that chunked pattern to others, as Cajal and other great artists, poets, scientists, and writers have done for millennia, Once other people grasp that chunk, not only can they use it, but also they can more easily create similar chunks that apply to other areas in their lives—an important part of the creative process.

I think I hate Capaldi because deep down I suspect he may be right. That what he claims is true. That science has now proved beyond doubt there’s nothing so unique about my daughter, nothing there our modern tools can’t excavate, copy, transfer. That people have been living with one another all this time, centuries, loving and hating each other, and all on a mistaken premise. A kind of superstition we kept going while we didn’t know better. That’s how Capaldi sees it, and there’s a part of me that fears he’s right. Chrissie, on the other hand, isn’t like me. She may not know it yet, but she’ll never let herself be persuaded. If the moment ever comes, never mind how well you play your part, Klara, never mind how much she wishes it to work, Chrissie just won’t be able to accept it. She’s too … old-fashioned. Even if she knows she’s going against the science and the math, she still won’t be able to do it. She just won’t stretch that far. But I’m different. I have … a kind of coldness inside me she lacks. Perhaps it’s because I’m an expert engineer, as you put it. This is why I find it so hard to be civil around people like Capaldi. When they do what they do, say what they say, it feels like they’re taking from me what I hold most precious in this life. Am I making sense?

Going through old papers I came across the transcript of a university debate on Rublyov. God, what a level. Abysmal, pathetic. But there is one remarkable contribution by a maths professor called Manin, Lenin Prize winner, who can hardly be more than thirty. I share his views. Not that one should say that about oneself. But it's exactly what I felt when I was making Andrey. And I'm grateful to Manin for that. "Almost every speaker has asked why they have to be made to suffer all through the three hours of the film. I'll try to reply to that question. It is because the twentieth century has seen the rise of a kind of emotional inflation. When we read in a newspaper that two million people have been butchered in Indonesia, it makes as much impression on us as an account of our hockey team winning a match. The same degree of impression! We fail to notice the monstrous discrpancy between these two events. The channels of our perception have been smoothed out to the point where we are no longer aware. However, I don't want to preach about this. It may be that without it life would be impossible. Only the point is that there are some artists who do make us feel the true measure of things. It is a burden which they carry throughout their lives, and we must be thankful to them.

All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply is. Take it moment by moment, and you will find that we are all, as I've said before, bugs in amber. Just because some of us can read and write and do a little math, that doesn't mean we deserve to conquer the Universe. Everything was beautiful and nothing hurt. Any reviewer who expresses rage and loathing for a novel is preposterous. He or she is like a person who has put on full armor and attacked a hot fudge sundae. Here is a lesson in creative writing. First rule: Do not use semicolons. They are transvestite hermaphrodites representing absolutely nothing. All they do is show you've been to college. Maturity is a bitter disappointment for which no remedy exists, unless laughter could be said to remedy anything. Life happens too fast for you ever to think about it. If you could just persuade people of this, but they insist on amassing information. Our awareness is all that is alive and maybe sacred in any of us. Everything else about us is dead machinery.

WE ALL DO IT, YOU know. Distract ourselves from noticing how time’s passing. We throw ourselves into our jobs. We focus on keeping the blight off our tomato plants. We fill up our gas tanks and top off our Metro cards and do the grocery shopping so that the weeks look the same on the surface. And then one day, you turn around, and your baby is a man. One day, you look in the mirror, and see gray hair. One day, you realize there is less of your life left than what you’ve already lived. And you think, How did this happen so fast? It was only yesterday when I was having my first legal drink, when I was diapering him, when I was young. When this realization hits, you start doing the math. How much time do I have left? How much can I fit into that small space? Some of us let this realization guide us, I guess. We book trips to Tibet, we learn how to sculpt, we skydive. We try to pretend it’s not almost over. But some of us just fill up our gas tanks and top off our Metro cards and do the grocery shopping, because if you only see the path that’s right ahead of you, you don’t obsess over when the cliff might drop off. Some of us never learn. And some of us learn earlier than others. —

The human mind is an incredible thing. It can conceive of the magnificence of the heavens and the intricacies of the basic components of matter. Yet for each mind to achieve its full potential, it needs a spark. The spark of enquiry and wonder. Often that spark comes from a teacher. Allow me to explain. I wasn’t the easiest person to teach, I was slow to learn to read and my handwriting was untidy. But when I was fourteen my teacher at my school in St Albans, Dikran Tahta, showed me how to harness my energy and encouraged me to think creatively about mathematics. He opened my eyes to maths as the blueprint of the universe itself. If you look behind every exceptional person there is an exceptional teacher. When each of us thinks about what we can do in life, chances are we can do it because of a teacher. [...] The basis for the future of education must lie in schools and inspiring teachers. But schools can only offer an elementary framework where sometimes rote-learning, equations and examinations can alienate children from science. Most people respond to a qualitative, rather than a quantitative, understanding, without the need for complicated equations. Popular science books and articles can also put across ideas about the way we live. However, only a small percentage of the population read even the most successful books. Science documentaries and films reach a mass audience, but it is only one-way communication.

It's an old story," Julia says, leaning back in her chair. "Only for me, it's new. I went to school for industrial design. All my life I've been fascinated by chairs - I know it sounds silly, but it's true. Form meets purpose in a chair. My parents thought I was crazy, but somehow I convinced them to pay my way to California. To study furniture design. I was all excited at first. It was totally unlike me to go so far away from home. But I was sick of the cold and sick of the snow. I figured a little sun might change my life. So I headed down to L.A. and roomed with a friend of an ex-girlfriend of my brother's. She was an aspiring radio actress, which meant she was home a lot. At first, I loved it. I didn't even let the summer go by. I dove right into my classes. Soon enough, I learned I couldn't just focus on chairs. I had to design spoons and toilet-bowl cleaners and thermostats. The math never bothered me, but the professors did. They could demolish you in a second without giving you a clue if how to rebuild. I spent more and more time in the studio, with other crazed students who guarded their projects like toy-jealous kids. I started to go for walks. Long walks. I couldn't go home because my roommate was always there. The sun was too much for me, so I'd stay indoors. I spent hours in supermarkets, walking aisle to aisle, picking up groceries and then putting them back. I went to bowling alleys and pharmacies. I rode buses that kept their lights on all night. I sat in Laundromats because once upon a time Laundromats made me happy. But now the hum of the machines sounded like life going past. Finally, one night I sat too long in the laundry. The woman who folded in the back - Alma - walked over to me and said, 'What are you doing here, girl?' And I knew that there wasn't any answer. There couldn't be any answer. And that's when I knew it was time to go.

How did you even get in here?” I asked him. “Would you believe they leave the door open all night?” Gus asked. “Um, no,” I said. “As well you shouldn’t.” Gus smiled. “Anyway, I know it’s a bit self-aggrandizing.” “Hey, you’re stealing my eulogy,” Isaac said. “My first bit is about how you were a self-aggrandizing bastard.” I laughed. “Okay, okay,” Gus said. “At your leisure.” Isaac cleared his throat. “Augustus Waters was a self-aggrandizing bastard. But we forgive him. We forgive him not because he had a heart as figuratively good as his literal one sucked, or because he knew more about how to hold a cigarette than any nonsmoker in history, or because he got eighteen years when he should have gotten more.” “Seventeen,” Gus corrected. “I’m assuming you’ve got some time, you interrupting bastard. “I’m telling you,” Isaac continued, “Augustus Waters talked so much that he’d interrupt you at his own funeral. And he was pretentious: Sweet Jesus Christ, that kid never took a piss without pondering the abundant metaphorical resonances of human waste production. And he was vain: I do not believe I have ever met a more physically attractive person who was more acutely aware of his own physical attractiveness. “But I will say this: When the scientists of the future show up at my house with robot eyes and they tell me to try them on, I will tell the scientists to screw off, because I do not want to see a world without him.” I was kind of crying by then. “And then, having made my rhetorical point, I will put my robot eyes on, because I mean, with robot eyes you can probably see through girls’ shirts and stuff. Augustus, my friend, Godspeed.” Augustus nodded for a while, his lips pursed, and then gave Isaac a thumbs-up. After he’d recovered his composure, he added, “I would cut the bit about seeing through girls’ shirts.” Isaac was still clinging to the lectern. He started to cry. He pressed his forehead down to the podium and I watched his shoulders shake, and then finally, he said, “Goddamn it, Augustus, editing your own eulogy.” “Don’t swear in the Literal Heart of Jesus,” Gus said. “Goddamn it,” Isaac said again. He raised his head and swallowed. “Hazel, can I get a hand here?” I’d forgotten he couldn’t make his own way back to the circle. I got up, placed his hand on my arm, and walked him slowly back to the chair next to Gus where I’d been sitting. Then I walked up to the podium and unfolded the piece of paper on which I’d printed my eulogy. “My name is Hazel. Augustus Waters was the great star-crossed love of my life. Ours was an epic love story, and I won’t be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because—like all real love stories—it will die with us, as it should. I’d hoped that he’d be eulogizing me, because there’s no one I’d rather have…” I started crying. “Okay, how not to cry. How am I—okay. Okay.” I took a few breaths and went back to the page. “I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set.