Math Equation Quotes

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

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?

In our travels, we have come across many equations--math for understanding the universe, for making music, for mapping stars, and also for tipping, which is important. Here is our favorite equation: Us plus Them equals All of Us. It is very simple math. Try it sometime. You probably won’t even need a pencil.

The simple act of moving your body will do more for your brain than any riddle, math equation, mystery book, or even thinking itself.

I feel like I'm playing some giant video game, or trying to solve a really complicated math equation. 'One girl is trying to avoid forty raiding parties of between fifteen to twenty people each, spread out across a radius of seven miles. If she has to make it 2.7 miles through the center, what is the probablitiy she will wake up tomorrow morning in a jail cell? Please feel free to round pi to 3.14'.

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.

I don’t need to be a Sheldon Cooper to add up that math equation.

Everybody has fucked-up families, even normal kids, even the ones who aren’t in here. There’s no magic math equation that makes us addicts, nothing that separates us from everyone else.

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!

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.

It was like trying to solve a math equation with a poem.

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!

Let’s take some extra time to talk about one: Only the number one can create all numbers with this simple equation, 111111111 x 111111111 = 12345678987654321. One, expressed nine times, multiplied by itself, produces all subsequent numbers progressively and then inversely. Zero is not a number.

I never had a mind for math. I simply couldn't hold the formulas and numbers in my head. It was logic that made little sense to me. In my perception, the world wasn't a graph or formula or an equation. It was a story

We, however, have all kinds of different ideas about what happiness is. Some must go bungee jumping to experience a rush of joy, while others find bliss staying home. Some are happy in a concert hall, listening to classical music, while children on a playground could be music to the ears of others. Some people experience elation when they solve a complicated equation, while for others a cancelled math class is a happy childhood memory.

He walked straight out of college into the waiting arms of the Navy. They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back? Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the average speed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn't prove his intelligence, what would? Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal. Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada. The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else.

Forty-six point two billion dollars, I thought, my heart attacking my rib cage and my mouth sandpaper-dry. Tobias Hawthorne was worth forty-six point two billion dollars, and he left his grandsons a million dollars, combined. A hundred thousand total to his daughters. Another half million to his servants, an annuity for Nan... The math in this equation did not add up. It couldn't add up. One by one, the other occupants of the room of the room turned to stare at me. 'The remainder of my estate,' Mr. Ortega read, 'including all properties, monetary assets, and worldly possessions not otherwise specified, I leave to Avery Kylie Grambs.

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.

. . . I still wouldn't be able to control myself around him, and I'm math geek enough to know that equation doesn't work out.

They turned their desks into a trigonometric war room, poring over equations scrawling ideas on blackboards, evaluating their work, erasing it, starting over.

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.

My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.

It does not take a math genius to understand that when you subtract a mother from the equation what remains is negative.

It should have been as easy as an elementary math equation: he hits you x broken bones = leave him.

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.

Can’t you make yourself likeable? Can’t you even try?” Something shifted in Tavi then. She was always so flippant, trailing sarcasm behind her like a duchess trailing furs. But not this time. Hugo had pierced her armor and blood was dripping from the wound. “Try for whom, Hugo?” she repeated, her voice raw. “For the rich boys who get to go to the Sorbonne even though they’re too stupid to solve a simple quadratic equation? For the viscount I was seated next to at a dinner who tried to put his hand up my skirt through all five courses? For the smug society ladies who look me up and down and purse their lips and say no, I won’t do for their sons because my chin is too pointed, my nose is too large, I talk too much about numbers?” “Tavi …” Isabelle whispered. She went to her, tried to put an arm around her, but Tavi shook her off. “I wanted books. I wanted maths and science. I wanted an education,” Tavi said, her eyes bright with emotion. “I got corsets and gowns and high-heeled slippers instead. It made me sad, Hugo. And then it made me angry. So no, I can’t make myself likeable. I’ve tried. Over and over. It doesn’t work. If I don’t like who I am, why should you?

He thought about explaining math’s beauty to her, the elegance of an equation, the simplicity within the complexity. The thrill of touching truth and knowing it as ancient and unassailable, as permanent and profound.

But had it been the wine? Maybe it was something else. I was no math expert, but this was an intoxicating equation: Hot Guy with Mysterious Past + Way With Pretty Words x Chivalry at Beach / His Aloofness at Coffee Shop (Immunity to My Face & Flirty Efforts) + Innuendo at Hardware Store x Honest Confession about OCD Struggles —> Curiosity + Arousal (Belly Flutters + Pulse Quickening)=ATTACKISS.

I tell my students they can procrastinate as long as they follow three rules: 1. No going onto the computer during their procrastination time. It’s just too engrossing. 2. Before procrastinating, identify the easiest homework problem. (No solving is necessary at this point.) 3. Copy the equation or equations that are needed to solve the problem onto a small piece of paper and carry the paper around until they are ready to quit procrastinating and get back to work. “I have found this approach to be helpful because it allows the problem to linger in diffuse mode—students are working on it even while they are procrastinating.” —Elizabeth Ploughman, Lecturer of Physics, Camosun College, Victoria, British Columbia

Success is math; not magic. It is the sum of a behavioral equation… not the spontaneous fruition of wishful thinking.

What if Loves are analogous to math? First, arithmetic, then geometry and algebra, then trig and quadratics…

Our blessings are never payment for the good we’ve done, and our trials are never punishment for the wrongs we’ve done. This cause-and-effect equation is always bad spiritual math.

Everyone hated Calculus. Quadratic equations, parabolas, logarithms, trigonometry - you name it. It was like floating in an endless, frictionless void traveling at x miles per hour at a descension rate of one half the speed of gravity. Solve for x.

The day passed. People had butchered my name, teachers hadn’t known what the hell to do with me, my math teacher looked at my face and gave a five-minute speech to the class about how people who don’t love this country should just go back to where they came from and I stared at my textbook so hard it was days before I could get the quadratic equation out of my head. Not one of my classmates spoke to me, no one but the kid who accidentally assaulted my shoulder with his bio book. I wished I didn’t care.

It's not for nothing that advanced mathematics tend to be invented in hot countries. It's because of the morphic resonance of all the camels who have that disdainful expression and famous curled lip as a natural result of an ability to do quadratic equations.

What You Missed That Day You Were Absent from Fourth Grade" Mrs. Nelson explained how to stand still and listen to the wind, how to find meaning in pumping gas, how peeling potatoes can be a form of prayer. She took questions on how not to feel lost in the dark. After lunch she distributed worksheets that covered ways to remember your grandfather’s voice. Then the class discussed falling asleep without feeling you had forgotten to do something else— something important—and how to believe the house you wake in is your home. This prompted Mrs. Nelson to draw a chalkboard diagram detailing how to chant the Psalms during cigarette breaks, and how not to squirm for sound when your own thoughts are all you hear; also, that you have enough. The English lesson was that I am is a complete sentence. And just before the afternoon bell, she made the math equation look easy. The one that proves that hundreds of questions, and feeling cold, and all those nights spent looking for whatever it was you lost, and one person add up to something.

Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-year-old to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It’s five-tens-nine.

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.

As the world continually multiplies, are we in a generation where people are divided, or people are equal?

The person who love MATHS can know better that how to do the equations.

I personally feel that the universe behaves more like a song than an equation because math is about static law and music is about dynamic expression.

You are the fucking equation, I want to yell in her face. The riddle and the answer and the numbers within it. You’re math. You make sense.

The world to him no longer seemed a math equation but rather a complex piece of art, a masterpiece of things not easily understood.

Math equations converted by mouth into Dizzy Gillespie noises. That's a tax service I offer.

Life is like a math equation,” he used to say. “It’s up to you to find the most beautiful solution.

I'm so good at math that you can ask me any question, any equation, and I'll convert it into trumpet sounds with my mouth. If it's tough enough, I may answer with Dizzy Gillespie noises.

He said he had an English degree, and I said, “I’m sorry to hear you’re jobless.” I need to network with people who encounter letters on a daily basis in math equations, not romantic poetry.

We’ve now established three things. First, we don’t need willpower when we don’t desire to do something, and it isn’t a thing some of us have in excess and some of us don’t have at all. It’s a cognitive function, like deciding what to eat or solving a math equation or remembering your dad’s birthday. Willpower is also a limited resource; we have more of it at the beginning of the day and lose it throughout the day as we use it to write emails or not eat cookies. When you automate some decisions or processes (through forming habits), you free up more brain power. Second, for us to make and change a habit, we need a cue, a routine, and a reward, and enough repetition must occur for the process to move from something we have to think about consciously (“I need to brush my teeth,” “I don’t want to drink wine”) to something we do naturally, automatically. Third, throughout the day, we must manage our energy so that we don’t blow out and end up in the place of no return—a hyperaroused state where the only thing that can bring us down is a glass (or a bottle) of wine. Maybe

I’d never had a mind for math. I simply couldn’t hold the formulas and numbers in my head. It was a logic that made little sense to me. In my perception, the world wasn’t a graph or formula or an equation. It was a story.

I've always been good at math. It's straightforward, black-and-white, right and wrong. Equations. Da thought of people as books to be read, but I've always thought of them more as formulas—full of variables, but always the sum of their parts. That's what their noise is, really: all of a person's components layered messily over one another. Thought and feeling and memory and all of it unorganized, until a person dies. Then it all gets compiled, straightened out into this linear thing, and you see exactly what the various parts add up to. What they equal.

Love isn't math; there are not precise answers. It's more like chemistry, governed by tiny, fast-moving, unpredictable particles that somehow find a way to collide. Every couple is its own equation, its own chemical reaction." -Lucy

Good Stories Always Beat Good Spreadsheets” “Whether you are raising money, pitching your product to customers, selling the company, or recruiting employees, never forget that underneath all the math and the MBA bullshit talk, we are all still emotionally driven human beings. We want to attach ourselves to narratives. We don’t act because of equations. We follow our beliefs. We get behind leaders who stir our feelings. In the early days of your venture, if you find someone diving too deep into the numbers, that means they are struggling to find a reason to deeply care about you.

I know you think the whole world is held together by some math formula.” His voice has an unaccustomed annoyance in it. “But I’ve thought about this a lot, and I think the world is held together by stories, not all those equations you stare at.

In the early part of the ninth century, Muhammad ibn Musa al-Khwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted (like 2, above) by adding it to the other side of an equation. He called this process al-jabr (Arabic for “restoring”), which later morphed into “algebra.” Then, long after his death, he hit the etymological jackpot again. His own name, al-Khwarizmi, lives on today in the word “algorithm.

They come in here every once in a while, and she goes to one corner and he goes to the other, and then they move around the store creating parabolas as they come together and bounce apart. They're the weirdest couple on Earth. I want to write math equations about them.

Today so many creative and devoted teachers not only have to struggle against unimaginative administrations, fearful parents, and wearied colleagues, they have also to battle entire legislative bodies that have never taught a child yet dare to equate educational success or failure with the ability of fourth graders to choose one out of four given answers to mind-numbing questions that have nothing to do with the joy of literature or the elegance of math.

I’ll be honest with you. The variables that construct my existence are confusing. Like handwritten math equations jammed together on a sloppy page of homework. They don’t make any sense. One math problem leads to another, and then another and so it goes. One day you realize that your life is one whole page of problems and nothing ever gets solved. One ongoing equation with no equal sign at the end. But it occurred to me, beneath the canopy of a starlight heaven, that I’d been looking at my life all wrong. It wasn’t a math equation. Things weren’t supposed to add up. There was no solution. In fact, there was no problem. Life’s variables and numbers and pages of chicken scratch weren’t mathematical marks. They were art. A drawing. An abstract painting. It was meant to be beautiful, not sensical. And embedded within the mess of it all were miracles. Small ones. I’d never paid attention to them because I was too busy, but it didn’t make them less real.

There are hidden meanings in equations, just as there are in poetry. If you are a novice looking at an equation in physics, and you’re not taught how to see the life underlying the symbols, the lines will look dead to you. It is when you begin to learn and supply the hidden text that the meaning slips, slides, then finally leaps to life.

Math is poetry, kid,” she growled. “Math is sex in the head. All that work of making your mind stroke the numbers? It’s a natural series of touches you already know by instinct. Once you get over your inhibitions, you can sit in class or lie in bed and practice formulae and sums, caress the equation till you find the climax of an elegant solution.

If you’re having trouble with a math problem, plug the equation into WolframAlpha.com and it will solve it for you.

Be on the right side of the equation

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.

Someone told me that each equation I included in the book would halve the sales.

Here is an equation worth remembering: Five dollars earned minus seven dollars spent = Unhappy Life." (Life Hacks, p.51)

Her brother's desk was austere, save for a small photo of Lewis and a coffee mug featuring a math geek's coy declaration of love: √-1 <3 μ.

But back then, at least for me, I didn't have that equation. And if you don't even realize that there's a formula to be working with, how the hell are you supposed to find the answer?

It's a random universe. Shit happens. Good people get stage 4 cancer and dipshits win the lottery. There is no justice. Everything doesn't always come out square in the end. Life isn't some elegant math equation -- it's a Sergio Leone screenplay and everyone gets snuffed. Not all of us have to ante up for our portion of the tab. Some get to do the ol' dine 'n' dash.

Always begin with a salutation. After you have finished your complete thought, place a period thusly. Commas are your friends but must be treated with respect and used to distinguish clauses separated by a conjunction. Remember that grammar is like a complicated math equation, except no one really understands the rules, because they were all made up long ago by dead white dudes.

I don’t know if you should be this happy. I’m not sure how much math they taught you at that place you came from, but although two is twice as much as one, in our equation, two still equals fucked.

Whenever you hear a snotty (and frustrated) European middlebrow presenting his stereotypes about Americans, he will often describe them as “uncultured,” “unintellectual,” and “poor in math” because, unlike his peers, Americans are not into equation drills and the constructions middlebrows call “high culture”—like knowledge of Goethe’s inspirational (and central) trip to Italy, or familiarity with the Delft school of painting. Yet the person making these statements is likely to be addicted to his iPod, wear blue jeans, and use Microsoft Word to jot down his “cultural” statements on his PC, with some Google searches here and there interrupting his composition. Well, it so happens that America is currently far, far more creative than these nations of museumgoers and equation solvers. It is also far more tolerant of bottom-up tinkering and undirected trial and error. And globalization has allowed the United States to specialize in the creative aspect of things, the production of concepts and ideas, that is, the scalable part of the products, and, increasingly, by exporting jobs, separate the less scalable components and assign them to those happy to be paid by the hour. There

Lao-tzu advised, “As soon as you have a thought, laugh at it,” because reality is not what we think. We perceive the world through a window colored by beliefs, interpretations, and associations. We see things not as they are but as we are. The same brain that enables us to contemplate philosophy, solve math equations, and create poetry also generates a stream of static known as discursive thoughts, which seem to arise at random, bubbling up into our awareness. Such mental noise is a natural phenomenon, no more of a problem than the dreams that appear in the sleep state. Therefore, our schooling aims not to struggle with random thoughts but to transcend them in the present moment, where no thoughts exist, only awareness. Our mind’s liberation awaits not in some imagined future but here and now.

I'm really good with problems. I can solve a differential equation in my head. I chew through trig angles like candy. I know this, and it just makes it worse. Because I don't know how to solve this one.

Never Ending Math Equation" I'm the same as I was when I was 6 years old And oh my God I feel so damn old I don't really feel anything On a plane, I can see the tiny lights below And oh my God, they look so alone Do they really feel anything? Oh my God, I've gotta gotta gotta gotta move on Where do you move when what you're moving from Is yourself? The universe works on a math equation that never even ever really even ends in the end Infinity spirals out creation We're on the tip of its tongue, and it is saying We ain't sure where you stand You ain't machines and you ain't land And the plants and the animals, they are linked And the plants and the animals eat each other Oh my God and oh my cat I told my Dad what I need Well I know what I have and want But I don't know what I need Well, he said he said he said he said "Where we're going I'm dead.

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.

Even the most complex math can be broken into a sequence of trivial steps. Each of these slaves has been trained to complete specific equations in an assembly-line fashion. When taken together, this collective human mind is capable of remarkable feats." Holtzman surveyed the room as if he expected his solvers to give him a resounding cheer. Instead, they studied their work with heavy-lidded eyes, moving through equation after equation with no comprehension of reasons or larger pictures.

For me, the most beautiful aspects of physics are not the complicated math equations or even the ability of predicting how things will happen. What attracts me to physics is what it teaches us about the bigger picture. The general philosophical lessons that are embedded in physical laws are what excite me. For example, the fact that all particles and forces get unified within string theory teaches us about the unity underlying our universe. The amazingly vast collection of solutions to equations of string theory suggests that there may be many universes besides ours. What happened before the big bang, or was there a time before big bang? The “duality symmetry” in string theory, which exchanges small spaces with large spaces, suggests that perhaps as we go back in time the universe was effectively getting bigger instead of smaller. This suggests we came from other universes. Physics teaches us deep facts about our universe and our place in it. I hope I can add a little to this beautiful story. That is my goal.

It's so unfair," he continues. "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? Like being decent human beings?

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.

POP QUIZ! WHAT’S GOING TO MAKE YOU SMARTER and less prone to brain diseases? Is it A. solving a complex brainteaser, or B. taking a walk? If you guessed A, I won’t come down hard on you, but I will encourage you to go for a walk first (as fast as you can) and then sit down to work on a brainy puzzle. The answer, it turns out, is B. The simple act of moving your body will do more for your brain than any riddle, math equation, mystery book, or even thinking itself. Exercise has numerous pro-health effects on the body—especially on the brain. It’s a powerful player in the world of epigenetics.

On the Electrodynamics of Moving Bodies” Now let’s look at how Einstein articulated all of this in the famous paper that the Annalen der Physik received on June 30, 1905. For all its momentous import, it may be one of the most spunky and enjoyable papers in all of science. Most of its insights are conveyed in words and vivid thought experiments, rather than in complex equations. There is some math involved, but it is mainly what a good high school senior could comprehend. “The whole paper is a testament to the power of simple language to convey deep and powerfully disturbing ideas,” says the science writer Dennis Overbye.

Mr. Duwitt taught me math. He was an older man, and when he leaned over to show me how to work an equation, the smell of smoke and tobacco on his body was so pungent, it made me gag. His famous expression was “The mind boggles,” as in, “Derek, you can learn a complicated dance routine yet not figure out a simple simultaneous equation. The mind boggles!

About 4,400 years ago 8 people stepped off Noah’s ark. According to the United Nations Population Growth Statistics, the world’s population grows at about .47% per year. That is the growth rate for all civilizations who kept records. Suppose you put $8.00 in the bank 4,400 years ago and received .47% a year. How much money would you have? What a coincidence! It would be about $7,000,000,000. That’s kind of odd, because 4,400 years ago 8 people stepped off the ark and now we have about 7,000,000,000 people on planet earth. God’s math works! Compound interest is something we teach to seventh-graders. You don’t have to be a professor to figure this out. A twelve-year-old can do the calculation. Ask any seventh-grader, the algebraic equation looks like this: A=P (1+r/n)t . . . where "A " is the ending amount (about 7,000,000,000 in this case), "P " is the beginning amount (8 in this case), "r " is the interest rate (.47% in this case), "n " is the number of compoundings a year (1 in this case), and "t " is the total number of years (4,400 in this case).

The remaining integer is either 6, 7, 8 or 9. It is more likely to be 8 or 9. The number of continents was either 68 or 76 and a half. Can you guess the equation? What is the formula for calculating the last integer, the continent one? I bet you don’t know unless you are skilled in maths. Fine. Here’s the answer. 68 divided by 8.5 is 8, and 76.5 divided by 8.5 is 9.

5.4 The question of accumulation. If life is a wager, what form does it take? At the racetrack, an accumulator is a bet which rolls on profits from the success of one of the horse to engross the stake on the next one. 5.5 So a) To what extent might human relationships be expressed in a mathematical or logical formula? And b) If so, what signs might be placed between the integers?Plus and minus, self-evidently; sometimes multiplication, and yes, division. But these sings are limited. Thus an entirely failed relationship might be expressed in terms of both loss/minus and division/ reduction, showing a total of zero; whereas an entirely successful one can be represented by both addition and multiplication. But what of most relationships? Do they not require to be expressed in notations which are logically improbable and mathematically insoluble? 5.6 Thus how might you express an accumulation containing the integers b, b, a (to the first), a (to the second), s, v? B = s - v (*/+) a (to the first) Or a (to the second) + v + a (to the first) x s = b 5.7 Or is that the wrong way to put the question and express the accumulation? Is the application of logic to the human condition in and of itself self-defeating? What becomes of a chain of argument when the links are made of different metals, each with a separate frangibility? 5.8 Or is "link" a false metaphor? 5.9 But allowing that is not, if a link breaks, wherein lies the responsibility for such breaking? On the links immediately on the other side, or on the whole chain? But what do you mean by "the whole chain"? How far do the limits of responsibility extend? 6.0 Or we might try to draw the responsibility more narrowly and apportion it more exactly. And not use equations and integers but instead express matters in the traditional narrative terminology. So, for instance, if...." - Adrian Finn

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

Today’s dating sites mean easy access to countless singles tailored to your exact desires, with your perfect match only a click of a button away. Or at least that’s how we think it should be—but sometimes too much choice can just make it harder to weed out the bad options. For some of us, online dating is a succession of frogs with no prince at the end of it. For others, more choice seems to equal more rejection. The good news, as ever, is that math can help.

Olo, Remi, Kwuga, Nur, Anajama, Rhoden. Only Olo and Remi were in my group. Everyone else I met in the dining area or the learning room where various lectures were held by professors onboard the ship. They were all girls who grew up in sprawling houses, who’d never walked through the desert, who’d never stepped on a snake in the dry grass. They were girls who could not stand the rays of Earth’s sun unless it was shining through a tinted window. Yet they were girls who knew what I meant when I spoke of “treeing.” We sat in my room (because, having so few travel items, mine was the emptiest) and challenged each other to look out at the stars and imagine the most complex equation and then split it in half and then in half again and again. When you do math fractals long enough, you kick yourself into treeing just enough to get lost in the shallows of the mathematical sea. None of us would have made it into the university if we couldn’t tree, but it’s not easy. We were the best and we pushed each other to get closer to “God.

Over the years, this revealing “Zurich Notebook” has been dissected and analyzed by a team of scholars including Jürgen Renn, John D. Norton, Tilman Sauer, Michel Janssen, and John Stachel.17 In it Einstein pursued a two-fisted approach. On the one hand, he engaged in what was called a “physical strategy,” in which he tried to build the correct equations from a set of requirements dictated by his feel for the physics. At the same time, he pursued a “mathematical strategy,” in which he tried to deduce the correct equations from the more formal math requirements using the tensor analysis that Grossmann and others recommended.

Therein lies the key, I think, to Einstein’s brilliance and the lessons of his life. As a young student he never did well with rote learning. And later, as a theorist, his success came not from the brute strength of his mental processing power but from his imagination and creativity. He could construct complex equations, but more important, he knew that math is the language nature uses to describe her wonders. So he could visualize how equations were reflected in realities—how the electromagnetic field equations discovered by James Clerk Maxwell, for example, would manifest themselves to a boy riding alongside a light beam. As he once declared, “Imagination is more important than knowledge.”6

Many people who celebrate the arts and the humanities, who applaud vigorously the tributes to their importance in our schools, will proclaim without shame (and sometimes even joke) that they don’t understand math or physics. They extoll the virtues of learning Latin, but they are clueless about how to write an algorithm or tell BASIC from C++, Python from Pascal. They consider people who don’t know Hamlet from Macbeth to be Philistines, yet they might merrily admit that they don’t know the difference between a gene and a chromosome, or a transistor and a capacitor, or an integral and a differential equation. These concepts may seem difficult. Yes, but so, too, is Hamlet. And like Hamlet, each of these concepts is beautiful.

He would have to keep her, somehow, and that would mean solving her. That would mean making her his impossible problem. Time travel no longer held any interest for him, only Regan and whatever it would take to make her a fixture in his life. Knowing her would mean knowing everything, not just her thoughts or her truths or the way she liked to be fucked. Knowing her would mean knowing her future, having it for himself. It was knowing what her children would look like, and what she would look like someday, when the youth was gone from her face and replaced by something else; by what? A mystery. It was a fucking mystery and Aldo couldn’t sit idly by while there were mysteries afoot. Uncertainty was something he lived with, yes, but not anymore. Frustration and restraint, she had said, equating his love of math with his love of her. I am Atlas, he thought, holding up the heavens. I will be endurance, I will have to endure.

The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math.

Einstein was distrustful of elaborate mathematics, odd as that sounds for a mathematical physicist. There was, Einstein considered, too much math around, and one could waste far too much time on it. His talent, despite the image in popular culture, lay not so much in mathematics – which he always found difficult – but in exceptional clarity of conceptual thinking. Einstein was never seduced by the easy flow of equations: he came to the hard labor of the math only when convinced the quest would be worth the effort.

Take a look at the following list of numbers: 4, 8, 5, 3, 9, 7, 6. Read them out loud. Now look away and spend twenty seconds memorizing that sequence before saying them out loud again. If you speak English, you have about a 50 percent chance of remembering that sequence perfectly. If you're Chinese, though, you're almost certain to get it right every time. Why is that? Because as human beings we store digits in a memory loop that runs for about two seconds. We most easily memorize whatever we can say or read within that two-second span. And Chinese speakers get that list of numbers—4, 8, 5, 3, 9, 7, 6—right almost every time because, unlike English, their language allows them to fit all those seven numbers into two seconds. That example comes from Stanislas Dehaene's book The Number Sense. As Dehaene explains: Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is "si" and 7 "qi"). Their English equivalents—"four," "seven"—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits. It turns out that there is also a big difference in how number-naming systems in Western and Asian languages are constructed. In English, we say fourteen, sixteen, seventeen, eighteen, and nineteen, so one might expect that we would also say oneteen, twoteen, threeteen, and five- teen. But we don't. We use a different form: eleven, twelve, thirteen, and fifteen. Similarly, we have forty and sixty, which sound like the words they are related to (four and six). But we also say fifty and thirty and twenty, which sort of sound like five and three and two, but not really. And, for that matter, for numbers above twenty, we put the "decade" first and the unit number second (twentyone, twenty-two), whereas for the teens, we do it the other way around (fourteen, seventeen, eighteen). The number system in English is highly irregular. Not so in China, Japan, and Korea. They have a logical counting system. Eleven is ten-one. Twelve is ten-two. Twenty-four is two- tens-four and so on. That difference means that Asian children learn to count much faster than American children. Four-year-old Chinese children can count, on average, to forty. American children at that age can count only to fifteen, and most don't reach forty until they're five. By the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills. The regularity of their number system also means that Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-yearold to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37+22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tensseven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It's five-tens-nine. "The Asian system is transparent," says Karen Fuson, a Northwestern University psychologist who has closely studied Asian-Western differences. "I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there's a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it's sensible. For fractions, we say three-fifths. The Chinese is literally 'out of five parts, take three.' That's telling you conceptually

In the online math class, there was almost no meaningful student/teacher or student/student interaction. To equate this type of online learning with a real-world classroom experience is a major stretch.

It’d be quite absurd to equate a math equation with love. But that is exactly what I’ve done. I’m giving a four-hour lecture on it on Friday night. Can I count you among the attendees?

The most important pillar behind innovation and opportunity—education—will see tremendous positive change in the coming decades as rising connectivity reshapes traditional routines and offers new paths for learning. Most students will be highly technologically literate, as schools continue to integrate technology into lesson plans and, in some cases, replace traditional lessons with more interactive workshops. Education will be a more flexible experience, adapting itself to children’s learning styles and pace instead of the other way around. Kids will still go to physical schools, to socialize and be guided by teachers, but as much, if not more, learning will take place employing carefully designed educational tools in the spirit of today’s Khan Academy, a nonprofit organization that produces thousands of short videos (the majority in science and math) and shares them online for free. With hundreds of millions of views on the Khan Academy’s YouTube channel already, educators in the United States are increasingly adopting its materials and integrating the approach of its founder, Salman Khan—modular learning tailored to a student’s needs. Some are even “flipping” their classrooms, replacing lectures with videos watched at home (as homework) and using school time for traditional homework, such as filling out a problem set for math class. Critical thinking and problem-solving skills will become the focus in many school systems as ubiquitous digital-knowledge tools, like the more accurate sections of Wikipedia, reduce the importance of rote memorization. For children in poor countries, future connectivity promises new access to educational tools, though clearly not at the level described above. Physical classrooms will remain dilapidated; teachers will continue to take paychecks and not show up for class; and books and supplies will still be scarce. But what’s new in this equation—connectivity—promises that kids with access to mobile devices and the Internet will be able to experience school physically and virtually, even if the latter is informal and on their own time.

It was like solving a misleading math equation, suddenly it all made perfect sense...

Our equation should not be that math is hard, and so programming is hard. Rather, it should be that programming can be fun, and this means that math can be fun, too.