Algebra Math Quotes

What music is to the heart, mathematics is to the mind.

Talk about getting off tangent. My mother's friend may have just killed his wife and my parents are sitting there talking about cows.

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.

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

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing. [Statement of the second law of thermodynamics, 1862]

Remember those old math questions you had in algebra class? Where water is entering a container at a certain rate and leaving at a different rate and you need to figure out when it’ll be empty? Well, that concept is critical to the “Mark Watney doesn’t die” project I’m working on.

What to Do During Algebra O what to do during Algebra! The possibilities are limitless: There's drawing, and yawning, and portable chess There's dozing, and dreaming, and feeling confused. There's humming, and strumming, and looking bemused. You can stare at the clock. You can hum a little song. I've tried just about everything to pass the time along.

Mathematics is the science which draws necessary conclusions.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.

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

Maths is at only one remove from magic.

He doesn't seem to mind at all that he's stupid about math.

If other people thought art was important, then it would be required to graduate. But no, I don’t have to take art. I do have to take math, which is just a waste of time because the numbers get all switched up in my brain, plus, calculators exist for a reason. I do have to take history, which is basically memorizing tariff acts till your brain bleeds. I do have to take four years of gym class with a bunch of jerks who punch me if they don’t like what I say. But art? Optional. Even though art and music and literature and all that are what make us human. Algebra doesn’t make us human. Games don’t make us human.

Ode to Algebra Thrust into this dingy classroom we die like lampless moths locked into the desolation of fluorescent lights and metal desks. Ten minutes until the bell rings. What use is the quadratic formula in our daily lives? Can we use it to unlock the secrets in the hearts of those we love? Five minutes until the bell rings. Cruel Algebra teacher, won't you let us go?

Who cares for Algebra? Who delights in solving math? I only want to live my life Along the creative path.

I don't see how it's doing society any good to have it's members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

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.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...

In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie.

To a scholar, mathematics is music.

If you are smart enough to add letters to math problems, you're smart enough to dig your own grave.

What was your job back on Earth? I’ve always been curious. I taught eighth-grade math in Tallahassee. Huh, I said. That’s not what I expected. Are you kidding? Powell said back. You try teaching algebra to a bunch of little shitheads for thirty-eight years straight. The way I figure it I’ve got about another decade before my rage from that gets entirely burned up.

For those with a math allergy, my duck soup may contain Algebra. 2X=2, solve for X, may cause an extreme reaction. Ask your doctor if BearPaw Duck Farm's SwimmingBird Soup is right for you.

remedial work needed? It often is. In my introductory political science classes, I encounter far too many students who cannot write coherently. I would like to think this is being remedied in composition courses, since without that competence they can’t do college-level work. But it’s quite another thing to say that all undergraduates need advanced algebra to proceed toward their degrees.

If you hate math and English, then you’ll really hate Algebra, with its numbers and letters, because it combines BOTH. To survive in life you must pivot, which is why I'm now tutoring at Used Duck Prices.

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).

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward. When you’re asked to solve

Weight Watchers points is a beautiful system for someone who is absentminded about food. They aren’t the greatest for someone who has had eating disorders all her life. The world became numbers to me and I was doing more math than I ever had before. I got off Weight Watchers and went back to just counting calories. The world became different kinds of numbers, the old, familiar kind. This is how I eat now. The world is still numbers, but it is algebra, not calculus.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

I had to do a whole entire two page--both front side and back--of exponets. finding the product and finding the quotient. My brain has never stopped functioning that quick in the span of one second. Didn't even need to pick up the pencil, the paper(s) itself sparked fear into my soul

C-minus in algebra; A plus in coolology. See, popularity is complicated, yo. You have to spend a lot of time thinking about liking; you have to really like being liked, and also sorta like being disliked." And reason three," Lindsey said, "is I gotta teach you how to shoot so you don't embarass yourself." "Shoot a gun"? A shotgun. I put one in your trunk this afternoon." Colin nervously glanced toward the back.

In a parallel universe, I’m still at Browick. I have another single in Gould, bigger this time, with more natural light. Instead of chemistry, U.S. history, and algebra, I take courses in stellar astronomy, the sociology of rock and roll, the art of math. I have a directed reading with Strane and we meet in the afternoons, in his office, to talk about the books he tells me to read. Thoughts flow from him straight into me, our brains and bodies connected.

Let us wonder, Carole, at the genius of hyperbolic geometry, where the sum of the angles adds up to tales than 180 degrees Let us wonder at how the ancient Egyptians worked out how to measure an irregularly-shaped field Let us wonder how X was just a rare letter until algebra came along and made it something special that can be unraveled to reveal its inner value You see, maths is a process of discovery, Carole, it is like the exploration of space, the planets were always there, it just took us a long time to find them

Tell me this- if you could have a guarantee that your child would be a National Merit Scholar and get into a prestigious college, have good work habits and a successful career, but that your relationship with him would be destroyed in the process, would you do it? Why not? Because you are made to love, that's why. We care about our relationships more than about our accomplishments. That's the way God made us. Then why don't we live that way? Why, come a damp and gloomy day in March, do we yell over a  math lesson or lose our temper over a writing assignment? Why do we see the lessons left to finish and get lost in an anxiety-ridden haze? We forget that we are dealing with a soul, a precious child bearing the Image of God, and all we can see is that there are only a few months left to the school year and we are still only halfway through the math book. When you are performing mommy triage- that is, when you have a crisis moment and have to figure out which fire to put out first- always choose your child. It's just a math lesson. It's only a writing assignment. It's a Latin declension. Nothing more. But your child? He is God's. And the Almighty put him in your charge for relationship. Don't damage that relationship over something so trivial as an algebra problem. And when you do (because you will, and so will I), repent. We like to feed our egos. When our children perform well, we can puff up with satisfaction and pat ourselves on the back for a job well done. But as important as it is to give our children a solid education (and it is important, don't misunderstand me), it is far more important that we love them well.  Our children need to know that the most important thing about them is not whether they finished their science curriculum or score well on the SAT. Their worth is not bound up in a booklist or a test score. Take a moment. Take ten. Look deep into your child's eyes. Listen, even when you're bored. Break out a board game or an old picture book you haven't read in ages. Resting in Him means relaxing into the knowledge that He has put these children in our care to nurture. And nurturing looks different than charging through the checklist all angst-like. Your children are not ordinary kids or ordinary people, because there are no ordinary kids or ordinary people. They are little reflections of the

Albert Einstein, considered the most influential person of the 20th century, was four years old before he could speak and seven before he could read. His parents thought he was retarded. He spoke haltingly until age nine. He was advised by a teacher to drop out of grade school: “You’ll never amount to anything, Einstein.” Isaac Newton, the scientist who invented modern-day physics, did poorly in math. Patricia Polacco, a prolific children’s author and illustrator, didn’t learn to read until she was 14. Henry Ford, who developed the famous Model-T car and started Ford Motor Company, barely made it through high school. Lucille Ball, famous comedian and star of I Love Lucy, was once dismissed from drama school for being too quiet and shy. Pablo Picasso, one of the great artists of all time, was pulled out of school at age 10 because he was doing so poorly. A tutor hired by Pablo’s father gave up on Pablo. Ludwig van Beethoven was one of the world’s great composers. His music teacher once said of him, “As a composer, he is hopeless.” Wernher von Braun, the world-renowned mathematician, flunked ninth-grade algebra. Agatha Christie, the world’s best-known mystery writer and all-time bestselling author other than William Shakespeare of any genre, struggled to learn to read because of dyslexia. Winston Churchill, famous English prime minister, failed the sixth grade.

Homework _Yes _No 1. Did you make a serious effort to understand the text? (Just hunting for relevant worked-out examples doesn’t count.) _Yes _No 2. Did you work with classmates on homework problems, or at least check your solutions with others? _Yes _No 3. Did you attempt to outline every homework problem solution before working with classmates? Test Preparation The more “Yes” responses you recorded, the better your preparation for the test. If you recorded two or more “No” responses, think seriously about making some changes in how you prepare for the next test. _Yes _No 4. Did you participate actively in homework group discussions (contributing ideas, asking questions)? _Yes _No 5. Did you consult with the instructor or teaching assistants when you were having trouble with something? _Yes _No 6. Did you understand ALL of your homework problem solutions when they were handed in? _Yes _No 7. Did you ask in class for explanations of homework problem solutions that weren’t clear to you? _Yes _No 8. If you had a study guide, did you carefully go through it before the test and convince yourself that you could do everything on it? _Yes _No 9. Did you attempt to outline lots of problem solutions quickly, without spending time on the algebra and calculations? _Yes _No 10. Did you go over the study guide and problems with classmates and quiz one another? _Yes _No 11. If there was a review session before the test, did you attend it and ask questions about anything you weren’t sure about? _Yes _No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.) _Yes _No TOTAL

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward.

My name is Charlie Chucky, I am in the sixth grade, I love playing Minecraft, and I am learning to become a Super Spy. My Dad is the world’s best Super Spy, and he is starting to teach me all his tricks. Lately, I’ve been battling invisible giants, crazy zombie teachers, and super ninjas! Life has been pretty crazy, and I’ve enjoyed every second of it. My best friend Harley is different to me. He doesn’t want to become a Super Spy. He doesn’t want to battle bad guys and save the world each week. Nope. He wants to sit indoors and stare at numbers all day. Harley’s dream is to become the world’s greatest math professor. He loves school, he loves studying, and he absolutely loves math tests.  He goes mad for them. It is the one thing he is really good at. He just loves numbers.  Numbers are like candy for him – he can’t get enough of it. He even asked Mrs. Jackson for extra math homework last night. Mrs. Jackson then decided to give the whole class extra math homework. Let’s just say Harley wasn’t that popular after school.  This is Harley. Mrs. Jackson always says that someday math will save our lives, but I can’t see how it will. Maybe one day, four giant numbers will attack our school, and I will defeat them using an algebra equation… or maybe the numbers in my textbook will go bad, and start attacking all the words on the pages, and I will stop them using a calculator!

Mathematics is not just a subject of education system, it is the soul of education system.

algebra. Once you fill in the blanks you have, you’ll go on to hold your own in any college math course. Maybe you won’t test out of the intro classes, but who cares about that? Universities want to train you in their style, anyway.

But it gradually dawned on her that she wasn’t an idiot. Not totally. In math and science, yes. But in the realm of creative thinking, she came to realize she was a sighted person in the kingdom of the blind. Because as much as she seemed unable to process algebra and geometry, she was a savant when it came to pure creativity. And not just in graphic design. In everything. Coming up with ideas for the company picnic. Throwing parties. Wording invitations. Writing poetry. She came to be thought of as a one-woman idea machine. The kind who could take four or five mundane office items and turn them into fifteen different stunning decorations. And she could figure out the most complex fictional mysteries. She was almost always able to see the coming plot twists, even when those who excelled at academics missed them entirely. So maybe she did have a different style of intellect. She thought her self-esteem had become off the charts high, but Hall’s offhanded remark had shown her that the scars of her early struggles in school still remained, as did deep-seated doubts.

My junior year, I tested into the honors Advanced Math class—a hybrid of trigonometry, advanced algebra, and pre-calculus. The class’s instructor, Ron Selby, enjoyed legendary status among the students for his brilliance and high demands. In twenty years, he had never missed a day of school. According to Middletown High School legend, a student called in a bomb threat during one of Selby’s exams, hiding the explosive device in a bag in his locker. With the entire school evacuated outside, Selby marched into the school, retrieved the contents of the kid’s locker, marched outside, and threw those contents into a trash can. “I’ve had that kid in class; he’s not smart enough to make a functioning bomb,” Selby told the police officers gathered at the school. “Now let my students go back to class to finish their exams.

Chris Argyris, professor emeritus at Harvard Business School, wrote a lovely article in 1977,191 in which he looked at the performance of Harvard Business School graduates ten years after graduation. By and large, they got stuck in middle management, when they had all hoped to become CEOs and captains of industry. What happened? Argyris found that when they inevitably hit a roadblock, their ability to learn collapsed: What’s more, those members of the organization that many assume to be the best at learning are, in fact, not very good at it. I am talking about the well-educated, high-powered, high-commitment professionals who occupy key leadership positions in the modern corporation.… Put simply, because many professionals are almost always successful at what they do, they rarely experience failure. And because they have rarely failed, they have never learned how to learn from failure.… [T]hey become defensive, screen out criticism, and put the “blame” on anyone and everyone but themselves. In short, their ability to learn shuts down precisely at the moment they need it the most.192 [italics mine] A year or two after Wave, Jeff Huber was running our Ads engineering team. He had a policy that any notable bug or mistake would be discussed at his team meeting in a “What did we learn?” session. He wanted to make sure that bad news was shared as openly as good news, so that he and his leaders were never blind to what was really happening and to reinforce the importance of learning from mistakes. In one session, a mortified engineer confessed, “Jeff, I screwed up a line of code and it cost us a million dollars in revenue.” After leading the team through the postmortem and fixes, Jeff concluded, “Did we get more than a million dollars in learning out of this?” “Yes.” “Then get back to work.”193 And it works in other settings too. A Bay Area public school, the Bullis Charter School in Los Altos, takes this approach to middle school math. If a child misses a question on a math test, they can try the question again for half credit. As their principal, Wanny Hersey, told me, “These are smart kids, but in life they are going to hit walls once in a while. It’s vital they master geometry, algebra one, and algebra two, but it’s just as important that they respond to failure by trying again instead of giving up.” In the 2012–2013 academic year, Bullis was the third-highest-ranked middle school in California.194

The Fundamental Theorem of Algebra If is a polynomial of degree , then has at least one zero in the complex number domain. In other words, there is at least one complex number such that .

Arithmetic numbers are merely algebraic general expression wherein x stands for 10 (Example- 351 = 3* x^2 + 5x +1 where x=10) is simple intuition (?) which is used by 'Father of Vedic math' to simplify basic operation. Those who want to advance 'Vedic math', should use it fully

This queer crotchet [of Hamilton's] that algebra is the science of pure time has attracted many philosophers, and quite recently it has been exhumed and solemnly dissected by owlish metaphysicians seeking the philosopher's stone in the gall bladder of mathematics.

There! I think it's another zombie." Off in the distance, we could see someone, or something, approaching at the edge of the parking lot. "I can't tell, hold on. I've got a pair of binoculars." I leaned inside, where we'd piled our supplies. "Well?" asked Misty. I adjusted the focus. "It's a zombie." "Are you sure? He doesn't look dead—maybe just a little pale." "Look for yourself, you'll see." I handed them to her and spit in disgust. "I can't see his eyes. He might be alive." "You don't recognize him?" "No, do you?" "It's Mr. Lopez. Teaches—well, taught Math," I said, rubbing my forehead. "Oh my gosh, you're right. How could I have forgotten?" Mr. Lopez had died of a heart attack last week while trying to teach Geometry in summer school—probably enough to kill anyone. It had been in the paper and on the local news. "You had his class last year, didn't you?" "Yeah, Pre-Algebra, hated it. It's just wrong to teach kids algebra. Still, to see him standing there...

My math teacher sucked as a kid in school. I'd ask him why do you do the problem that way and he would say "because the book says to do it." Later I learned algebra and advanced calculus because a guy explained the application to me. I now know that “If you can't explain it to a six-year-old, you don't understand it yourself.

You’re still concentrating, right?” BT asked to my retreating back. “Yes I’m still concentrating, Mrs. Weinstedder.” “What?” “Nothing, just my old algebra teacher.” “So somehow this whole scene reminded you of an old math teacher? Who did the wiring in your head? Because you should get your deposit back.

even the formidable deputy seemed lost for words – or was saving them for later. Maths followed a similar pattern. While the others struggled over algebra, Janet spent the first half of the lesson hidden behind her ponytail of tangled hair – ‘looking for split ends,’ she explained to Edie afterwards – until Mr Robinson, a nervous young teacher who had joined the school the previous term, invited her to come to the front of the class and write an answer to the question he had just chalked up on the board. ‘Why are you picking on me?’ Janet asked sulkily. ‘Because I don’t think you’ve been paying attention,’ Mr Robinson replied. Janet scraped back her chair, and walked to the front of the class with her shoulders swaying. ‘What’s the point trying to work out the answer when the question doesn’t make sense?’ she said, and proceeded to insert a missing bracket into Mr Robinson’s equation. ‘That was awesome,’ said Belinda later, over tea. ‘He looked so embarrassed! Oh, Janet, you should have seen him when you were walking back to your desk – his face was like strawberry jam!’ ‘I felt sorry for him,’ said Anastasia. ‘He’s so shy, and sometimes I think he’s frightened of us. Do you remember that time he was on supper duty last term and

Mathiness: British economic journalist John Kay defines mathiness as a “use of algebraic symbols and quantitative data to give an appearance of scientific content to ideological preconceptions.” Expressing an idea in mathematical symbols instead of straightforward literary terms helps legitimize it in the minds of many people, thanks to a seeming similarity with natural science. In this respect math is basically a form of numerical rhetoric. “The American economist Paul Romer has recently written of ‘mathiness,’ by analogy with ‘truthiness,’ a term coined by American talk show host Stephen Colbert. Truthiness presents narratives which are not actually true, but consistent with the world view of the person who spins the story. It is exemplified in rightwing fabrications about European health systems – their death panels and forced euthanasia.” Paul Samuelson, for instance, trivialized economics in terms that give the outward appearance of science by being expressed mathematically, even when its assumptions are purely hypothetical (and not all realistic)and there are no quantitative statistics to illustrate its categories.

Dear Algebra, Stop intimidating me! You know I don't have a math's brain

By convention, I have been taught to isolate the variables on the left side and the constants on the right But you still have that characteristic freewill of wallowing in the abstraction of algebra You could also isolate the variables on the right side and the constants on the left.

Your equation—your choice! You could do whatever you want with an equation— just as long as it’s done on both sides!

You cannot read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast.

You cannot read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast.

Understanding develops slowly.

The customary units of measurement? They have practical applications, but learning them is mostly done through rote memorization— There aren’t any proofs or critical evaluations regarding REASONS why a foot equals twelve inches There are only facts to memorize, but not puzzles to solve, With algebra—YES! There isn’t just memorization— There is the rearrangement of jigsaw pieces— jigsaw pieces that you can solve, not just memorize!

The fact of zero He added nonstop: Did you know that zero was not used throughout human history! Until 781 A.D, when it was first embodied and used in arithmetic equations by the Arab scholar Al-Khwarizmi, the founder of algebra. Algorithms took their name from him, and they are algorithmic arithmetic equations that you have to follow as they are and you will inevitably get the result, the inevitable result. And before that, across tens and perhaps hundreds of thousands of years, humans refused to deal with zero. While the first reference to it was in the Sumerian civilization, where inscriptions were found three thousand years ago in Iraq, in which the Sumerians indicated the existence of something before the one, they refused to deal with it, define it and give it any value or effect, they refused to consider it a number. All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect. Like the wrong frame of reference, if you rely on it, you will inevitably get a wrong result, and you will fall into the inevitability of error, and if you ignore it, your chance of getting it right remains. Throughout their history, humans have preferred to ignore zero, not knowing its true impact, while we simply decided to deal with it, and even rely on it. Today we build all our ideas, our civilization, our software, mathematics, physics, everything, on the basis that 1 + 0 equals one, because we need to find the effect of zero so that our equations succeed, and our lives succeed with, but what if 1 + 0 equals infinity?! Why did we ignore the zero in summation, and did not ignore it in multiplication?! 1×0 equals zero, why not one? What is the reason? He answered himself: There is no inevitable reason, we are not forced. Humans have lived throughout their ages without zero, and it did not mean anything to them. Even when we were unable to devise any result that fits our theorems for the quotient of one by zero, then we admitted and said unknown, and ignored it, but we ignored the logic that a thousand pieces of evidence may not prove me right, and one proof that proves me wrong. Not doing our math tables in the case of division, blowing them up completely, and with that, we decided to go ahead and built everything on that foundation. We have separated the arithmetic tables in detail at our will, to fit our calculations, and somehow separate the whole universe around us to fit these tables, despite their obvious flaws. And if we decide that the result of one multiplied by zero is one instead of zero, and we reconstruct the whole world on this basis, what will happen? He answered himself: Nothing, we will also succeed, the world, our software, our thoughts, our dealings, and everything around us will be reset according to the new arithmetic tables. After a few hundred years, humans will no longer be able to understand that one multiplied by zero equals zero, but that it must be one because everything is built on this basis.

This reminds me of an old story from the Harvard math department, concerning one of the grand old Russian professors, whom we shall call O. Professor O is midway through an intricate algebraic derivation when a student in the back row raises his hand. “Professor O, I didn’t follow that last step. Why do those two operators commute?” The professor raises his eyebrows and says, “Eet ees obvious.” But the student persists: “I’m sorry, Professor O, I really don’t see it.” So Professor O goes back to the board and adds a few lines of explanation. “What we must do? Well, the two operators are both diagonalized by . . . well, it is not exactly diagonalized but . . . just a moment . . .” Professor O pauses for a little while, peering at what’s on the board and scratching his chin. Then he retreats to his office. About ten minutes go by. The students are about to start leaving when Professor O returns, and again assumes his station in front of the chalkboard. “Yes,” he says, satisfied. “Eet ees obvious

In 1958, Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory,

The modulus (%) and the floor division (//) operations are not valid for complex numbers.

I headed back to university to study engineering. I started at the lowest possible level of math—algebra for people who had failed it in high school.

When you do the math problems at the back of a chapter in an algebra textbook, you are problem solving. If the chapter is entitled “Systems of two equations with two unknowns,” you know exactly which methods to use. In such a constrained situation, the pertinent context in which to view the problem has already been determined, so there is no effort of interpretation required. But in the real world, problems don’t present themselves in this predigested way; usually there is too much information, and it is difficult to know what is pertinent and what isn’t.

There are smart people and wise people. Smart people can tutor you in English or help you with math. Wise people teach you about life. It’s best if you have both smart and wise people in your circle. That’s not the case for me. That’s why I flunked algebra, but I know it’s possible and sane to love a broken mother.

Probably you are discouraged by this solution because it seems impossible to invent it. The authors share your feeling.