Math Majors Quotes

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.

The vast majority of us imagine ourselves as like literature people or math people. But the truth is that the massive processor known as the human brain is neither a literature organ or a math organ. It is both and more.

It surprised him that his grief was sharper than in the past few days. He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big pile of garden rubbish full both of heavy lumps of dirt and of sharp thorny brush that would stab him when he least expected it.

Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too try, philosophy too difficult, geology too petroleum-oriented, and math too mathematical - because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

Nora, what’s the math?” June says, rounding on her, a slightly frantic look in her eyes. “I majored in nouns.

Matt laughed. "Close. That was last year. This year it's Obsessive Deovtion to Fourier Analysis Theory and Applications. And my personal favorite, Quantum Physics II: Romantic Entanglements of Energy and Matter." Julie turned her head to Matt. "You're a double major? Physics and math? Jesus..." "I know. Nerdy." He shrugged. "No, I'm impressed. I'm just surprised your brains fit in your head." "I was fitted with a specially desinged compression filter that allows excessive information to lie dormant until I need to access it. It's only the Beta version, so excuse any kinks that may appear. I really can't be held responsible.

Before the work of Georg Cantor in the nineteenth century, the study of the infinite was as much theology as science; now, we understand Cantor’s theory of multiple infinities, each one infinitely larger than the last, well enough to teach it to first-year math majors. (To be fair, it does kind of blow their minds.)

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

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.

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchhoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.

Mostly, though, students get what economist Bryan Caplan called narrow vocational training for jobs few of them will ever have. Three-quarters of American college graduates go on to a career unrelated to their major—a trend that includes math and science majors—after having become competent only with the tools of a single discipline. One good tool is rarely enough in a complex, interconnected, rapidly changing world. As the historian and philosopher Arnold Toynbee said when he described analyzing the world in an age of technological and social change, “No tool is omnicompetent.” •

One whose testimony made a major impact more than a decade ago is Ben Barres, formerly Barbara Barres, a biologist at Stanford University. In 2006, he wrote in the journal Nature about the bias he had experienced as a woman in the sciences, from losing fellowships to less qualified male candidates to being told a boyfriend must have helped her with her math. He was told that he was smarter than his sister by a man who confused his former, female self for that sister. (“A Short History of Silence”)

And yet sometimes she worried about what those musty old books were doing to her. Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too dry, philosophy too difficult, geology too petroleum-oriented, and math too mathematical--because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

Joanna gave me a leveling look. "You think we're the only major that's superinsular and clique-ish and gossips about everyone else in it? Believe me, if Nathan bought a new brand of toothpaste, those math nerds probably already know about it.

...a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too dry, philosophy too difficult, geology too petroleum-oriented, and math too mathematical--because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child's math book. Instead, it was almost as if his body contained a big like of garden rubbish full both of heavy lumps of dirt and of harp thorny brush that would stab him when he least expected it.

Whatever laws we make mixing religion with government for the sake of appeasing our (currently) predominantly Christian constituency will only pave the way for the next religious majority, who will take advantage of whatever permissions we've already established and which we thought were harmless enough at the time. Christians very often have no concept of the value of a secular government, until or unless they understand that they won't always hold the majority. Once they realize that their religion is in a general state of decline even in this country and that the fastest growing religion globally is Islam, then the math isn't very hard to work out.

This is one of the reasons science has made such dramatic progress. An undergraduate science major today knows more about science and math than did Sir Isaac Newton, one of the most renowned scientists who ever lived. Even in this introductory astronomy course, you will learn about objects and processes that no one a few generations ago even dreamed existed.

Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques. I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.

It surprised him that his grief was sharper than in the past few days. He had forgotten that grief does not decline in a straight line or along a slow curve like a graph in a child’s math book. Instead, it was almost as if his body contained a big pile of garden rubbish full both of heavy lumps of dirt and of sharp thorny brush that would stab him when he least expected it.

A third positive result even further from the traditional tool kit of financial incentives comes from a recent randomized control trial conducted in the U.K., using the increasingly popular and low-cost method of text reminders. This intervention involved sending texts to half the parents in some school in advance of a major math test to let them know that their child had a test coming up in five days, then in three days, then in one day. The researchers call this approach “pre-informing.” The other half of parents did not receive the texts. The pre-informing texts increased student performance on the math test by the equivalent of one additional month of schooling, and students in the bottom quartile benefited most. These children gained the equivalent of two additional months of schooling, relative to the control group. Afterward, both parents and students said they wanted to stick with the program, showing that they appreciated being nudged. This program also belies the frequent claim, unsupported by any evidence, that nudges must be secret to be effective.

strategy of kaizen, which is Japanese for “continuous improvement” and which just as easily could be called corporate deep practice. Kaizen is the process of finding and improving small problems. Each employee, from the janitor on up, has authority to halt the production line if they spot a problem. (Each factory has pull cords on the factory floor, called andons.) The vast majority of improvements come from employees, and the vast majority of those changes are small: a one-foot shift in the location of a parts bin, for instance. But they add up. It's

THE TRUTH ABOUT PUBLIC SCHOOL EDUCATION • American fifteen-year-olds rank thirty-fifth out of fifty-seven developed countries in math and literacy. • 30 percent of public school students don’t graduate from high school. • Every day, 7,000 kids drop out of high school. • Of the 50 million children currently in public school, 15 million of them will drop out. • 25 percent of all public school math teachers did not major in mathematics or a math-related subject at a college or university. • Less than two-thirds of high school graduates are accepted to college every year. • One half...

Q: What are in your eyes the major defects in the West? A: The West has come to regard the values of freedom, the yardstick of human rights, as something Western. Many of them [westerns] specially in Europe take the values and the institutions on freedom, the institutions on science, curiosity, the individual, i mean, the rule of law and they’ve come to take that all for granted that they are not aware of the threat against it and not aware of the fact that you have to sustain it day by day as with all man made things. I mean, a building for example, the roof will leak, the paint will fall and you have to repaint it, you have to maintain it all the time it seems that people have forgotten that and perhaps part of the reason is because the generation that is now enjoying all the freedoms in the West is not the generations that built it; these are generations that inherited and like companies, family companies, often you’ll see the first generation or the second generation are almost always more passionate about the brand and the family company and name and keeping it all int he family and then the third generation live, use, take the money and they are either overtaken by bigger companies, swallowed up or they go bankrupt and I think there is an analogy there in that the generations after the second world war living today in Europe, United States may be different but I’m here much too short to say anything about it, is that there are people who are so complacent, they’ve always been free, they just no longer know what it is that freedom costs and for me that would be making the big mistake and you can see it. The education system in Europe where history is no longer an obligatory subject, science is no longer an obligatory subject, school systems have become about, look at Holland, our country where they have allowed parents, in the name of freedom, to build their own schools that we now have schools founded on what the child wants so if the child wants to play all day long then that is an individual freedom of the child and so it’s up to the child to decide whether to do math or to clay and now in our country in Holland, in the name of freedom of education, the state pays for these schools and I was raving against muslim schools and i thought about this cuz i was like you know ok in muslin schools at least they learn to count.

Here are the basic principles of Constructivism as practiced by Kronecker and codified by J.H. Poincare and L.E.J. Brouwer and other major figures in Intuitionism: (1) Any mathematical statement or theorem that is more complicated or abstract than plain old integer-style arithmetic must be explicitly derived (i.e. 'constructed') from integer arithmetic via a finite number of purely deductive steps. (2) The only valid proofs in math are constructive ones, with the adjective here meaning that the proof provides a method for finding (i.e., 'constructing') whatever mathematical entities it's concerned with.

This need for me to settle somewhere, on something. To make some choices about my life. What is the life I've dreamed of? Growing up in America, when I was younger, I didn't see many kids who looked like me in books, in video games, on television. What I did see were stereotypes---good at math, studying, working hard. Narrow versions of myself. Now, my world has expanded. I can have things at the touch of my fingertips. But there are still rules to abide by. Princess rules. What I can do and can't. Like my major. I may choose it but within certain parameters. Does life always come with constraints? Is that part of growing up?

Deacon met my glare with an impish grin. “Anyway, did you celebrate Valentine’s Day when you were slumming with the mortals?” I blinked. “Not really. Why?” Aiden snorted and then disappeared into one of the rooms. “Follow me,” Deacon said. “You’re going to love this. I just know it.” I followed him down the dimly-lit corridor that was sparsely decorated. We passed several closed doors and a spiral staircase. Deacon went through an archway and stopped, reaching along the wall. Light flooded the room. It was a typical sunroom, with floor-to-ceiling glass windows, wicker furniture, and colorful plants. Deacon stopped by a small potted plant sitting on a ceramic coffee table. It looked like a miniature pine tree that was missing several limbs. Half the needles were scattered in and around the pot. One red Christmas bulb hung from the very top branch, causing the tree to tilt to the right. “What do you think?” Deacon asked. “Um… well, that’s a really different Christmas tree, but I’m not sure what that has to do with Valentine’s Day.” “It’s sad,” Aiden said, strolling into the room. “It’s actually embarrassing to look at. What kind of tree is it, Deacon?” He beamed. “It’s called a Charlie Brown Christmas Tree.” Aiden rolled his eyes. “Deacon digs this thing out every year. The pine isn’t even real. And he leaves it up from Thanksgiving to Valentine’s Day. Which thank the gods is the day after tomorrow. That means he’ll be taking it down.” I ran my fingers over the plastic needles. “I’ve seen the cartoon.” Deacon sprayed something from an aerosol can. “It’s my MHT tree.” “MHT tree?” I questioned. “Mortal Holiday Tree,” Deacon explained, and smiled. “It covers the three major holidays. During Thanksgiving it gets a brown bulb, a green one for Christmas, and a red one for Valentine’s Day.” “What about New Year’s Eve?” He lowered his chin. “Now, is that really a holiday?” “The mortals think so.” I folded my arms. “But they’re wrong. The New Year is during the summer solstice,” Deacon said. “Their math is completely off, like most of their customs. For example, did you know that Valentine’s Day wasn’t actually about love until Geoffrey Chaucer did his whole courtly love thing in the High Middle Ages?” “You guys are so weird.” I grinned at the brothers. “That we are,” Aiden replied. “Come on, I’ll show you your room.” “Hey Alex,” Deacon called. “We’re making cookies tomorrow, since it’s Valentine’s Eve.” Making cookies on Valentine’s Eve? I didn’t even know if there was such a thing as Valentine’s Eve. I laughed as I followed Aiden out of the room. “You two really are opposites.” “I’m cooler!” Deacon yelled from his Mortal Holiday Tree room

There are no single guys who don’t have at least one major flaw, and a flaw, I might add, that would stop you from dating them – even if everything else was great. Why? Simple math. Women are interesting and honest and sensitive. Most men are not. There is only one normal, decent single guy for every five women in this city. This is what’s known as the Great Male Statistic. Girls don’t want to face the GMS. They want to believe there’s someone for everyone. The truth hurts. You only start coming to terms with the GMS when you’re twenty-six or twenty-seven. It actually killed Sylvia Plath. She finally found this guy in grad school who she thought was so great, and she married him, and he cheated on her.

When you add in the US immigration processes encouraging a “brain drain” of elites from countries like China and India, the vast majority of the “academic success” we see when we think of Asian Americans is only available to wealthy, highly skilled immigrants who already have a high level of education, and their offspring—while only 17 percent of Pacific Islanders, 14 percent of Cambodian Americans, and 13 percent of Laotian and Hmong Americans have four-year college degrees,4 compared to 22 percent of black Americans and 15 percent of Hispanic Americans.5 The stereotype that Asian Americans naturally excel at math and science also discourages Asian American students from pursuing careers in the arts and humanities and keeps those who do pursue those careers from being taken seriously in their fields. A 2009 census report showed that under 15 percent of Asian American degree holders majored in the arts and humanities, less than any other racial or ethnic group in America.6

Brunelleschi’s successor as a theorist of linear perspective was another of the towering Renaissance polymaths, Leon Battista Alberti (1404 –1472), who refined many of Brunelleschi’s experiments and extended his discoveries about perspective. An artist, architect, engineer, and writer, Alberti was like Leonardo in many ways: both were illegitimate sons of prosperous fathers, athletic and good-looking, never-married, and fascinated by everything from math to art. One difference is that Alberti’s illegitimacy did not prevent him from being given a classical education. His father helped him get a dispensation from the Church laws barring illegitimate children from taking holy orders or holding ecclesiastical offices, and he studied law at Bologna, was ordained as a priest, and became a writer for the pope. During his early thirties, Alberti wrote his masterpiece analyzing painting and perspective, On Painting, the Italian edition of which was dedicated to Brunelleschi. Alberti had an engineer’s instinct for collaboration and, like Leonardo, was “a lover of friendship” and “open-hearted,” according to the scholar Anthony Grafton. He also honed the skills of courtiership. Interested in every art and technology, he would grill people from all walks of life, from cobblers to university scholars, to learn their secrets. In other words, he was much like Leonardo, except in one respect: Leonardo was not strongly motivated by the goal of furthering human knowledge by openly disseminating and publishing his findings; Alberti, on the other hand, was dedicated to sharing his work, gathering a community of intellectual colleagues who could build on each other’s discoveries, and promoting open discussion and publication as a way to advance the accumulation of learning. A maestro of collaborative practices, he believed, according to Grafton, in “discourse in the public sphere.” When Leonardo was a teenager in Florence, Alberti was in his sixties and spending much of his time in Rome, so it is unlikely they spent time together. Alberti was a major influence nonetheless.

At the same time, surveillance will change the very nature of insurance. Insurance is an industry, traditionally, that draws on the majority of the community to respond to the needs of an unfortunate minority. In the villages we lived in centuries ago, families, religious groups, and neighbors helped look after each other when fire, accident, or illness struck. In the market economy, we outsource this care to insurance companies, which keep a portion of the money for themselves and call it profit. As insurance companies learn more about us, they’ll be able to pinpoint those who appear to be the riskiest customers and then either drive their rates to the stratosphere or, where legal, deny them coverage. This is a far cry from insurance’s original purpose, which is to help society balance its risk. In a targeted world, we no longer pay the average. Instead, we’re saddled with anticipated costs. Instead of smoothing out life’s bumps, insurance companies will demand payment for those bumps in advance. This undermines the point of insurance, and the hits will fall especially hard on those who can least afford them.

He’s threatening the President of the United States if we take you into custody?” Creek asked, his thoughts apparently in order. “Actually, it would be more like a declaration of war on the US government, if you abduct me.” “He thinks he can take on the entire US military?” Creek asked, incredulous. “General, he’s a lot more powerful than I thought.  He’s way beyond demigod status, more like elder god.  He can appear anywhere, anytime. His claws cut through anything. Who knows what else he can do!” Roma said, looking at me for additional information. I shrugged.  Hell, I didn’t know what he could do.  Elder god? “Christian, you could have avoided capture or escaped, right?” Tanya asked. “Yeah,” I said. “Okwari knows this?” she asked. “Yeah, but see, here’s the thing.  He spent a thousand years as a slave in Hell.  I set him free.  His math is pretty simple.” It was quiet for a moment, except for the personnel trying to clean up the lobby.  “Major Deckert, how are you hooked up in all this?” the general asked, obviously acquainted with the security chief. “I work for Ms. Demidova, General,” he said, rocking back on his heels, hands clasped behind his back.  “For what it’s worth, General, in my opinion, I wouldn’t touch Gordon here with a four-mile pole.” “You think that monster could really fight the government?” Creek asked. “Hell, Sir, I was talking about my employer.” He waved in Tanya’s direction. “I didn’t even know that thing existed.  But nothing surprises me with Gordon around.” I gave him my best glare, but it just bounced right off.

Newell and Simon predicted that by 1970 computers would be capable of composing classical music, discovering important new mathematical theorems, and understanding and translating spoken language.

Shut up okay?” Lori stuck her tongue out at him. “I’m a math major.

with elements of artistry and creativity, workers are not interchangeable units of labor.

Brooks’s Law, states: “Adding manpower to a late software project makes it later.

had a girl in this class,” Corcoran said. “She was a horrible math student in fifth grade. She cried every Saturday when we did remedial stuff. Huge tears and tears.” At the memory, Corcoran got a little emotional himself. He looked down. “She just e-mailed us a couple weeks ago. She’s in college now. She’s an accounting major.

Our schools display an enormous bias in educating the mind rather than the whole person. We place major emphasis on reasoning, logic and math, with almost no concern for emotions, intuition and creativity. Our students become memorizing mimics and dull conformists, rather than exciting and feeling creators.

frustration has flared up over the Common Core initiative, involving the implementation of national reading and maths standards for primary and secondary school children. The Gates Foundation played a central role in bringing the standards to fruition. Spending over $233 million to back the standards, the foundation dispersed money liberally to both conservative and progressive interest groups. The two major teachers' unions, the National Education Association and the American Federation of Teachers, each received large donations, as did the US Chamber of Commerce. Gates himself suggested that a benefit of the standards is that they open avenues towards increasing digital learning. In 2014, Microsoft announced it was partnering with Pearson to load Pearson's Common Core classroom material onto Microsoft's Surface tablet. Previously, the iPad was the classroom frontrunner; the Pearson partnership helps to make Microsoft more competitive.

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.

With such an illustrious reputation, it would be easy to assume Einstein rarely made mistakes—but that is not the case. To begin with, his development was described as “slow,” and he was considered to be a below-average student.16 It was apparent from an early age that his way of thinking and learning was different from the rest of the students in his class. He liked working out the more complicated problems in math, for example, but wasn’t very good at the “easy” problems.17 Later on in his career, Einstein made simple mathematical mistakes that appeared in some of his most important work. His numerous mistakes include seven major gaffes on each version of his theory of relativity, mistakes in clock synchronization related to his experiments, and many mistakes in the math and physics calculations used to determine the viscosity of liquids.18 Was Einstein considered a failure because of his mistakes? Hardly. Most importantly he didn’t let his mistakes stop him. He kept experimenting and making contributions to his field. He is famously quoted as having said, “A person who never made a mistake never tried anything new.” What’s more, no one remembers him for his mistakes—we only remember him for his contributions.

Let’s be honest here too. Most working-age adults need between seven and nine hours per day, with the majority of those landing between seven and eight. Few people need less than six and a half hours per day, aside from a handful of genetic short sleepers who sleep short hours on weekends and vacations too. If you aren’t sure, aim for seven and a half hours and see how it goes. If you’re still crashing on weekends, you need more. If you wake up consistently before your alarm clock, you might need less. Calculate what time you need to be in bed in order to get this amount of sleep. This is a math problem. If you need to wake up at 6 a.m. on most weekday mornings, and you need seven and a half hours of sleep, then count back seven and a half hours. This gives you a 10:30 p.m. bedtime.

While the symptoms of CTE can include difficulty with math or memory, some common early symptoms also include disorientation, dizziness, headaches, irritability, outbursts of violent or aggressive behavior, confusion, speech abnormalities, and major depressive disorder (McKee, et al., 2009). A large number of CTE symptoms have very little to do with how “smart” you are, and CTE can make daily life or maintaining simple human relationships extremely difficult. A disproportionately large number of retired athletes with CTE commit suicide, including Chicago Bears defensive back Dave Duerson, who texted his family to ask that his brain be used for research into the disease before fatally shooting himself in the chest in 2011.

Critical Race Theorists have argued that math education is inherently racist, that the very notion of objective truth is rooted in white supremacy, and that Western values—moral standards, in particular—are tools of oppression. According to CRT, every major aspect of our culture is riddled with racism.

IT POPS, A new discovery, by: Jonathan Roy Mckinney IT POPS is relative to space time in that it has two major components that follow the 3 laws of thermodynamics. The PIrandom creator injects an object with the relative XYZ coordinates in a model view projection that are derived by utilizing the correct Matrix math 11,10,10,10. Once Injected, the two way hash coin creator in time will create the entropy required to derive random shapes and reverse or abstract them into full objects for a complete wire frame like Michaelangelo could carve an Angel out of marble.

I narrowed my eyes. I couldn't understand anything. Has math changed since I graduated from high school? These weird alien symbols look nothing like math to me. “Sorry...I can't help you with this...” “Ehhhh? I thought you studied this before!” “That was ten years ago. After high school everybody forgets this stuff.” “And you went to university too!” “After high school no one ever uses these weird formulas. In university most students never touch math again, unless it is part of their major.

I’m a numbers guy. I was a math major at UConn back in the day.” He pumps a fist. “Go Huskies!

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. ....A relationship is dynamic this way, full of change always evolving. At no point will both of you feel like things are perfectly fair and equal, someone will always be adjusting, someone will always be sacrificing, one person may be up while the other is down. One might bear more of the financial pressures while the other bears caregiving and family obligations. Those choices and the stresses that go along with them are real. I've come to realized though that life happens in seasons. Your fulfillment in love, family and career rarely happens all at once. In a strong partnership both people will take turns at compromise building a shared sense of home together, there in the in-between, regardless of how wildly and deeply in love you are, you will be asked to onboard a lot of your partners foibles, you will be required to ignore all minor irritations and a few major ones too...

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. ....A relationship is dynamic this way, full of change always evolving. At no point will both of you feel like things are perfectly fair and equal, someone will always be adjusting, someone will always be sacrificing, one person may be up while the other is down. One might bear more of the financial pressures while the other bears caregiving and family obligations. Those choices and the stresses that go along with them are real. I've come to realized though that life happens in seasons. Your fulfillment in love, family and career rarely happens all at once. In a strong partnership both people will take turns at compromise building a shared sense of home together, there in the in-between, regardless of how wildly and deeply in love you are, you will be asked to onboard a lot of your partners foibles, you will be required to ignore all minor irritations and a few major ones too...

In the largest and most thorough analyses to date, with the sample of more than one million people and comparisons of 124 possible gender differences, Hyde found that 78 percent of the studies found either nonexistent or very few gender differences. In other words, the vast majority of studies conducted to look for differences between males and females found, in fact, no or very few differences. This is ironic because most of these studies were looking for gender differences in those areas where we are most likely to think we are different, such as emotions, verbal skills, and math abilities.

Female college students performed better on a hard mathematics test when it included at the beginning the statement “You may have heard that women typically do less well at math tests than men, but this is not true for this particular test.”34 Conversely, white male math and engineering majors who received high scores on the math portion of the SAT (a group of people quite confident about their mathematical abilities) did worse on a math test when told the experiment was intended to investigate “why Asians appear to outperform other students on tests of math ability.

I believe that what the vast majority of the masses call life is just fiction. A therapist's work ends up being trying to bring them into nonfiction. Although I feel that many are just replacing a novel by another. Too many people tell me: 'Why do you talk like you know the truth? There is no truth'. It is as if they felt that I'm destroying their inner world by being direct. They feel the need to project a defense mechanism to protect it. Another common phrase is: 'You don't know me better than I know myself'. This one is also interesting. Because it is as if the person was saying: 'You don't know my novel better than I do because I am the author of it.’ Life pretty much follows the same principles — gravity, air, water, fire, weight, hight; all of which is represented in maths, physics, and other sciences. But most people these days consider a personal attack when you make them observe something that may touch their inner world. It's the oversensitivity paradox in which we live today, for people want to feel more alive but are afraid to live at the same time. Allegorically speaking, they need to float like a bubble of steel. And many times they are perfectly fine in discussing others' issues until those issues are projected at them for self-analysis. Quite often, we are not really talking to a human being, but to his alter-ego. There's not much difference between the real self and the alternate version of that self for such person. And how ironic when both the therapist and the patient play the same game from different perspectives. This is why people don't want the truth anymore, but an alternate version of reality where they can merge themselves as if they were merely a chemical solution melting with another. They are too afraid of the truth because they have often been hurt when trying to find it. However, the concept of truth merges with the personality of the individual. And that is why having a personality is now an outdated concept, often falling into the realm of the abstract — Everything is relative, everything is fine, and everyone is everything you can decide for yourself. So why live if life has no meaning? Well, life does have a meaning, but won't be found by running away from it.

To counter the effects of too-early learning, here are some things you can do: Where possible, choose schools that are developmentally sensitive in their curriculum and appropriate for your child. Some kids will do really well as big fish in small ponds. It gives them the confidence to tackle the currents without being afraid of being swept away. They get to grow strong and feel strong. So what if there are bigger fish in bigger ponds? Help your children find the right curricular environments for them. Relax and take a long view, even if no one else around you is. Most kids who learn to read at five aren’t better readers at nine than those who learn to read at six or seven. Bill remembers vividly the mild panicky feeling he and Starr had when their daughter was five years old and some of her friends were starting to read. Even though they knew that kids learn to read much easier at age seven than at age five, and that pushing academics too early was harmful and produced no lasting benefit, Bill and Starr wondered if they were jeopardizing their child’s future by letting her fall behind her peers. They briefly considered pulling her out of her nonacademic kindergarten. But they stuck to their guns and left her in a school that did not push and did not give her any homework until the fourth grade. Despite an unrushed start, she received her PhD in economics from the University of Chicago at the age of twenty-six and is a successful economist. Bill loves telling that story, not to brag (okay, just a little), but to emphasize that it is difficult to buck the tide even when you know the current is carrying you the wrong way. Remember that any gains from rushing development will wash out. Parents often tell Bill that their third grader is doing fourth- or fifth-grade math—but he never hears twenty-six-year-olds brag that they’re more successful than most twenty-eight-year-olds. Don’t go overboard on AP classes. You are doing your child no favors if you let her take more APs at the cost of her mental health and sleep. There’s a reason why kids get more out of Moby-Dick in college than in high school. When we consider the enormous differences in the maturation of their prefrontal cortex—and the associated development in their capacity for abstraction and emotional maturity—it should come as no surprise that the majority of students will understand and appreciate novels written for adults better when they’re older. The same is true for complex scientific theories and data, quantitative concepts, and historical themes, which are easier for most kids to grasp when they are college aged. This isn’t to say that some students aren’t ready for college-level courses when they’re fifteen. The problem is that when this becomes the default for most students (I’ll never get into college if I don’t have five AP classes) it’s destructive.

All of this told of harm done, of a drug that made a child depressed, lonely, and filled with a sense of inadequacy, and when researchers looked at whether Ritalin at least helped hyperactive children fare well academically, to get good grades and thus succeed as students, they found that it wasn’t so. Being able to focus intently on a math test, it turned out, didn’t translate into long-term academic achievement. This drug, Sroufe explained in 1973, enhances performance on “repetitive, routinized tasks that require sustained attention,” but “reasoning, problem solving and learning do not seem to be [positively] affected.”26 Five years later, Herbert Rie was much more negative. He reported that Ritalin did not produce any benefit on the students’ “vocabulary, reading, spelling, or math,” and hindered their ability to solve problems. “The reactions of the children strongly suggest a reduction in commitment of the sort that would seem critical for learning.”27 That same year, Russell Barkley at the Medical College of Wisconsin reviewed the relevant scientific literature and concluded “the major effect of stimulants appears to be an improvement in classroom manageability rather than academic performance.”28 Next it was James Swanson’s turn to weigh in. The fact that the drugs often left children “isolated, withdrawn and overfocused” could “impair rather than improve learning,” he said.29 Carol Whalen, a psychologist from the University of California at Irvine, noted in 1997 that “especially worrisome has been the suggestion that the unsalutary effects [of Ritalin] occur in the realm of complex, high-order cognitive functions such as flexible problem-solving or divergent thinking.”30 Finally, in 2002, Canadian investigators conducted a meta-analysis of the literature, reviewing fourteen studies involving 1,379 youths that had lasted at least three months, and they determined that there was “little evidence for improved academic performance.”31

If you choose to try to make a life with another person, you will live by that choice. You’ll find yourself having to choose again and again to remain rather than run. It helps if you enter a committed relationship prepared to work, ready to be humbled, and willing to accept and even enjoy living in that in-between 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’s no such thing as a fifty-fifty balance. Instead, it’ll be like beads on an abacus, sliding back and forth—the math rarely tidy, the equation never quite solved. A relationship is dynamic this way, full of change, always evolving. At no point will both of you feel like things are perfectly fair and equal. Someone will always be adjusting. Someone will always be sacrificing. One person may be up while the other person is down, one might bear more financial pressures, while the other person handles household and caregiving responsibilites. Those choices and the stress that goes along with them are real. I’ve come to realize though, that life happens in seasons. Your fulfillment—in love, family and career—rarely happens all at once. In a strong relationship both people will take their turns at compromise, building that shared sense of home together, there in the in-between Regardless of how wildly and deeply in love you are, you will be asked to on board a whole lot of your partners' foibles, you will be required to ignore all sorts of minor irritations and at least a few major ones too trying to assert love and constancy over all of it over all the rough spots and an invisible disruptions you will need to do this as often and as compassionately as you can. And you will need to be doing it with someone who is equally able and willing to create the same latitude and show this same forbearance toward you --to love you despite all the baggage you show up with, despite what you look like and how you behave when you are at your absolute worst.

Flower of life: A figure composed of evenly-spaced, overlapping circles creating a flower-like pattern. Images of the Platonic solids and other sacred geometrical figures can be discerned within its pattern. FIGURE 3.14 FLOWER OF LIFE The Platonic solids: Five three-dimensional solid shapes, each containing all congruent angles and sides. If circumscribed with a sphere, all vertices would touch the edge of that sphere. Linked by Plato to the four primary elements and heaven. FIGURE 3.15 PENTACHORON The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres,” a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. He determined that stopping a string halfway along its length created an octave; a ratio of three to two resulted in a fifth; and a ratio of four to three produced a fourth. These ratios were seen as forming harmonics that could restore a disharmonic body—or heal. Hans Jenny furthered this work through the study of cymatics, discussed later in this chapter, and the contemporary sound healer and author Jonathan Goldman considers the proportions of the body to relate to the golden mean, with ratios in relation to the major sixth (3:5) and the minor sixth (5:8).100 Geometry also seems to serve as an “interdimensional glue,” according to a relatively new theory called causal dynamical triangulation (CDT), which portrays the walls of time—and of the different dimensions—as triangulated. According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. A pentachoron is made of five tetrahedral cells and a triangle combined with a tetrahedron. Each simple, triangulated piece is geometrically flat, but they are “glued together” to create curved time-spaces. This theory allows the transfer of energy from one dimension to another, but unlike many other time-space theories, this one makes certain that a cause precedes an event and also showcases the geometric nature of reality.101 The creation of geometry figures at macro- and microlevels can perhaps be explained by the notion called spin, first introduced in Chapter 1. Everything spins, the term spin describing the rotation of an object or particle around its own axis. Orbital spin references the spinning of an object around another object, such as the moon around the earth. Both types of spin are measured by angular momentum, a combination of mass, the distance from the center of travel, and speed. Spinning particles create forms where they “touch” in space.

In this moment I’m reminded of Thor tutoring me math in the second grade. Thor was a math major in college, and in fact, Thor has an Erdős number of three. This means that Thor studied with someone who studied with someone who studied with Paul Erdős. Erdős was a brilliant mathematician who was as famous for his eccentric lifestyle as his mathematical theorems. I guess this give me an Erdős number of four.

During my time in India, the commitment level of the believers there shocked me. I visited thousands of Christians who had been beaten or watched relatives murdered for their faith. At one point, I said to one of the leaders, “Every believer seems so serious about his or her commitment to Christ. Aren’t there people who just profess Christ but don’t really follow Him?” He answered by explaining that nominal Christianity doesn’t make sense in India. Calling yourself a Christian means you lose everything. Your family and friends reject you, and you lose your home, status, and job. So why would anyone choose that unless he or she is serious about Jesus? I witnessed that same passion during my time in mainland China. The highlight was attending a meeting with underground church members training to become missionaries. The way they prayed and gave testimony about being persecuted was convicting and encouraging. The most surprising part of our time together was when they asked me about church in America. They laughed hysterically when I told them that church for Americans tends to focus on buildings and that people will sometimes switch churches based on music, child care, preaching, or disagreements with other believers. I honestly was not trying to be funny. They laughed in disbelief at our church experiences, thinking it was ridiculous that we would call this Christianity. Keep in mind that the population of China is over 1.3 billion, and in India it’s over 1.2 billion. Meanwhile, there are around 300 million people in the United States. This means that we are a small minority. Our views of “Christianity” are peculiar to the vast majority of the world. I used to think of those “radical believers” overseas as the strange ones. Some simple math revealed to me that in actuality we are the weird ones. The majority of believers on this earth find it laughable that we could reduce the call to follow Jesus and make disciples to an invitation to sit in church service.

Andromeda said, “I see that you understand the paradox involved. These are axiomatic beliefs. If life is finite, there can be no math, no logic, nothing which says using the Eschaton Engine to obliterate the majority of the universe in self-preservation is wrong. No game theory applies, because there is no retaliation, no tit for tat. No punishment. But if life is infinite, then an infinite game theory applies, and no act where the ends justifies the means is allowed, because there is no Concubine Vector, no eternal imbalance, no chance of any act escaping unpunished.

Those who majored in the humanities, social sciences, hard sciences, and math did the best. And the majors that did the worst? Education, social work, and the most popular major on US college campuses: business.

INTROSPECTION AND INSANITY: A GODELIAN PROBLEM I think it can have suggestive value to translate Godel's Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Godel's Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Godel's second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent...

> In the 21st century, intellectual capital is what will matter in the job market and will help a country grow its economy. Investments in biosciences, computers and electronics, engineering, and other growing high-tech industries have been the major differentiator in recent decades. More careers than ever now require technical skills so in order to be competitive in those fields, a nation must invest in STEM studies. Economic growth has slowed and unemployment rates have spiked, making employers much pickier about qualifications to hire. There is now an overabundance of liberal arts majors. A study from Georgetown University lists the five college majors with the highest unemployment rates (crossed against popularity): clinical psychology, 19.5 percent; miscellaneous fine arts, 16.2 percent; U.S. history, 15.1 percent; library science, 15 percent; and (tied for No. 5) military technologies and educational psychology, 10.9 percent each. Unemployment rates for STEM subjects hovered around 0 to 3 percent: astrophysics/astronomy, around 0 percent; geological and geophysics engineering, 0 percent; physical science, 2.5 percent; geosciences, 3.2 percent; and math/computer science, 3.5 percent. 

tutor in the computer lab. Claire was an art history major. She had never been good at math. Or at least she’d never tried to be, which was the same thing. She could vividly remember the first time she’d sat down with Paul and gone over one of her assignments.

A third positive result even further from the traditional tool kit of financial incentives comes from a recent randomized control trial conducted in the U.K., using the increasingly popular and low-cost method of text reminders. This intervention involved sending texts to half the parents in some school in advance of a major math test to let them know that their child had a test coming up in five days, then in three days, then in one day. The researchers call this approach “pre-informing.” The other half of parents did not receive the texts. The pre-informing texts increased student performance on the math test by the equivalent of one additional month of schooling, and students in the bottom quartile benefited most. These children gained the equivalent of two additional months of schooling, relative to the control group. Afterward, both parents and students said they wanted to stick with the program, showing that they appreciated being nudged.

At the moment of measuring one electron, a collapse of the wave function of both electrons occurs regardless of the distance between them.

Brian Wecht was born in New Jersey to an interfaith couple. His father ran an army-navy store and enjoyed going to Vegas to see Elvis and Sinatra. Brian loved school, especially math and science, but also loved jazz saxophone and piano. “A large part of my identity came from being a fat kid who was bullied through most of my childhood,” he said. “I remember just not having many friends.” Brian double majored in math and music and chose graduate school in jazz composition. But when his girlfriend moved to San Diego, he quit and enrolled in a theoretical physics program at UC San Diego. Six months later the relationship failed; six years later he earned a PhD. When he solved a longstanding open problem in string theory (“the exact superconformal R-symmetry of any 4d SCFT”), Brian became an international star and earned fellowships at MIT, Harvard, and the Institute for Advanced Study in Princeton, New Jersey. He secured an unimaginable job: a lifetime professorship in particle physics in London. He was set. Except. Brian never lost his interest in music. He met his wife while playing for an improv troupe. He started a comedic band with his friend Dan called Ninja Sex Party. “I was always afraid it was going to bite me in the ass during faculty interviews because I dressed up like a ninja and sang about dicks and boning.” By the time Brian got to London, the band’s videos were viral sensations. He cried on the phone with Dan: Should they try to turn their side gig into a living? Brian and his wife had a daughter by this point. The choice seemed absurd. “You can’t quit,” his physics adviser said. “You’re the only one of my students who got a job.” His wife was supportive but said she couldn’t decide for him. If I take the leap and it fails, he thought, I may be fucking up my entire future for this weird YouTube career. He also thought, If I don’t jump, I’ll look back when I’m seventy and say, “Fuck, I should have tried.” Finally, he decided: “I’d rather live with fear and failure than safety and regret.” Brian and his family moved to Los Angeles. When the band’s next album was released, Ninja Sex Party was featured on Conan, profiled in the Washington Post, and reached the top twenty-five on the Billboard charts. They went on a sold-out tour across the country, including the Brooklyn Bowl in Las Vegas.

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.

grief does not decline in a straight line or along a slow curve like a graph in a child’s math book.

all of its paths to reduce its losses—charging higher prices, paying its workers less—would destroy the advantages that it has built. So it sits there, widely regarded as one of the defining success stories of the Internet era, a unicorn unlike any other, with billions in losses and a plan to become profitable that involves vague promises to somehow monetize all its user data and a specific promise that its investment in a different new technology—the self-driving car, much ballyhooed but as yet not exactly real—will square the circle and make the math add up. That’s the story of Uber—so far. It isn’t a pure Instagram fantasy like the Fyre Festival or a naked fraud like Theranos; it managed to go public and maintain its outsize valuation, unlike its fellow money-losing unicorn WeWork, whose recent attempt at an IPO hurled it into crisis. But like them, it is, for now, an example of a major twenty-first-century company invented entirely out of surplus, less economically efficient so far than the rivals it is supposed to leapfrog, sustained by investors who believe its promises in defiance of the existing evidence, floated by the hope that with enough money and market share, you can will a profitable company into existence, and goldwashed by an “Internet company” identity that obscures the weakness of its real-world fundamentals. Maybe it won’t crash like the others; maybe the tens of billions in investor capital won’t be wasted; maybe we won’t be watching a documentary on its hubris five or ten years hence. But Uber’s trajectory to this point, the strange unreality of its extraordinary success, makes it a good place to begin a discussion of economic

First, Dweck gave every child a test that consisted of fairly easy puzzles. Afterward the researcher informed all the children of their scores, adding a single six-word sentence of praise. Half of the kids were praised for their intelligence (“You must be smart at this”), and half were praised for their effort (“You must have worked really hard”). The kids were tested a second time, but this time they were offered a choice between a harder test and an easier test. Ninety percent of the kids who'd been praised for their effort chose the harder test. A majority of the kids who'd been praised for their intelligence, on the other hand, chose the easy test. Why? “When we praise children for their intelligence,” Dweck wrote, “we tell them that's the name of the game: look smart, don't risk making mistakes.” The third level of tests was uniformly harder; none of the kids did well. However, the two groups of kids—the praised-for-effort group and the praised-for-intelligence group—responded very differently to the situation. “[The effort group] dug in and grew very involved with the test, trying solutions, testing strategies,” Dweck said. “They later said they liked it. But the group praised for its intelligence hated the harder test. They took it as proof they weren't smart.

In terms of funding, Google dwarfs even its own government: U.S. federal funding for math and computer science research amounts to less than half of Google’s own R&D budget. That spending spree has bought Alphabet an outsized share of the world’s brightest AI minds. Of the top one hundred AI researchers and engineers, around half are already working for Google. The other half are distributed among the remaining Seven Giants, academia, and a handful of smaller startups. Microsoft and Facebook have soaked up substantial portions of this group, with Facebook bringing on superstar researchers like Yann LeCun. Of the Chinese giants, Baidu went into deep-learning research earliest—even trying to acquire Geoffrey Hinton’s startup in 2013 before being outbid by Google—and scored a major coup in 2014 when it recruited Andrew Ng to head up its Silicon Valley AI Lab.

There is an almost complete overlap between men and women’s math scores. The majority of women have a male math twin: a man with the same math score as they do.

Young children reinvent arithmetic. Spontaneously or by imitating their peers, they imagine new strategies for calculation. They also learn to select the best strategy for each problem. The majority of their strategies are based on counting, with or without words, with or without fingers. Children often discover them by themselves, even before they are taught to calculate.

Three major technical issues have to be overcome in designing a spacecraft using nuclear bombs: shielding the passengers from the radiation produced in blowing up a nuclear bomb every second or so behind them; keeping the average thrust low enough so that people wouldn’t be smashed to jelly by the high acceleration; and designing a system to throw a nuclear bomb behind the ship once a second and detonate it there—a difficult design problem.

In all racial groups, students from wealthy households tend to score better than those who are poor, but income does not explain group differences. A study by McKinsey and Company found that white fourth graders living in poverty scored higher—by the equivalent of about half-a-year’s instruction—than black fourth graders who were not poor. These differences increase in high school. On the 2009 math and verbal SAT tests, whites from families with incomes of less than $20,000 not only had an average combined score that was 117 points (out of 1600) higher than the average for all blacks, they even outscored by 12 points blacks who came from families with incomes of $160,000 to $200,000. Educators and legislators have not ignored the problem. The race gap in achievement is such a preoccupation that in 2007, 4,000 educators and experts attended an “Achievement Gap Summit” in Sacramento. They took part in no fewer than 125 panels on ways to help blacks and Hispanics do as well as whites and Asians. Overwhelming majorities in Congress passed the No Child Left Behind Act in 2002 to improve student performance and bridge achievement gaps. The government budgeted $24.4 billion for the program for fiscal year 2007, and its requirements for “Adequate Yearly Progress” have forced change on many schools. This is only the latest effort in more than 25 years of federal involvement. The result? In 2009, Chester E. Finn, Jr., a former education official in the Reagan administration, put it this way: “This is a nearly unrelenting tale of woe and disappointment. If there’s any good news here, I can’t find it.