Maths Famous Quotes

Anyway. I’m not allowed to watch TV, although I am allowed to rent documentaries that are approved for me, and I can read anything I want. My favorite book is A Brief History of Time, even though I haven’t actually finished it, because the math is incredibly hard and Mom isn’t good at helping me. One of my favorite parts is the beginning of the first chapter, where Stephen Hawking tells about a famous scientist who was giving a lecture about how the earth orbits the sun, and the sun orbits the solar system, and whatever. Then a woman in the back of the room raised her hand and said, “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” So the scientist asked her what the tortoise was standing on. And she said, “But it’s turtles all the way down!” I love that story, because it shows how ignorant people can be. And also because I love tortoises.

He is like the fox, who effaces his tracks in the sand with his tail. {Describing the writing style of famous mathematician Carl Friedrich Gauss}

This phrase did not have the ring of verisimilitude because I am famously bad at math. If I'm in charge of tipping at a restaurant, the waiter will either fall to his knees in gratitude or slash my tires. There ain't no Mr. In Between.

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

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

To your party I'll bring my World-Famous Leftover Duck Meatloaf. It's from 1999, and the only reason I have it in my possession is because my old high-school math teacher called me up to come remove it from my old locker, because it was making his class smell like Savage Garden.

We know next to nothing with any certainty about Pythagoras, except that he was not really called Pythagoras. The name by which he is known to us was probably a nickname bestowed by his followers. According to one source, it meant ‘He who spoke truth like an oracle’. Rather than entrust his mathematical and philosophical ideas to paper, Pythagoras is said to have expounded them before large crowds. The world’s most famous mathematician was also its first rhetorician.

Richard Feynman famously said that the first step in discovering a new physical law is to guess it. It

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

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

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

Most of us do not like not being able to see what others see or make sense of something new. We do not like it when things do not come together and fit nicely for us. That is why most popular movies have Hollywood endings. The public prefers a tidy finale. And we especially do not like it when things are contradictory, because then it is much harder to reconcile them (this is particularly true for Westerners). This sense of confusion triggers in a us a feeling of noxious anxiety. It generates tension. So we feel compelled to reduce it, solve it, complete it, reconcile it, make it make sense. And when we do solve these puzzles, there's relief. It feels good. We REALLY like it when things come together. What I am describing is a very basic human psychological process, captured by the second Gestalt principle. It is what we call the 'press for coherence.' It has been called many different things in psychology: consonance, need for closure, congruity, harmony, need for meaning, the consistency principle. At its core it is the drive to reduce the tension, disorientation, and dissonance that come from complexity, incoherence, and contradiction. In the 1930s, Bluma Zeigarnik, a student of Lewin's in Berlin, designed a famous study to test the impact of this idea of tension and coherence. Lewin had noticed that waiters in his local cafe seemed to have better recollections of unpaid orders than of those already settled. A lab study was run to examine this phenomenon, and it showed that people tend to remember uncompleted tasks, like half-finished math or word problems, better than completed tasks. This is because the unfinished task triggers a feeling of tension, which gets associated with the task and keeps it lingering in our minds. The completed problems are, well, complete, so we forget them and move on. They later called this the 'Zeigarnik effect,' and it has influenced the study of many things, from advertising campaigns to coping with the suicide of loved ones to dysphoric rumination of past conflicts.

George Dantzig was a graduate student in math at Berkeley. One day, as usual, he rushed in late to his math class and quickly copied the two homework problems from the blackboard. When he later went to do them, he found them very difficult, and it took him several days of hard work to crack them open and solve them. They turned out not to be homework problems at all. They were two famous math problems that had never been solved.

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.

As you know, there was a famous quarrel between Max Planck and Einstein, in which Einstein claimed that, on paper, the human mind was capable of inventing mathematical models of reality. In this he generalized his own experience because that is what he did. Einstein conceived his theories more or less completely on paper, and experimental developments in physics proved that his models explained phenomena very well. So Einstein says that the fact that a model constructed by the human mind in an introverted situation fits with outer facts is just a miracle and must be taken as such. Planck does not agree, but thinks that we conceive a model which we check by experiment, after which we revise our model, so that there is a kind of dialectic friction between experiment and model by which we slowly arrive at an explanatory fact compounded of the two. Plato-Aristotle in a new form! But both have forgotten something- the unconscious. We know something more than those two men, namely that when Einstein makes a new model of reality he is helped by his unconscious, without which he would not have arrived at his theories...But what role DOES the unconscious play?...either the unconscious knows about other realities, or what we call the unconscious is a part of the same thing as outer reality, for we do not know how the unconscious is linked with matter.

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.

With the threat of failure looming, students with the growth mindset set instead mobilized their resources for learning. They told us that they, too, sometimes felt overwhelmed, but their response was to dig in and do what it takes. They were like George Danzig. Who? George Danzig was a graduate student in math at Berkeley. One day, as usual, he rushed in late to his math class and quickly copied the two homework problems from the blackboard. When he later went to do them, he found them very difficult, and it took him several days of hard work to crack them open and solve them. They turned out not to be homework problems at all. They were two famous math problems that had never been solved.

[Tolstoy] denounced [many historians'] lamentable tendency to simplify. The experts stumble onto a battlefield, into a parliament or public square, and demand, "Where is he? Where is he?" "Where is who?" "The hero, of course! The leader, the creator, the great man!" And having found him, they promptly ignore all his peers and troops and advisors. They close their eyes and abstract their Napoleon from the mud and the smoke and the masses on either side, and marvel at how such a figure could possibly have prevailed in so many battles and commanded the destiny of an entire continent. "There was an eye to see in this man," wrote Thomas Carlyle about Napoleon in 1840, "a soul to dare and do. He rose naturally to be the King. All men saw that he was such." But Tolstoy saw differently. "Kings are the slaves of history," he declared. "The unconscious swarmlike life of mankind uses every moment of a king's life as an instrument for its purposes." Kings and commanders and presidents did not interest Tolstoy. History, his history, looks elsewhere: it is the study of infinitely incremental, imperceptible change from one state of being (peace) to another (war). The experts claimed that the decisions of exceptional men could explain all of history's great events. For the novelist, this belief was evidence of their failure to grasp the reality of an incremental change brought about by the multitude's infinitely small actions.

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.

As I was completing this book, I saw news reports quoting NASA chief Charles Bolden announcing that from now on the primary mission of America’s space agency would be to improve relations with the Muslim world. Come again? Bolden said he got the word directly from the president. “He wanted me to find a way to reach out to the Muslim world and engage much more with dominantly Muslim nations to help them feel good about their historic contribution to science and math and engineering.” Bolden added that the International Space Station was a kind of model for NASA’s future, since it was not just a U.S. operation but included the Russians and the Chinese. Bolden, who made these remarks in an interview with Al-Jazeera, timed them to coincide with the one-year anniversary of Obama’s own Cairo address to the Muslim world.3 Bolden’s remarks provoked consternation not only among conservatives but also among famous former astronauts Neil Armstrong and John Glenn and others involved in America’s space programs. No surprise: most people think of NASA’s job as one of landing on the moon and Mars and exploring other faraway destinations. Even some of Obama’s supporters expressed puzzlement. Sure, we are all for Islamic self-esteem, and seven or eight hundred years ago the Muslims did make a couple of important discoveries, but what on earth was Obama up to here?

No one would choose this sort of painful adolescence, but the fact is that the solitude of Woz’s teens, and the single-minded focus on what would turn out to be a lifelong passion, is typical for highly creative people. According to the psychologist Mihaly Csikszentmihalyi, who between 1990 and 1995 studied the lives of ninety-one exceptionally creative people in the arts, sciences, business, and government, many of his subjects were on the social margins during adolescence, partly because “intense curiosity or focused interest seems odd to their peers.” Teens who are too gregarious to spend time alone often fail to cultivate their talents “because practicing music or studying math requires a solitude they dread.” Madeleine L’Engle, the author of the classic young adult novel A Wrinkle in Time and more than sixty other books, says that she would never have developed into such a bold thinker had she not spent so much of her childhood alone with books and ideas. As a young boy, Charles Darwin made friends easily but preferred to spend his time taking long, solitary nature walks. (As an adult he was no different. “My dear Mr. Babbage,” he wrote to the famous mathematician who had invited him to a dinner party, “I am very much obliged to you for sending me cards for your parties, but I am afraid of accepting them, for I should meet some people there, to whom I have sworn by all the saints in Heaven, I never go out.”)

When I first started coming to the seminar, Gelfand had a young physicist, Vladimir Kazakov, present a series of talks about his work on so-called matrix models. Kazakov used methods of quantum physics in a novel way to obtain deep mathematical results that mathematicians could not obtain by more conventional methods. Gelfand had always been interested in quantum physics, and this topic had traditionally played a big role at his seminar. He was particularly impressed with Kazakov’s work and was actively promoting it among mathematicians. Like many of his foresights, this proved to be golden: a few years later this work became famous and fashionable, and it led to many important advances in both physics and math. In his lectures at the seminar, Kazakov was making an admirable effort to explain his ideas to mathematicians. Gelfand was more deferential to him than usual, allowing him to speak without interruptions longer than other speakers. While these lectures were going on, a new paper arrived, by John Harer and Don Zagier, in which they gave a beautiful solution to a very difficult combinatorial problem.6 Zagier has a reputation for solving seemingly intractable problems; he is also very quick. The word was that the solution of this problem took him six months, and he was very proud of that. At the next seminar, as Kazakov was continuing his presentation, Gelfand asked him to solve the Harer–Zagier problem using his work on the matrix models. Gelfand had sensed that Kazakov’s methods could be useful for solving this kind of problem, and he was right. Kazakov was unaware of the Harer–Zagier paper, and this was the first time he heard this question. Standing at the blackboard, he thought about it for a couple of minutes and immediately wrote down the Lagrangian of a quantum field theory that would lead to the answer using his methods. Everyone in the audience was stunned.

Many of the really great, famous proofs in the history of math have been reduction proofs. Here's an example. It is Euclid's proof of Proposition 20 in Book IX of the Elements. Prop. 20 concerns the primes, which-as you probably remember from school-are those integers that can't be divided into smaller integers w/o remainder. Prop. 20 basically states that there is no largest prime number. (What this means of course is that the number of prime numbers is really infinite, but Euclid dances all around this; he sure never says 'infinite'.) Here is the proof. Assume that there is in fact a largest prime number. Call this number Pn. This means that the sequence of primes (2,3,5,7,11,...,Pn) is exhaustive and finite: (2,3,5,7,11,...,Pn) is all the primes there are. Now think of the number R, which we're defining as the number you get when you multiply all the primes up to Pn together and then add 1. R is obviously bigger than Pn. But is R prime? If it is, we have an immediate contradiction, because we already assumed that Pn was the largest possible prime. But if R isn't prime, what can it be divided by? It obviously can't be divided by any of the primes in the sequence (2,3,5,...,Pn), because dividing R by any of these will leave the remainder 1. But this sequence is all the primes there are, and the primes are ultimately the only numbers that a non-prime can be divided by. So if R isn't prime, and if none of the primes (2,3,5,...,Pn) can divide it, there must be some other prime that divides R. But this contradicts the assumption that (2,3,5,...,Pn) is exhaustive of all the prime numbers. Either way, we have a clear contradiction. And since the assumption that there's a largest prime entails a contradiction, modus tollens dictates that the assumption is necessarily false, which by LEM means that the denial of the assumption is necessarily true, meaning there is no largest prime. Q.E.D.

How to live (forty pieces of advice I feel to be helpful but which I don’t always follow) 1. Appreciate happiness when it is there 2. Sip, don’t gulp. 3. Be gentle with yourself. Work less. Sleep more. 4. There is absolutely nothing in the past that you can change. That’s basic physics. 5. Beware of Tuesdays. And Octobers. 6. Kurt Vonnegut was right. “Reading and writing are the most nourishing forms of meditation anyone has so far found.” 7. Listen more than you talk. 8. Don’t feel guilty about being idle. More harm is probably done to the world through work than idleness. But perfect your idleness. Make it mindful. 9. Be aware that you are breathing. 10. Wherever you are, at any moment, try to find something beautiful. A face, a line out of a poem, the clouds out of a window, some graffiti, a wind farm. Beauty cleans the mind. 11. Hate is a pointless emotion to have inside you. It is like eating a scorpion to punish it for stinging you. 12. Go for a run. Then do some yoga. 13. Shower before noon. 14. Look at the sky. Remind yourself of the cosmos. Seek vastness at every opportunity, in order to see the smallness of yourself. 15. Be kind. 16. Understand that thoughts are thoughts. If they are unreasonable, reason with them, even if you have no reason left. You are the observer of your mind, not its victim. 17. Do not watch TV aimlessly. Do not go on social media aimlessly. Always be aware of what you are doing and why you are doing it. Don’t value TV less. Value it more. Then you will watch it less. Unchecked distractions will lead you to distraction. 18. Sit down. Lie down. Be still. Do nothing. Observe. Listen to your mind. Let it do what it does without judging it. Let it go, like Snow Queen in Frozen. 19. Don’t’ worry about things that probably won’t happen. 20. Look at trees. Be near trees. Plant trees. (Trees are great.) 21. Listen to that yoga instructor on YouTube, and “walk as if you are kissing the earth with your feet”. 22. Live. Love. Let go. The three Ls. 23. Alcohol maths. Wine multiplies itself by itself. The more you have, the more you are likely to have. And if it is hard to stop at one glass, it will be impossible at three. Addition is multiplication. 24. Beware of the gap. The gap between where you are and where you want to be. Simply thinking of the gap widens it. And you end up falling through. 25. Read a book without thinking about finishing it. Just read it. Enjoy every word, sentence, and paragraph. Don’t wish for it to end, or for it to never end. 26. No drug in the universe will make you feel better, at the deepest level, than being kind to other people. 27. Listen to what Hamlet – literature’s most famous depressive – told Rosencrantz and Guildenstern. “There is nothing either good or bad, but thinking makes it so.” 28. If someone loves you, let them. Believe in that love. Live for them, even when you feel there is no point. 29. You don’t need the world to understand you. It’s fine. Some people will never really understand things they haven’t experienced. Some will. Be grateful. 30. Jules Verne wrote of the “Living Infinite”. This is the world of love and emotion that is like a “sea”. If we can submerge ourselves in it, we find infinity in ourselves, and the space we need to survive. 31. Three in the morning is never the time to try and sort out your life. 32. Remember that there is nothing weird about you. You are just a human, and everything you do and feel is a natural thing, because we are natural animals. You are nature. You are a hominid ape. You are in the world and the world is in you. Everything connects. 33. Don’t believe in good or bad, or winning and losing, or victory and defeat, or ups and down. At your lowest and your highest, whether you are happy or despairing or calm or angry, there is a kernel of you that stays the same. That is the you that matters.

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.

The famous Dutch tulip bubble largely involved the frenzied trading of options to buy or sell the bulbs—a precursor to modern-day stock options—rather than transactions involving the actual flowers.

For the man on the street, science and math sound too and soulless. It is hard to appreciate their significance Most of us are just aware of Newton's apple trivia and Einstein's famous e mc2. Science, like philosophy, remains obscure and detached, playing role in our daily lives. There is a general perception that science is hard to grasp and has direct relevance to what we do. After all, how often do we discuss Dante or Descartes over dinner anyway? Some feel it to be too academic and leave it to the intellectuals or scientists to sort out while others feel that such topics are good only for academic debate. The great physicist, Rutherford, once quipped that, "i you can't explain a complex theory to a bartender, the theory not worth it" Well, it could be easier said than done (applications of tools

I believe maths should be applied to the arts. So I claim that it was in Britain that the famous equation E = mc2 was proved: E = exposure (of nether parts) m = much c = chuckling chuckling squared = helpless laughter

Double-entry accounting was popularized in Europe toward the end of the fifteenth century, and most scholars believe it set the table for the flowering of the Renaissance and the emergence of modern capitalism. What is far less well understood is the why. Why was something as dull as bookkeeping so integral to a complete cultural revolution in Europe? Over nearly seven centuries, “the books” have become something that, in our collective minds, we equate with truth itself—even if only subconsciously. When we doubt a candidate’s claims of wealth, we want to go to his bank records—his personal balance sheet. When a company wants to tap the public markets for capital, they have to open their books to prospective investors. To remain in the market, they need accountants to verify those books regularly. Well-maintained and clear accounting is sacrosanct. The ascendance of bookkeeping to a level equal to truth itself happened over many centuries, and began with the outright hostility European Christendom had to lending before double-entry booking came along. The ancients were pretty comfortable with debt. The Babylonians set the tone in the famous Code of Hammurabi, which offered rules for handling loans, debts, and repayments. The Judeo-Christian tradition, though, had a real ax to grind against the business of lending. “Thou shalt not lend upon usury to thy brother,” Deuteronomy 23:19–20 declares. “In thee have they taken gifts to shed blood; thou hast taken usury and increase, and thou hast greedily gained of thy neighbors by extortion, and hast forgotten me, saith the Lord God,” Ezekiel 22:12 states. As Christianity flourished, this deep anti-usury culture continued for more than a thousand years, a stance that coincided with the Dark Ages, when Europe, having lost the glories of ancient Greece and Rome, also lost nearly all comprehension of math. The only people who really needed the science of numbers were monks trying to figure out the correct dates for Easter.

I never thought that I will be famous in math with this that with wrong solving the problems in math I get the right answer. But it looks I'm now Famous!

Schools, in a noble effort to interest more girls in math and science, often try to combat stereotypes by showing children images of famous female scientists. “See, they did it. You can do it, too!” Unfortunately, these attempts rarely work, according to the research. Girls are more likely to remember the women as lab assistants. This is frustrating for those of us who try to combat gender stereotypes in children.

You probably know what Sherlock Holmes had to say about inference, the most famous thing he ever said that wasn’t “Elementary!”: “It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth.” Doesn’t that sound cool, reasonable, indisputable? But it doesn’t tell the whole story. What Sherlock Holmes should have said was: “It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn’t occur to you to consider.” Less pithy, more correct. The

Benjamin Franklin famously observed that “an ounce of prevention is worth a pound of cure.” Dozens of experiments have shown that early interventions can help students facing disadvantages and learning disabilities make leaps in math and reading.

Across the English Channel, the biggest champion of the new mechanical worldview was René Descartes. Bacon was entirely ignorant of mathematics. Descartes was steeped in it. Reducing the operations of the universe to a series of lines, circles, numbers, and equations suited his reclusive personality. His most famous saying, “I think, therefore I am” (cogito, ergo sum), could be stated less succinctly but more accurately as “Because we are the only beings who do math, we rule.

A young reporter for the Post named Tom Wolfe followed up after my talk with an interview. The Post ran his story, “You Can So Beat the Gambling House at Blackjack, Math Expert Insists.” He was curious rather than skeptical, sympathetic but probing. Wolfe later became one of America’s most famous authors.

So I went to Case, and the Dean of Case says to us, says, it’s a all men’s school, says, “Men, look at, look to the person on your left, and the person on your right. One of you isn’t going to be here next year; one of you is going to fail.” So I get to Case, and again I’m studying all the time, working really hard on my classes, and so for that I had to be kind of a machine. I, the calculus book that I had, in high school we — in high school, as I said, our math program wasn’t much, and I had never heard of calculus until I got to college. But the calculus book that we had was great, and in the back of the book there were supplementary problems that weren’t, you know, that weren’t assigned by the teacher. The teacher would assign, so this was a famous calculus text by a man named George Thomas, and I mention it especially because it was one of the first books published by Addison-Wesley, and I loved this calculus book so much that later I chose Addison-Wesley to be the publisher of my own book. But Thomas’s Calculus would have the text, then would have problems, and our teacher would assign, say, the even numbered problems, or something like that. I would also do the odd numbered problems. In the back of Thomas’s book he had supplementary problems, the teacher didn’t assign the supplementary problems; I worked the supplementary problems. I was, you know, I was scared I wouldn’t learn calculus, so I worked hard on it, and it turned out that of course it took me longer to solve all these problems than the kids who were only working on what was assigned, at first. But after a year, I could do all of those problems in the same time as my classmates were doing the assigned problems, and after that I could just coast in mathematics, because I’d learned how to solve problems. So it was good that I was scared, in a way that I, you know, that made me start strong, and then I could coast afterwards, rather than always climbing and being on a lower part of the learning curve.

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.

glory, at the Science Museum of London. Charles Babbage was a well-known scientist and inventor of the time. He had spent years working on his Difference Engine, a revolutionary mechanical calculator. Babbage was also known for his extravagant parties, which he called “gatherings of the mind” and hosted for the upper class, the well-known, and the very intelligent.4 Many of the most famous people from Victorian England would be there—from Charles Darwin to Florence Nightingale to Charles Dickens. It was at one of these parties in 1833 that Ada glimpsed Babbage’s half-built Difference Engine. The teenager’s mathematical mind buzzed with possibilities, and Babbage recognized her genius immediately. They became fast friends. The US Department of Defense uses a computer language named Ada in her honor. Babbage sent Ada home with thirty of his lab books filled with notes on his next invention: the Analytic Engine. It would be much faster and more accurate than the Difference Engine, and Ada was thrilled to learn of this more advanced calculating machine. She understood that it could solve even harder, more complex problems and could even make decisions by itself. It was a true “thinking machine.”5 It had memory, a processor, and hardware and software just like computers today—but it was made from cogs and levers, and powered by steam. For months, Ada worked furiously creating algorithms (math instructions) for Babbage’s not-yet-built machine. She wrote countless lines of computations that would instruct the machine in how to solve complex math problems. These algorithms were the world’s first computer program. In 1840, Babbage gave a lecture in Italy about the Analytic Engine, which was written up in French. Ada translated the lecture, adding a set of her own notes to explain how the machine worked and including her own computations for it. These notes took Ada nine months to write and were three times longer than the article itself! Ada had some awesome nicknames. She called herself “the Bride of Science” because of her desire to devote her life to science; Babbage called her “the Enchantress of Numbers” because of her seemingly magical math

Gandhi is famous as a pacifist who led India to independence from the UK. But, since 1991, he has also gained a reputation as a warmonger leader who launches unprovoked nuclear strikes.

Yet the Woke messaging keeps flying. Speaking in New York’s Washington Square on September 18, 2019, Senator Warren let fire this zinger. “We’re not here today because of famous arches or famous men. In fact, we’re not here because of men at all.”20 But if Warren ever arrives in the White House, it will be because of men—not all of them, obviously, but sufficient numbers of them. And the lesson of the Trump presidency is that insulting voters loses their votes. Those who aspire to conjure up a counter-Trump movement of militant progressive forces imagine that American demographics have tilted to the point that a politics of (in their view) righteous grievance can outvote the (in their view) wrongful grievance that Trump has summoned up. They are kidding themselves about their math, but even if they were correct, what kind of answer would that be? Trump is president not only because many of your fellow citizens are racists, or sexists, or bigots of some other description, although surely some are. Trump is president also because many of your fellow citizens feel that accusations of bigotry are deployed casually and carelessly, even opportunistically. Anti-racism can easily devolve from a call to equal justice for all into a demand for power and privilege. We speak, you listen. We demand, you comply. We win, you lose.

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.

creation, we see the conscious, ordering mind of God.23 What God has put into the world, a preordained mathematical order, we can trace back to God through that same order. Like Leonardo da Vinci’s famous drawing of the man standing in the square and circle, divine geometric proportion turns out to be written into every feature of our lives and is only waiting to be revealed like a crucial message inscribed in invisible ink. Thanks to Pythagoras’s mystical math, Socrates’s cave suddenly comes alive in the divine order and meaning.

This part of the analysis, like any collection of human opinion, was sure to include old-fashioned prejudice and ignorance. It tended to protect the famous schools at the top of the list, because they were the ones people knew about. And it made it harder for up-and-comers.

(dollar word) Peter will grow up to be a world-famous thief. I had no clue anything was even happening until I heard the giggling and Peter said, “Hey, Luke, what kind of sneaks are those? Elmer’s?” I popped my head up. “What are you talking about?” “Better be careful. If you try to go anywhere in those, you might get stuck.” I looked back at my feet. Mess-around Peter had struck. The bottoms of my sneakers were completely covered in Elmer’s glue. “You jerk,” I said, without any real authority. Truth is, I didn’t really care. It wasn’t worth getting upset over. Besides, I’m sort of used to Peter’s antics. I thought they were always harmless. I untied my shoes and placed them next to me—bottoms up, of course—until I finished my math. Peter’s victory celebration was cut short by my easy solution. Maybe I don’t get upset with Peter because I know I’ll always outwit him. This drives him nuts, and I love it. Once I finished my calculations, I grabbed my sneakers and headed to the bathroom. Mr. Terupt was still busy with a different group so he didn’t see any of Peter’s shenanigans or me leaving the