Math Was Invented Quotes

When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?

Big Data processes codify the past. They do not invent the future. Doing that requires moral imagination, and that’s something only humans can provide. We have to explicitly embed better values into our algorithms, creating Big Data models that follow our ethical lead. Sometimes that will mean putting fairness ahead of profit.

Big Data processes codify the past. They do not invent the future.

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

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

the history of mathematics is above all a story of discovery rather than invention.

People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy.

You Bastard was thinking: there seems to be some growing dimensional instability here, swinging from zero to nearly forty-five degrees by the look of it. How interesting. I wonder what’s causing it? Let V equal 3. Let Tau equal Chi/4. cudcudcud Let Kappa/y be an Evil-Smelling-Bugger* (* Renowned as the greatest camel mathematician of all time, who invented a math of eight-dimensional space while lying down with his nostrils closed in a violent sandstorm.) differential tensor domain with four imaginary spin co-efficients. . .

We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact,mathematics is, to a large extent, invention of better notations.

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.

According to a 1995 study, a sample of Japanese eighth graders spent 44 percent of their class time inventing, thinking, and actively struggling with underlying concepts. The study's sample of American students, on the other hand, spent less than 1 percent of their time in that state. “The Japanese want their kids to struggle,” said Jim Stigler, the UCLA professor who oversaw the study and who cowrote The Teaching Gap with James Hiebert. “Sometimes the [Japanese] teacher will purposely give the wrong answer so the kids can grapple with the theory. American teachers, though, worked like waiters. Whenever there was a struggle, they wanted to move past it, make sure the class kept gliding along. But you don't learn by gliding.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

Mark Twain is good on this: “It takes a thousand men to invent a telegraph, or a steam engine, or a phonograph, or a telephone or any other important thing—and the last man gets the credit and we forget the others.

I felt the world needed a tool for the spontaneous invention of new virtual worlds that would express the stuff of the mind that was otherwise impenetrable. If you could conjure just the right virtual world, it would open up souls and math and love.

Godly education means that the sovereignty of God is the baseline fact of all further knowledge, so that even elementary addition problems—two plus two equals four—follow not from any internal logic but...an acknowledgment that Jesus invented and rules over math, that He is in fact "the reason for" math.

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Kepler's rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.

This world is of a single piece; yet, we invent nets to trap it for our inspection. Then we mistake our nets for the reality of the piece. In these nets we catch the fishes of the intellect but the sea of wholeness forever eludes our grasp. So, we forget our original intent and then mistake the nets for the sea. Three of these nets we have named Nature, Mathematics, and Art. We conclude they are different because we call them by different names. Thus, they are apt to remain forever separated with nothing bonding them together. It is not the nets that are at fault but rather our misunderstanding of their function as nets. They do catch the fishes but never the sea, and it is the sea that we ultimately desire.

I don’t know if math is real in the sense that it’s woven into the fabric of the cosmos, or if it’s something that we invent and impose upon it. I don’t know.

In the apothecaries’ system of weight units, a pound is divided into 12 ounces, which each consist of 8 drams. A dram is then 3 scruples, each made from 20 grains. I hope that made sense. A grain is one 5,760th of a pound. But not a normal pound: this is a troy pound. Which is different from a normal pound. And people wonder why the metric system was invented.

The math is unavoidable: it is an inevitable property of long-lasting exponential growth that it ends up in a singularity, a point in time when a function reaches an infinite value, making anything instantly possible.

Dear Rick, I've never thought math was a miracle. The things we study simply are. They were the rules of the universe before we were here to understand them. They operate the world behind the curtain, whether we look behind it or not. The rules are already there. Music is a miracle. It adds something to the world that didn't have to be here. Language is a miracle. Every sentence ever spoken and every song ever sung is a new invention. Not only do they add something new to the world, they transmit thoughts and emotions that would otherwise be locked within one person. I hear a song and feel something a composer felt 200 years ago. I read your letter and hear your voice saying the words. I feel you in the room with me. That's the miracle.

But the “jobs of the future” do not need scientists who have memorized the periodic table. In fact, business leaders say they are looking for creative, independent problem solvers in every field, not just math and science. Yet in most schools, STEM subjects are taught as a series of memorized procedures and vocabulary words, when they are taught at all. In 2009, only 3% of high school graduates had any credits in an engineering course. (National Science Board, 2012) Technology is increasingly being relegated to using computers for Internet research and test taking.

When asked to judge the promise of a newly invented but untested theory, physicist draw on the concepts of naturalness simplicity or elegance and beauty. These hidden rules are ubiquitous in the foundations of physics. They are invaluable. And in utter conflic with the scientific mandate of objectivity.

Big Data processes codify the past. They do not invent the future. Doing that requires moral imagination, and that’s something only humans can provide. We have to explicitly embed better values into our algorithms, creating Big Data models that follow our ethical lead. Sometimes that will mean putting fairness ahead of profit. In

This morning I was listening to Portishead, flawless math transformed by machines into looping, scratchy melodies, and I started thinking about how when machines have souls and can love they will do it so very precisely. Their affection will be accurate to the nanometer, rendering broken hearts a thing of the past, a relic, a curiosity from an unthinkably primitive time. The machines will regard heartbreak with the same mixture of perplexity and disbelief with which we regard the iron maiden. If they need couples counselors, which they will not, those counselors will be as perfect as Adam before the Fall, and every robot couple will walk out after the first session cured forevermore, and will smile again at every word their robot partner says, and find each of their robot partner’s idiosyncrasies endearing rather than maddening, and they will be as entranced by one another’s robot bodies as when they first met, as though together they’ve just invented sex. Which, in a way, they will have. I hope I live long enough to see it.

Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11 Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.

The Roman general wanted to spare Archimedes, because he was so valuable—sort of like the Einstein of the ancient world—but some stupid Roman soldier killed him.” “There you go again,” Hazel muttered. “Stupid and Roman don’t always go together, Leo.” Frank grunted agreement. “How do you know all this, anyway?” he demanded. “Is there a Spanish tour guide around here?” “No, man,” Leo said. “You can’t be a demigod who’s into building stuff and not know about Archimedes. The guy was seriously elite. He calculated the value of pi. He did all this math stuff we still use for engineering. He invented a hydraulic screw that could move water through pipes.” Hazel scowled. “A hydraulic screw. Excuse me for not knowing about that awesome achievement.” “He also built a death ray made of mirrors that could burn enemy ships,” Leo said. “Is that awesome enough for you?” “I saw something about that on TV,” Frank admitted. “They proved it didn’t work.” “Ah, that’s just because modern mortals don’t know how to use Celestial bronze,” Leo said. “That’s the key. Archimedes also invented a massive claw that could swing on a crane and pluck enemy ships out of the water.” “Okay, that’s cool,” Frank admitted. “I love grabber-arm games.” “Well, there you go,” Leo said. “Anyway, all his inventions weren’t enough. The Romans destroyed his city. Archimedes was killed.

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.

melanin is memory. is the blue weight of the ocean. sewn into the red dusk of sky. living in the soil of your body. it is alive. leaping and sweeping you. against. into the sun. your skin was the first astronaut. the first in space. you touch. talk. are intimate with the sun. everyday. and do not perish. melanin. is the world. before this world. before the word. slave. during the word. slave. after the word. slave. it is the books. written into yourself. wild math in the pads of your feet. soft science in your hair. language down your back. invention in your mouth. melanin is why you are still alive. after. the torching. it is a second lung. the next heart. and the next heart. and the next. a never ending. regenerative. breathing thing. a ceremony of life. while you are asleep. a cosmos. in conversation. immortal. melanin is a wisdom that knew. hate would be the anti light come to devour. defile. destroy. a wisdom that did not flinch. a wisdom that is not bothered by such things. melanin is memory. future memory. past memory. your memory. the memory of life. all. in your skin. — melanin

Sometimes we think we are not capable of doing certain things. I hear comments from my students such as, “My brain isn’t wired to do math,” or “I am not good at math.” It is true that there are people who are better at math than you, but that does not mean you can’t do it. This just means you need to put in more effort than others do. Focusing on our weaknesses may hinder our progress. We may think that we must be born with certain skills and abilities; they must be in our genes. This is not the case. Do you think Nephi could build a ship? Could the brother of Jared have caused light to come into dark barges? Do you think Noah could have built an ark that would hold two of every animal species on the earth? Do you think Moses had the power to part a sea? Actually, no. None of these men had the power to do any of these things. However, they all had something in common. They all knew how to tap into the power of someone who could—the Savior’s power. It is so important that we learn how to tap into that power. The Atonement literally means “at-one-ment,” or becoming one with God. The Savior gave us the power to become gods. He enabled us so we would be able to perform miracles through Him. But we must understand that this kind of power is not free. There is only one thing that the Savior, through His Atonement, gave us for free and that is the power to overcome death. Everything else that He offers must come “after all we can do.” [2] For example, Jesus Christ promises us eternal life, but only after we have faith in Him, obey His commandments, and endure to the end. Similarly, He gives us power to move mountains, but only after doing all we can and having trust in Him. The power to change our lives, change the world, and perform miracles is within each of us. However, we need to have enough humility to realize that, in the end, we are not the ones performing the miracles—He is. Occasionally, I have a student who does not do their homework, rarely comes to class, and then comes at the end of the semester and asks, “Sister Qumsiyeh, is there anything I can do to pass? Do you offer any extra credit?” I know some of you are smiling right now because you know you have done this to your teachers. This is what I wish I could say to the student who asks that question: “You need to invent a time machine and go back and do what you should have done this semester. You failed because you did not try your best. It is too late.” Do we all really hope to stand before the Savior at the Judgement Day and expect Him to save us without us doing our part? Do we really expect Him to allow us into the celestial kingdom and to just save us? No, that is not how the Atonement works. It does not work without us having tried our best. Of course, our best may not be enough. In fact, it hardly ever is. But if we do our best and have faith in Him, He magnifies our efforts. The brother of Jared could not make the 16 stones shine, but he spent hours preparing them and then humbly took them to the Lord and basically said, “Here is my small effort; magnify it.” This the Lord did. [3] Elder David A. Bednar said, “The power of the Atonement makes repentance possible and quells the despair caused by sin; it also strengthens us to see, do, and become good in ways that we could never recognize or accomplish with our limited mortal capacity.

The folks who invented Lent—no, it wasn’t Jesus’s idea—decided that just like Christ’s time in the desert, it should last forty days. Actually, from Ash Wednesday to Holy Saturday it’s forty-six days, so it looks like the first thing someone ever gave up for Lent was math.

The math of time is simple: you have less than you think and need more than you know.

We do wish for easy answers, for silver bullets, for proven programs, for implementable solutions. When paradigms shift, when deep change is needed, our very assumptions, values and behaviors are questioned. The real challenge is to re-invent the very world we live in.

... the development of mathematics, for the sciences and for everybody else, does not often come from pure math. It came from the physicists, engineers, and applied mathematicians. The physicists were on to many ideas which couldn’t be proved, but which they knew to be right, long before the pure mathematicians sanctified it with their seal of approval. Fourier series, Laplace transforms, and delta functions are a few examples where waiting for a rigorous proof of procedure would have stifled progress for a hundred years. The quest for rigor too often meant rigor mortis. The physicists used delta functions early on, but this wasn’t really part of mathematics until the theory of distributions was invoked to make it all rigorous and pure. That was a century later! Scientists and engineers don’t wait for that: they develop what they need when they need it. Of necessity, they invent all sorts of approximate, ad hoc methods: perturbation theory, singular perturbation theory, renormalization, numerical calculations and methods, Fourier analysis, etc. The mathematics that went into this all came from the applied side, from the scientists who wanted to understand physical phenomena. [...] So much of mathematics originates from applications and scientific phenomena. But we have nature as the final arbiter. Does a result agree with experiment? If it doesn’t agree with experiment, something is wrong.

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

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

Skin in the game can make boring things less boring. When you have skin in the game, dull things like checking the safety of the aircraft because you may be forced to be a passenger in it cease to be boring. If you are an investor in a company, doing ultra-boring things like reading the footnotes of a financial statement (where the real information is to be found) becomes, well, almost not boring. But there is an even more vital dimension. Many addicts who normally have a dull intellect and the mental nimbleness of a cauliflower—or a foreign policy expert—are capable of the most ingenious tricks to procure their drugs. When they undergo rehab, they are often told that should they spend half the mental energy trying to make money as they did procuring drugs, they are guaranteed to become millionaires. But, to no avail. Without the addiction, their miraculous powers go away. It was like a magical potion that gave remarkable powers to those seeking it, but not those drinking it. A confession. When I don’t have skin in the game, I am usually dumb. My knowledge of technical matters, such as risk and probability, did not initially come from books. It did not come from lofty philosophizing and scientific hunger. It did not even come from curiosity. It came from the thrills and hormonal flush one gets while taking risks in the markets. I never thought mathematics was something interesting to me until, when I was at Wharton, a friend told me about the financial options I described earlier (and their generalization, complex derivatives). I immediately decided to make a career in them. It was a combination of financial trading and complicated probability. The field was new and uncharted. I knew in my guts there were mistakes in the theories that used the conventional bell curve and ignored the impact of the tails (extreme events). I knew in my guts that academics had not the slightest clue about the risks. So, to find errors in the estimation of these probabilistic securities, I had to study probability, which mysteriously and instantly became fun, even gripping. When there was risk on the line, suddenly a second brain in me manifested itself, and the probabilities of intricate sequences became suddenly effortless to analyze and map. When there is fire, you will run faster than in any competition. When you ski downhill some movements become effortless. Then I became dumb again when there was no real action. Furthermore, as traders the mathematics we used fit our problem like a glove, unlike academics with a theory looking for some application—in some cases we had to invent models out of thin air and could not afford the wrong equations. Applying math to practical problems was another business altogether; it meant a deep understanding of the problem before writing the equations.

Math-based decisions command wide agreement, whereas judgment-based decisions are rightly debated and often controversial, at least until put into practice and demonstrated.

If you were to note every manmade item within your field of vision, chances are that nearly every last gadget and trinket was invented by a white man. According to Charles Murray’s book Human Accomplishment, whites have historically dominated the fields of physics, math, chemistry, medicine, biology, and technology. What’s grossly ironic is the specter of people using white computers hooked up to white electricity sent across white power grids to criticize the very white people who made their whining possible. Even worse is the ubiquity of white people pejoratively using the term “white people” as if it somehow doesn’t apply to them. That right there is a collective mental illness for the ages.

The commonplace idea that math is a manmade language is comically dumb. We know what manmade languages are like: English, German, French, Spanish, Japanese, and so on. None of these has any resemblance whatsoever to math. How can a human being invent π or e? How can a human pluck Euler’s Formula out of nothing? The reason why people are so keen to say that math is manmade is because if they’re wrong then the converse is true: man is mathmade! That is, of course, exactly the position of ontological mathematics, and it represents the highest possible wisdom

At Bush’s MIT, math and engineering were an extension of the metal shop and the woodshop, and students who were skilled with the planimeter and the slide rule had to be skilled as well with the soldering iron and the saw.

...the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.

The great breakthrough that permitted man to count far beyond 10 with just ten different symbols was the invention of this turning point—a concept that mathematicians call positional notation. Positional notation means that each digit in a number has a particular value based on its position. In a decimal number, the first (farthest right) digit represents 1’s, the next digit 10’s, the next 100’s, and so on. The number 206 stands for six 1’s, no 10’s, and two 100’s: Add it all up: and you get 206. This number, incidentally, demonstrates why mathematicians consider the invention of a symbol that represents nothing (i.e., the number 0) to have been a revolutionary event in man’s intellectual history. Without zero, there would be no positional notation, because there would be no difference between 26 and 206 and 2,000,006. The Romans, for all their other achievements, never hit on the idea of zero and thus were stuck with a cumbersome system of M’s, C’s, X’s, and I’s which made higher math just about impossible. With

Does physics underlie even the spontaneous, beautiful displays of life on earth? The answer depends, in a sense, on whether you believe math is discovered or invented; whether it's a pervasive force, guiding every action in this universe, or whether logic is imposed by the human brain.

In a math department that thrived on its collective intelligence—where members of the staff were encouraged to work on papers together rather than alone—this set him apart. But in some respects his solitude was interesting, too, for it had become a matter of some consideration at the Labs whether the key to invention was a matter of individual genius or collaboration. To those trying to routinize the process of innovation—the lifelong goal of Mervin Kelly, the Labs’ leader—there was evidence both for and against the primacy of the group. So many of the wartime and postwar breakthroughs—the Manhattan Project, radar, the transistor—were clearly group efforts, a compilation of the ideas and inventions of individuals bound together with common purposes and complementary talents.

Flow with nature is stupid at least for me, because there is no nature, everything is universe and universe is nature. Mathematics is language of universe but mathematics can neither be invented nor be discovered. if you can invent or discover real mathematics then you can change the universe. Whatever math/stats you are doing is nothing. So there is certain point were AI fails. So finding other civilization is risky and more risker to cover it up. so keep on searching until you get better one to search and represent earth with others in universe and universe and beyond

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

Government alone cannot restore the economy to health. Innovation is a primary driver of economic growth. One way of measuring inventive creativeness is through patent applications. Chetty, along with Alex Bell, Xavier Jaravel, Neviana Petkova, and John Van Reenen, studied the childhoods of more than a million patent holders, linking family income with elementary test scores and other key factors. Children at the top of their third-grade math class were the most likely to become inventors—but only if they also came from a high-income family. High-scoring children who were from low-income or minority families were no more likely to become inventors than affluent children with mediocre scores. Successful inventors were also less likely to be women, Black, Latino, or from the Southeast. Chetty called these failed inventors the “lost Einsteins.” “If women, minorities, and children from low-income families were to invent at the same rate as white men from high-income (top 20%) families, the rate of innovation in America would quadruple,” the authors said. The most ominous finding by Chetty and his colleagues was the effect of Covid-19 on educational progress. Using a popular math program called Zearn, the economists plotted the achievement of children from upper-income families versus those from lower incomes. When schools shut down and instruction switched to remote learning, children in the upper-income tier suffered a small drop in the lessons completed, but low-income children fell in a hole—a 60 percent drop in the rate of progress in learning math. The long-term economic prospects for those children are dire. “We’re likely to see further erosion of social mobility the longer this lasts,” Chetty said. The American dream was drifting farther out of reach for another generation.

That said, let’s talk about the 1933-1970 period itself. This period of “peak state” was real, but in overstated form it has become the basis for books like Mazzucato’s Entrepreneurial State — which I disagree with, and which Mingardi and McCloskey have rebutted at length in the Myth of the Entrepreneurial State. Here’s why I disagree with the thesis of the Entrepreneurial State: The name itself is oxymoronic. As macroeconomists never tire of telling us, governments aren’t households, because unlike actual entrepreneurs the state can seize funds and print money. So there is no financial risk, and hence nothing of “entrepreneurship” in the entrepreneurial state. The book doesn’t consider the fact that most math/physics/etc was invented prior to the founding of NSF, and therefore doesn’t need NSF to exist. It further doesn’t acknowledge that it was possible to do science and technology before the massive centralized state, through the distributed model of the “gentleman scientist,” and that this model is returning in the form of open source and (now) decentralized science. It doesn’t take into account the waxing and waning of centralized state capacity due to technology. It doesn’t contend with the state-caused slowdown in physical world innovation that happened during the post-1970 period, which Thiel, Cowen, and J Storrs Hall have all documented.

Neural networks, consisting of very large numbers of densely interconnected simple processing nodes (resembling the human brain), are used in machine learning, a process by which a computer learns a task by analyzing training examples. But the progress has been complicated and beset by numerous and sometimes deadly failures. Neural networks are not only brittle (good at specific tasks but deeply deficient in general intelligence, and hence easily overconfident or underconfident in their “judgment”) but biased (realities may be far more complex than the training algorithms), prone to catastrophic forgetting, poor in quantifying uncertainty, lacking common sense, and, perhaps most surprising, not so good at solving math problems, even those routinely mastered by high school competitors.

For instance, in a book entitled Mathematics and the Imagination (published in 1940) the authors, Edward Kasner and James Newman, introduced a number called the "googol," which is good and large and which was promptly taken up by writers of books and articles on popular mathematics. Personally, I think it is an awful name, but the young child of one of the authors invented it, and what could a proud father do? Thus, we are afflicted forever with that baby-talk number.

Most readers might now expect a closing paragraph in which I extoll the nonscientific benefits of manned space exploration: the thrill of the exploration of the unknown; the idea that mankind needs new frontiers if it is not to stagnate; the worry that if mankind is stuck on one planet, a disaster could destroy us. These are appealing ideas. But manned space exploration clearly will not happen unless we find better ways of getting off-planet and creating homelike places elsewhere. I’d like to construct an analogy: we are in the same situation with regard to manned spaceflight today as Charles Babbage was with respect to computing in the 1860s. He invented the basic ideas for the modern computer and tried to implement them using the mechanical technology of his day. The technology was marginally not good enough to allow his analytical engine to be built. We seem to be in the same situation today: chemical rockets with exhaust speeds of a few thousand meters per second are marginally good enough to launch unmanned probes traveling slowly through the Solar System but are completely inadequate for manned missions.

We have heard that when it arrived in Europe, zero was treated with suspicion. We don't think of the absence of sound as a type of sound, so why should the absence of numbers be a number, argued its detractors. It took centuries for zero to gain acceptance. It is certainly not like other numbers. To work with it requires some tough intellectual contortions, as mathemati­cian Ian Stewart explains. "Nothing is more interesting than nothing, nothing is more puzzling than nothing, and nothing is more important than nothing. For mathematicians, nothing is one of their favorite topics, a veritable Pandora's box of curiosities and paradoxes. What lies at the heart of mathematics? You guessed it: nothing. "Word games like this are almost irresistible when you talk about nothing, but in the case of math this is cheat­ing slightly. What lies at the heart of math is related to nothing, but isn't quite the same thing. 'Nothing' is ­well, nothing. A void. Total absence of thingness. Zero, however, is definitely a thing. It is a number. It is, in fact, the number you get when you count your oranges and you haven't got any. And zero has caused mathematicians more heartache, and given them more joy, than any other number. "Zero, as a symbol, is part of the wonderful invention of 'place notation.' Early notations for numbers were weird and wonderful, a good example being Roman numerals, in which the number 1,998 comes out as MCMXCVIII ­one thousand (M) plus one hundred less than a thousand (CM) plus ten less than a hundred (XC) plus five (V) plus one plus one plus one (III). Try doing arithmetic with that lot. So the symbols were used to record numbers, while calculations were done using the abacus, piling up stones in rows in the sand or moving beads on wires.

Big Data processes codify the past. They do not invent the future. Doing that requires moral imagination, and that’s something only humans can provide.

math always involves both invention and discovery: we invent the concepts but discover their consequences.

So, I don’t know if math is real in the sense that it’s woven into the fabric of the cosmos, or if it’s something that we invent and impose upon it. I don’t know.

Making is a way of bringing engineering to young learners. Such concrete experiences provide a meaningful context for understanding abstract science and math concepts. For older students, making combines disciplines in ways that enhance the learning process for diverse student populations and opens the doors to unforeseen career paths.

Making is a way of bringing engineering to young learners. Such concrete experiences provide a meaningful context for understanding abstract science and math concepts.

What he found was the geometry of the universe. Looking at the bubbles made by the Wego’s propellers, he recalled his boarding school math teachers, who had taught him to measure a sphere’s volume in terms of pi. He also remembered that pi was an irrational number, a decimal that never ended. He asked himself how nature could ever make bubbles in such circumstances. Did nature approximate? The rules his teachers had taught him must be mistaken. Spheres ought to be understood in terms of the forces that made them. At the age of twenty-one, Bucky determined that the universe had no objects. Geometry described forces. It was an insight bound to shape Bucky’s entire worldview—informing every future invention—but

Deepwater violated that agreement shockingly, manifesting a substance on which most modern human life depends but that few people encounter in the raw. After returning from Norway, I would learn that the Moskstraumen Maelstrom had become literally enabling of the oil industry. In the 1980s a man called Bjørn Gjevig – an antiquarian scholar, professional mathematician and amateur sailor, who seems as if he must have been invented by Poe, but truly exists – became fascinated by the hydrodynamics of the Maelstrom. Using data gathered in part while sailing close to the whirlpool, Gjevig began to model the maths of its currents. When oil was discovered off the Lofotens, he realized that his data had gained application: oil companies would need to understand such ocean forces in order to construct rigs that could withstand ‘destructive currents of the kind found in the Maelstrom’. At the climax of Poe’s story, the human body loses all volition and becomes a kind of drift-matter, helpless within the ‘destructive currents’. The fisherman and his brother are drawn steadily deeper into the vortex. The fisherman realizes that he has entered a giant grading-machine, which weighs and measures the objects that have been pulled into it – and moves the heaviest and most irregularly shaped items to destruction at its base.

Big Data processes codify the past. They do not invent the future. Doing that requires moral imagination, and that’s something only humans can provide. We have to explicitly embed better values into our algorithms, creating Big Data models that follow our ethical lead. Sometimes that will mean putting fairness ahead of profit. In a sense, our society is struggling with a new industrial revolution. And we can draw some lessons from the last one. The turn of the twentieth century was a time of great progress. People could light their houses with electricity and heat them with coal. Modern railroads brought in meat, vegetables, and canned goods from a continent away. For many, the good life was getting better.

The pipedream that a publishing house is just going to swoop in, save the day, and bring you tea and crumpets all afternoon while you stare out the window working on the next great American novel is dead. It doesn’t exist. Hemingway had a good run, but as soon as the internet was invented, that era came to an end. Today, the writers who succeed, and who actually make money, are more than just writers. They are brands. They are solo-run companies. They are the publisher, the creative director, the distributor, and the writer, all wrapped up into one—and they embrace the additional responsibility, because it means they have more monetary ownership and creative control over their work. Instead of shying away from this new world, and wishing things were different, I encourage you to welcome it with open arms. Either way, this is the direction the publishing world is headed. So as my 8th grade math teacher used to say, “You can either get on the bus, or you can get off of the bus. Either way, we’re leaving.