# THE MATH BOOK CLIFFORD PICKOVER PDF

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A passion for mathematics: numbers, puzzles, madness, religion, and the quest for . of the original puzzles in this book at my Pickover Discussion Group. This item:The Math Book: From Pythagoras to the 57th Dimension, Milestones in the History of Mathematics by Clifford A. Pickover Paperback $ The Math Book by Clifford A. Pickover, , available at Book Depository with free delivery worldwide.

This book was interesting because so many of the topics dealt with number theory and topology, two topics that are not covered in engineering or finance. Problems in number theory are often easy to state, since they normally only involve positive integers, but difficult to solve. Here is the thing that bugged me: Every single time he mentioned prime numbers, he explained what prime numbers are using the exact same sentences. Every time. I thought that was lazy too. If there was one thing you could actually learn from this book, it is how to recognize a prime number.

On the other hand, even problem statement in topology involves a lot of opaque language about abstruse concepts. Annoyance 3: When he introduced topology problems, he breezily threw around "invariant," "Hilbert space," and "n-dimensional symmetry" like they were every day topics at lunch.

Maybe they are, but I don't hang out with that crowd. I'm only annoyed because I did not feel like going to another source to try to understand what he was talking about. Brian Greene would have found a way to explain it. What about propositions whose proofs require arguments beyond our capabilities? What about propositions whose proofs require millions of pages? Or a million, million pages? Are there proofs that are possible, but beyond us?

The multiplication symbol. Mathematics and reality. Do humans invent mathematics or discover mathematics? Mathematics and the universe. Here is a deep thought to start our mathematical journey.

Isaac Newton supposed that the planets were originally thrown into orbit by God, but even after God decreed the law of gravitation, the planets required continual adjustments to their orbits.

Incidentally, this Anglican minister is also famous for having invented the slide rule, which was used by generations of scientists and mathematicians.

Numbers, History, Society, and People 13 Math and madness. Many mathematicians throughout history have had a trace of madness or have been eccentric. What triple murderer was also a brilliant French mathematician who did his finest work while confined to a hospital for the criminally insane?

Creativity and madness. To put it simply, people who fit in with their communities have insufficient motivation to risk their psyches in creating something truly new, while those who are out of sync are driven by the constant need to prove their worth. Over the years, many of my readers have assumed that famous mathematicians are not religious. In actuality, a number of important mathematicians were quite religious.

As an interesting exercise, I conducted an Internet survey in which I asked respondents to name important mathematicians who were also religious. Isaac Newton and Blaise Pascal were the most commonly cited religious mathematicians.

In many ways, the mathematical quest to understand infinity parallels mystical attempts to understand God.

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Both religion and mathematics struggle to express relationships between humans, the universe, and infinity. Both have arcane symbols and rituals, as well as impenetrable language. Both exercise the deep recesses of our minds and stimulate our imagination. Are mathematics and religion the most powerful evidence of the inventive genius of the human race?

Is faith—or a cosmic sense of mystery—like the air that allows some seekers to soar? Whatever mathematical or scientific advances humans make, we will always continue to swim in a sea of mystery.

Leaving mathematics and approaching God. What famous French mathematician and teenage prodigy finally decided that religion was more to his liking and joined his sister in her convent, where he gave up mathematics and social life? After receiving visions from these gods in the form of blood droplets, Ramanujan saw scrolls that contained very complicated mathematics. When he woke from his dreams, he set down on paper only a fraction of what the gods showed him.

Throughout history, creative geniuses have been open to dreams as a source of inspiration. Apparently, the tune seemed so beautiful and haunting that for a while he was not certain it was original. The Danish physicist Niels Bohr conceived the model of an atom from a dream. Elias Howe received in a dream the image of the kind of needle design required for a lock-stitch sewing machine. It is not an exaggeration to suggest that many scientific and mathematical advances arose from the stuff of dreams.

Blaise Pascal — , a Frenchman, was a geometer, a probabilist, a physicist, a philosopher, and a combinatorist. He was also deeply spiritual and a leader of the Jansenist sect, a Calvinistic quasi-Protestant group within the Catholic Church. He believed that it made sense to become a Christian.

If the person dies, and there is no God, the person loses nothing. If there is a God, then the person has gained heaven, while skeptics lose everything in hell. Legend has it that Pascal in his early childhood sought to prove the existence of God. Because Pascal could not simply command God to show Himself, he tried to prove the existence of a devil so that he could then infer the existence of God.

He drew a pentagram on the ground, but the exercise scared him, and he ran away. May I not forget your words. Numbers, History, Society, and People 15 Transcendence. And yet, this is not the whole story. Genuine saints occasionally play an important role, both in religion and science.

The value of eccentricity. Counting and the mind. I quickly toss a number of marbles onto a pillow. You may stare at them for an instant to determine how many marbles are on the pillow. Obviously, if I were to toss just two marbles, you could easily determine that two marbles sit on the pillow.

What is the largest number of marbles you can 16 A Passion for Mathematics quantify, at a glance, without having to individually count them? Why are there degrees in a circle? The mystery of Ramanujan. The special number 7. In the s, the German ethnologist Karl von Steinen described how certain South American Indian tribes had very few words for numbers.

As a test, he repeatedly asked them to count ten grains of corn.

Today, mathematics affects society in the funniest of ways. I once read an article about someone who claimed to have devised the most forgettable license plate, but the article did not divulge the secret sequence. What is the most forgettable license plate? Or maybe a binary number like What do you think? What would a mathematician think? Carl Friedrich Gauss — , a German, was a mathematician, an astronomer, and a physicist with a wide range of contributions.

He was also the author of many books on biblical subjects, especially prophecy. Perhaps less well known is the fact that Newton was a creationist who wanted to be known as much for his theological writings as for his scientific and mathematical texts. Newton believed in a Christian unity, as opposed to a trinity. He developed calculus as a means of describing motion, and perhaps for understanding the nature of God through a clearer understanding of nature and reality.

He respected the Bible and accepted its account of Creation. Genius and eccentricity. Mathematics and God. Geometry has supplied God with the models for the creation of the world.

Numbers, History, Society, and People 17 Leonhard Euler — was a prolific Swiss mathematician and the son of a vicar. Although he was a devout Christian all his life, he could not find the enthusiasm for the study of theology, compared to that of mathematics.

He was completely blind for the last seventeen years of his life, during which time he produced roughly half of his total output. George Boole — , an Englishman, was a logician and an algebraist. Today, Boolean algebra has found wide applications in the design of computers. The value of puzzles. A mathematical nomad. What legendary mathematician, and one of the most prolific mathematicians in history, was so devoted to math that he lived as a nomad with no home and no job?

Sexual contact revolted him; even an accidental touch by anyone made him feel uncomfortable. Marin Mersenne — was another mathematician who was deeply religious. Mersenne, a Frenchman, was a theologian, a philosopher, a number theorist, a priest, and a monk.

What brilliant, handsome mathematician so hated mirrors that he covered them wherever he went? What is a mathematician? Animal math. Can animals count?

## Keys to Infinity – Clifford A. Pickover

He created just one world, instead of many, because the one world would be infinite in every part. His first publications were theological studies against atheism and skepticism. Mersenne was fascinated by prime numbers numbers like 7 that were divisible only by themselves and 1 , and he tried to find a formula that he could use to find all primes.

Mersenne numbers are the easiest type of number to prove prime, so they are usually the largest primes of which humanity is aware. Mersenne himself found several prime numbers of the form 2p — 1, but he underesti- mated the future of computing power by stating that all eternity would not be sufficient to decide if a or digit number were prime.

Unfortunately, the prime number values for p that make 2p — 1 a prime number seem to form no regular sequence. The fortieth Mersenne prime was discovered in , and it contained 6,, digits!

## Clifford Pickover_The Math Book From Pythagoras to the 57th Dimension

In particular, the Michigan State University graduate student Michael Shafer discovered that ,, — 1 is prime. The number is so large that it would require about fifteen hundred pages to write on paper using an ordinary font. Shafer, age twenty-six, helped find the number as a volunteer on a project called the Great Internet Mersenne Prime Search. Tens of thousands of people volunteer the use of their personal computers in a worldwide project that harnesses the power of hundreds of thousands of computers, in effect creating a supercomputer capable of performing trillions of calculations per second.

Shafer used an ordinary Dell computer in his office for nineteen days. What would Mersenne have thought of this large beast? In , the German eye surgeon Martin Nowak, also part of the Great Internet Mersenne Prime Search, discovered the forty-second Mersenne prime number, ,, — 1, which has over seven million digits.

The Electronic Frontier Foundation, a U. The division symbol. Donald Knuth — is a computer scientist and a mathematician.

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He is also a fine example of a mathematician who is interested in religion. For example, he has been an active Lutheran and a Sunday school teacher. His attractive book titled consists entirely of commentary on chapter 3, verse 16, of each of the books in the Bible. Knuth also includes calligraphic renderings of the verses. The fact is that everything we learn reveals more things that we do not understand. Reverence for God comes naturally if we are honest about how little we know.

Landsburg, in a post to the newsgroup sci. Brain limitation. Around A. Mathematician starves.

What famous mathematician deliberately starved himself to death in ? Hint: He was perhaps the most brilliant logician since Aristotle. Understanding brilliance. Georg Friedrich Bernhard Riemann — was a German mathematician who made important contributions to geometry, number theory, topology, mathematical physics, and the theory of complex variables.

He also attempted to write a mathematical proof of the truth of the Book of Genesis, was a student of theology and bibli- Calculating prodigy has plastic brain. He did poorly at mathematics in school but is now a world-famous human calculator, able to access regions of his brain that are off limits to most of us.

He is not autistic but has been able to train his brain to perform lightning calculations. For example, he can calculate 53 to the ninth power in his head. He can divide prime numbers and calculate the answer to 60 decimal points and more. He can calculate fifth roots. These breathtaking studies reveal that Gamm is now able to use areas of his brain that ordinary humans can use for other purposes.

In particular, he can make use of the areas of his brain that are normally responsible for long-term memory, in order to perform his rapid calculations. Gamm is essentially doing what computers do when they extend their capabilities by using swap space on the hard drive to increase their capabilities.

Scientists are not sure how Gamm acquired this ability, considering that he became interested in mathematical calculation only when he was in his twenties. Chapter 3 describes the hypothesis further. A dislike for mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. Mathematics and humanity. Heinlein, Time Enough for Love, As discussed in Answer 1. Math and madness. The closer he came to the answers he sought, the further away they seemed.

According to Leibniz, God chooses to actualize this world out of an infinite number of possible worlds. In other words, limited only by contradiction, God first conceives of every possible world, and then God simply chooses which of them to create. Greater-than symbol. Greater-than or equal-to symbol. Mathematician murdered. Why was the first woman mathematician murdered? Going to the movies. What was the largest number ever used in the title of an Ameri- can movie? Name the movie!

What is the largest number less than a billion ever used in a major, full-length movie title? Hint: The song was popular in the late s and the early s. Many mathematicians were depressed and religious at the same time. The Number Pope. As I Mathematics and diapering. Gerbert of Aurillac c. His advanced knowledge of mathematics convinced some of his enemies that he was an evil magician. In Reims, he transformed the floor of the cathedral into a giant abacus. That must have been a sight to see!

He contributed to the invention of the pendulum clock, invented devices that tracked planetary orbits, and wrote on geometry. When he realized that he lacked knowledge of formal logic, he studied under German logicians. In the s, the British mathematician G.

Just as Babbage could program strange behavior on his calculating machines, God could program similar irregularities in nature. While investigating biblical miracles, he assumed that the chance of a man rising from the dead is one in Babbage is famous for conceiving an enormous handcranked mechanical calculator, an early progenitor of our modern computers. Babbage thought the device would be most useful in producing mathematical tables, but he worried about mistakes that would be made by humans who transcribed the results from its thirty-one metal output wheels.

Today, we realize that Babbage was a hundred years ahead of his time and that the politics and the technology of his era were inadequate for his lofty dreams. Tinkertoy computer. In the early s, the computer geniuses Danny Hillis, Brian Silverman, and friends built a Tinkertoy computer that played tic-tac-toe. The device was made from 10, Tinkertoy pieces. I often fantasize about the outcome of placing mathematicians from different eras in the same room.

What profound knowledge might we gain if we had the power to bring together great thinkers of various ages for a conference on mathematics? Could ancient mathematicians contribute any useful ideas to modern mathemati- cians?

Would a meeting of time-traveling mathematicians offer more to humanity than a meeting of other scientists— for example, biologists or sociologists? Power notation. Numerical religion.Hofstadter, Douglas , "Metamagical Themas: This is a wonderful book Gage, and H.

Three-Armed Protractor Com and Bn. Ball, Keith M. Pures Appl. According to Leibniz, God chooses to actualize this world out of an infinite number of possible worlds.