A Brief History Of Infinity

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A Brief History of Infinity

A Brief History of Infinity [Pdf/ePub] eBook ISBN-10: 1472107640
Author: ,
Publisher: Robinson
File Size: 1723 KB
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Read Count: 9308585


A Brief History of Infinity by , Book Resume:

'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

Achilles In the Quantum Universe

Achilles In the Quantum Universe [Pdf/ePub] eBook ISBN-10: 1627797505
Author: Richard Morris
Publisher: Henry Holt and Company
File Size: 1432 KB
File Format: Pdf
Read Count: 2376234


Achilles In the Quantum Universe by Richard Morris Book Resume:

Centuries ago, when the ancient philosopher Zeno proposedhis famous paradox involving Achilles and the Tortoise, he struck at the heart of one of science's most enduring and intractable problems: How do we define the infinite? From then on, our greatest natural philosophers, logicians, mathematicians, and scientists, from Aristotle to Stephen Hawking, have been stymied-and driven-by infinity. Acclaimed Science writer Richard Morris guides us on a fascinating, literate and entertaining tour of the efforts made throughout history to make sense of the mind-bending concept of the infinite. In tracing this quest, Morris shows us how each new encounter with infinity drove the advancement of physics and mathematics. Along the way, we encounter such luminaries as Galileo and Newton, Tycho Brahe and Giordano Bruno, and the giants of modern physics: Planck, Einstein, Bohr, Feynmann, Hawking, and numerous others. Beginning with simple logical puzzles and progressing to the latest cosmological theories, Morris shows how these same infinity problems helped spawn such groundbreaking scientific developments as relativity and quantum mechanics. Though in many ways, the infinite is just as baffling today as it was in antiquity, contemporary scientists are probing ever deeper into the nature of our universe and catching fleeting glimpses of the infinite in ways the ancients could never have imagined. Ultimately, we see that hidden within the theoretical possibility of an infinite number of universes may lie the answers to some of humankind's most fundamental questions: Why is there something rather than nothing? Why are we here?

To Infinity and Beyond

To Infinity and Beyond [Pdf/ePub] eBook ISBN-10: 1461253942
Author: Eli Maor
Publisher: Springer Science & Business Media
File Size: 1431 KB
File Format: Pdf
Read Count: 7826284


To Infinity and Beyond by Eli Maor Book Resume:

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and settled down for the night. But a numbing thought kept him from sleep: How could it be that by merely moving the occupants from one room to another, the first room had become vacated? (Remember, all of the rooms were occupied when he arrived.

The Beginning of Infinity

The Beginning of Infinity [Pdf/ePub] eBook ISBN-10: 0141969695
Author: David Deutsch
Publisher: Penguin UK
File Size: 1824 KB
File Format: Pdf
Read Count: 5279830


The Beginning of Infinity by David Deutsch Book Resume:

A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers. Throughout history, mankind has struggled to understand life's mysteries, from the mundane to the seemingly miraculous. In this important new book, David Deutsch, an award-winning pioneer in the field of quantum computation, argues that explanations have a fundamental place in the universe. They have unlimited scope and power to cause change, and the quest to improve them is the basic regulating principle not only of science but of all successful human endeavor. This stream of ever improving explanations has infinite reach, according to Deutsch: we are subject only to the laws of physics, and they impose no upper boundary to what we can eventually understand, control, and achieve. In his previous book, The Fabric of Reality, Deutsch describe the four deepest strands of existing knowledge-the theories of evolution, quantum physics, knowledge, and computation-arguing jointly they reveal a unified fabric of reality. In this new book, he applies that worldview to a wide range of issues and unsolved problems, from creativity and free will to the origin and future of the human species. Filled with startling new conclusions about human choice, optimism, scientific explanation, and the evolution of culture, The Beginning of Infinity is a groundbreaking book that will become a classic of its kind.

Naming Infinity

Naming Infinity [Pdf/ePub] eBook ISBN-10: 0674053915
Author: Loren Graham,Jean-Michel Kantor
Publisher: Harvard University Press
File Size: 803 KB
File Format: Pdf
Read Count: 6637363


Naming Infinity by Loren Graham,Jean-Michel Kantor Book Resume:

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

A Short History of Nearly Everything

A Short History of Nearly Everything [Pdf/ePub] eBook ISBN-10: 0385674503
Author: Bill Bryson
Publisher: Anchor Canada
File Size: 630 KB
File Format: Pdf
Read Count: 391567


A Short History of Nearly Everything by Bill Bryson Book Resume:

One of the world’s most beloved and bestselling writers takes his ultimate journey -- into the most intriguing and intractable questions that science seeks to answer. In A Walk in the Woods, Bill Bryson trekked the Appalachian Trail -- well, most of it. In In A Sunburned Country, he confronted some of the most lethal wildlife Australia has to offer. Now, in his biggest book, he confronts his greatest challenge: to understand -- and, if possible, answer -- the oldest, biggest questions we have posed about the universe and ourselves. Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining.

Infinite Powers

Infinite Powers [Pdf/ePub] eBook ISBN-10: 132888001X
Author: Steven Strogatz
Publisher: Houghton Mifflin Harcourt
File Size: 1092 KB
File Format: Pdf
Read Count: 5218405


Infinite Powers by Steven Strogatz Book Resume:

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better. Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‐to‐earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‐world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

Visions of Infinity

Visions of Infinity [Pdf/ePub] eBook ISBN-10: 0465065996
Author: Ian Stewart
Publisher: Basic Books
File Size: 636 KB
File Format: Pdf
Read Count: 511076


Visions of Infinity by Ian Stewart Book Resume:

It is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility. In Visions of Infinity, celebrated mathematician Ian Stewart provides a fascinating overview of the most formidable problems mathematicians have vanquished, and those that vex them still. He explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. The three-century effort to prove Fermat's last theorem—first posited in 1630, and finally solved by Andrew Wiles in 1995—led to the creation of algebraic number theory and complex analysis. The Poincaré conjecture, which was cracked in 2002 by the eccentric genius Grigori Perelman, has become fundamental to mathematicians' understanding of three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which Stewart refers to as the “Holy Grail of pure mathematics,” and the P/NP problem, which straddles mathematics and computer science, could easily remain unproved for another hundred years. An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematicians the world over are rising to the challenges set by their predecessors—and how the enigmas of the past inevitably surrender to the powerful techniques of the present.

The Infinite

The Infinite [Pdf/ePub] eBook ISBN-10: 1351381261
Author: A.W. Moore
Publisher: Routledge
File Size: 1665 KB
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Read Count: 1317653


The Infinite by A.W. Moore Book Resume:

We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor’s remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Gödel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, ‘Infinity superseded’, which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.

The Infinite Book

The Infinite Book [Pdf/ePub] eBook ISBN-10: 1407072749
Author: John D. Barrow
Publisher: Random House
File Size: 1615 KB
File Format: Pdf
Read Count: 2718695


The Infinite Book by John D. Barrow Book Resume:

‘A delight. Popular science doesn’t come much better than this’ Independent Everything you might want to know about infinity - in history and all the way to today's cutting-edge science. Infinity is surely the strangest idea that humans have ever had. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Can you do an infinite number of things in a finite amount of time? Is the Universe infinite? Infinity is also the place where things happen that don't. What is it like to live in a Universe where nothing is original, where you can live forever, where anything that can be done, is done, over and over again? These are some of the deep questions that the idea of the infinite pushes us to ask. Throughout history, the infinite has been a dangerous concept. Many have lost their lives, their careers, or their freedom for talking about it. The Infinite Book will take you on a tour of these dangerous questions and the strange answers that scientists, mathematicians, philosophers and theologians have come up with to deal with its threats to our sanity.

Everything and More: A Compact History of Infinity

Everything and More: A Compact History of Infinity [Pdf/ePub] eBook ISBN-10: 0393241998
Author: David Foster Wallace
Publisher: W. W. Norton & Company
File Size: 371 KB
File Format: Pdf
Read Count: 5129292


Everything and More: A Compact History of Infinity by David Foster Wallace Book Resume:

"A gripping guide to the modern taming of the infinite."—The New York Times. With a new introduction by Neal Stephenson. Is infinity a valid mathematical property or a meaningless abstraction? David Foster Wallace brings his intellectual ambition and characteristic bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that there was more than one kind of infinity. Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

Beyond Infinity

Beyond Infinity [Pdf/ePub] eBook ISBN-10: 0465094821
Author: Eugenia Cheng
Publisher: Basic Books
File Size: 1557 KB
File Format: Pdf
Read Count: 8278760


Beyond Infinity by Eugenia Cheng Book Resume:

"[Cheng] does a great service by showing us non-mathematician schlubs how real mathematical creativity works." --Wall Street Journal How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

The Man Who Knew Infinity

The Man Who Knew Infinity [Pdf/ePub] eBook ISBN-10: 1439121869
Author: Robert Kanigel
Publisher: Simon and Schuster
File Size: 1035 KB
File Format: Pdf
Read Count: 1241277


The Man Who Knew Infinity by Robert Kanigel Book Resume:

NOW A MAJOR MOTION PICTURE STARRING JEREMY IRONS AND DEV PATEL! A moving and enlightening look at the unbelievable true story of how gifted prodigy Ramanujan stunned the scholars of Cambridge University and revolutionized mathematics. In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the preeminent English mathematician's opinion on several ideas he had about numbers. Realizing the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England. Thus began one of the most improbable and productive collaborations ever chronicled. With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, "the Prince of Intuition," tested his brilliant theories alongside the sophisticated and eccentric Hardy, "the Apostle of Proof." In time, Ramanujan's creative intensity took its toll: he died at the age of thirty-two, but left behind a magical and inspired legacy that is still being plumbed for its secrets today.

Infinite Ascent

Infinite Ascent [Pdf/ePub] eBook ISBN-10: 0307778177
Author: David Berlinski
Publisher: Modern Library
File Size: 781 KB
File Format: Pdf
Read Count: 1704176


Infinite Ascent by David Berlinski Book Resume:

In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.

Introducing Infinity

Introducing Infinity [Pdf/ePub] eBook ISBN-10: 1848318839
Author: Brian Clegg
Publisher: Icon Books Ltd
File Size: 1417 KB
File Format: Pdf
Read Count: 2462531


Introducing Infinity by Brian Clegg Book Resume:

Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers – and provoked and shocked others. The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh’s brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.

The Mathematics of Infinity

The Mathematics of Infinity [Pdf/ePub] eBook ISBN-10: 111824382X
Author: Theodore G. Faticoni
Publisher: John Wiley & Sons
File Size: 1918 KB
File Format: Pdf
Read Count: 4505103


The Mathematics of Infinity by Theodore G. Faticoni Book Resume:

Praise for the First Edition ". . . an enchanting book for those people in computer scienceor mathematics who are fascinated by the concept ofinfinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easyto read and well suited for self-study . . . highlyrecommended."—Choice The concept of infinity has fascinated and confused mankind forcenturies with theories and ideas that cause even seasonedmathematicians to wonder. The Mathematics of Infinity: A Guide toGreat Ideas, Second Edition uniquely explores how we can manipulatethese ideas when our common sense rebels at the conclusions we aredrawing. Continuing to draw from his extensive work on the subject, theauthor provides a user-friendly presentation that avoidsunnecessary, in-depth mathematical rigor. This Second Editionprovides important coverage of logic and sets, elements andpredicates, cardinals as ordinals, and mathematical physics.Classic arguments and illustrative examples are provided throughoutthe book and are accompanied by a gradual progression ofsophisticated notions designed to stun readers' intuitive view ofthe world. With an accessible and balanced treatment of both concepts andtheory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, TheMathematics of Infinity: A Guide to Great Ideas, Second Edition isan insightful supplement for mathematics courses on set theory atthe undergraduate level. The book also serves as a fascinatingreference for mathematically inclined individuals who areinterested in learning about the world of counterintuitivemathematics.

Infinite Jest

Infinite Jest [Pdf/ePub] eBook ISBN-10: 0316073857
Author: David Foster Wallace
Publisher: Back Bay Books
File Size: 1362 KB
File Format: Pdf
Read Count: 1013330


Infinite Jest by David Foster Wallace Book Resume:

A gargantuan, mind-altering comedy about the Pursuit of Happiness in America Set in an addicts' halfway house and a tennis academy, and featuring the most endearingly screwed-up family to come along in recent fiction, Infinite Jest explores essential questions about what entertainment is and why it has come to so dominate our lives; about how our desire for entertainment affects our need to connect with other people; and about what the pleasures we choose say about who we are. Equal parts philosophical quest and screwball comedy, Infinite Jest bends every rule of fiction without sacrificing for a moment its own entertainment value. It is an exuberant, uniquely American exploration of the passions that make us human - and one of those rare books that renew the idea of what a novel can do. "The next step in fiction...Edgy, accurate, and darkly witty...Think Beckett, think Pynchon, think Gaddis. Think." --Sven Birkerts, The Atlantic

Origin Story

Origin Story [Pdf/ePub] eBook ISBN-10: 0316392022
Author: David Christian
Publisher: Little, Brown Spark
File Size: 998 KB
File Format: Pdf
Read Count: 3073832


Origin Story by David Christian Book Resume:

This New York Times bestseller "elegantly weaves evidence and insights . . . into a single, accessible historical narrative" (Bill Gates) and presents a captivating history of the universe -- from the Big Bang to dinosaurs to mass globalization and beyond. Most historians study the smallest slivers of time, emphasizing specific dates, individuals, and documents. But what would it look like to study the whole of history, from the big bang through the present day -- and even into the remote future? How would looking at the full span of time change the way we perceive the universe, the earth, and our very existence? These were the questions David Christian set out to answer when he created the field of "Big History," the most exciting new approach to understanding where we have been, where we are, and where we are going. In Origin Story, Christian takes readers on a wild ride through the entire 13.8 billion years we've come to know as "history." By focusing on defining events (thresholds), major trends, and profound questions about our origins, Christian exposes the hidden threads that tie everything together -- from the creation of the planet to the advent of agriculture, nuclear war, and beyond. With stunning insights into the origin of the universe, the beginning of life, the emergence of humans, and what the future might bring, Origin Story boldly reframes our place in the cosmos.

The Nothing that Is

The Nothing that Is [Pdf/ePub] eBook ISBN-10: 9780198029458
Author: Robert Kaplan
Publisher: Oxford University Press
File Size: 1927 KB
File Format: Pdf
Read Count: 9243139


The Nothing that Is by Robert Kaplan Book Resume:

A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything. Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists. The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

A Brief History of Mathematical Thought

A Brief History of Mathematical Thought [Pdf/ePub] eBook ISBN-10: 1472117158
Author: Luke Heaton
Publisher: Robinson
File Size: 1769 KB
File Format: Pdf
Read Count: 9031422


A Brief History of Mathematical Thought by Luke Heaton Book Resume:

Mathematics is a product of human culture which has developed along with our attempts to comprehend the world around us. In A Brief History of Mathematical Thought, Luke Heaton explores how the language of mathematics has evolved over time, enabling new technologies and shaping the way people think. From stone-age rituals to algebra, calculus, and the concept of computation, Heaton shows the enormous influence of mathematics on science, philosophy and the broader human story. The book traces the fascinating history of mathematical practice, focusing on the impact of key conceptual innovations. Its structure of thirteen chapters split between four sections is dictated by a combination of historical and thematic considerations. In the first section, Heaton illuminates the fundamental concept of number. He begins with a speculative and rhetorical account of prehistoric rituals, before describing the practice of mathematics in Ancient Egypt, Babylon and Greece. He then examines the relationship between counting and the continuum of measurement, and explains how the rise of algebra has dramatically transformed our world. In the second section, he explores the origins of calculus and the conceptual shift that accompanied the birth of non-Euclidean geometries. In the third section, he examines the concept of the infinite and the fundamentals of formal logic. Finally, in section four, he considers the limits of formal proof, and the critical role of mathematics in our ongoing attempts to comprehend the world around us. The story of mathematics is fascinating in its own right, but Heaton does more than simply outline a history of mathematical ideas. More importantly, he shows clearly how the history and philosophy of maths provides an invaluable perspective on human nature.