The math book: from Pythagoras to the 57th dimension, 250 milestones in the history of mathematics

555 Pages·2009·26 MB·English

by  Clifford A. Pickover

Books by Clifford A. Pickover The Alien IQ Test
Archimedes to Hawking
A Beginner’s Guide to Immortality Black Holes: A Traveler’s Guide Calculus
and Pizza
Chaos and Fractals
Chaos in Wonderland
Computers, Pattern, Chaos, and Beauty Computers and the Imagination
Cryptorunes: Codes and Secret Writing Dreaming the Future
Egg Drop Soup
Future Health
Fractal Horizons: The Future Use of Fractals Frontiers of Scientific
Visualization The Girl Who Gave Birth to Rabbits The Heaven Virus
Keys to Infinity
Liquid Earth
The Lobotomy Club
The Loom of God
The Mathematics of Oz
Mazes for the Mind: Computers and the Unexpected Mind-Bending Visual
Puzzles (calendars and card sets) The Möbius Strip
The Paradox of God and the Science of Omniscience A Passion for Mathematics
The Pattern Book: Fractals, Art, and Nature The Science of Aliens Sex, Drugs,
Einstein, and Elves Spider Legs (with Piers Anthony) Spiral Symmetry (with
Istvan Hargittai) Strange Brains and Genius
Sushi Never Sleeps
The Stars of Heaven
Surfing through Hyperspace
Time: A Traveler’s Guide
Visions of the Future
Visualizing Biological Information Wonders of Numbers
The Zen of Magic Squares, Circles, and Stars The Physics Book

For Martin Gardner
STERLING and the distinctive Sterling logo are registered trademarks of
Sterling Publishing Co., Inc.
Library of Congress Cataloging-in-Publication Data Pickover, Clifford A.
The math book / Clifford A. Pickover.
p. cm.
ISBN 978-1-4027-5796-9
1. Mathematics–History. I. Title.
QA21.P53 2009
510.9–dc22
2008043214
Published by Sterling Publishing Co., Inc.
387 Park Avenue South, New York, NY 10016
© 2009 by Clifford A. Pickover All rights reserved
Sterling ISBN 978-1-4027-9749-1
For information about custom editions, special sales, premium and
corporate purchases, please contact Sterling Special Sales Department at 800–805–5489 or
[email protected].
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a
beauty cold and austere, like that of sculpture.”
—Bertrand Russell, Mysticism and Logic, 1918
“Mathematics is a wonderful, mad subject, full of imagination, fantasy, and
creativity that is not limited by the petty details of the physical world, but only by
the strength of our inner light.”
—Gregory Chaitin, “Less Proof, More Truth,”
New Scientist, July 28, 2007
“Perhaps an angel of the Lord surveyed an endless sea of chaos, then troubled it
gently with his finger. In this tiny and temporary swirl of equations, our cosmos
took shape.”
—Martin Gardner, Order and Surprise, 1950
“The great equations of modern physics are a permanent part of scientific
knowledge, which may outlast even the beautiful cathedrals of earlier ages.”
—Steven Weinberg, in Graham Farmelo’s
It Must Be Beautiful, 2002
HOW TO USE THIS BOOK
The 250 chronological milestones are easily viewed in the selectable table of
contents that follows. Each milestone consists of a synopsis, followed by at least
one image that helps to illustrate an aspect of the seminal event, publication, or
concept. Occasional text in bold type points the reader to related entries.
Additionally, a small “See also” section at the bottom of each entry helps weave
entries together in a web of interconnectedness and may help the reader traverse
the book in a playful quest for discovery.
Contents
Introduction
c. 150 Million B.C. Ant Odometer
c. 30 Million B.C. Primates Count
c. 1 Million B.C. Cicada-Generated Prime Numbers
c. 100,000 B.C. Knots
c. 18,000 B.C. Ishango Bone
c. 3000 B.C. Quipu
c. 3000 B.C. Dice
c. 2200 B.C. Magic Squares
c. 1800 B.C. Plimpton 322
c. 1650 B.C. Rhind Papyrus
c. 1300 B.C. Tic Tac Toe
c. 600 B.C. Pythagorean Theorem and Triangles
548 B.C. Go
c. 530 B.C. Pythagoras Founds Mathematical Brotherhood
c. 445 B.C. Zeno’s Paradoxes
c. 440 B.C. Quadrature of the Lune
c. 350 B.C. Platonic Solids
c. 350 B.C. Aristotle’s Organon
c. 320 B.C. Aristotle’s Wheel Paradox
300 B.C. Euclid’s Elements
c. 250 B.C. Archimedes: Sand, Cattle & Stomachion
c. 250 B.C. π
c. 240 B.C. Sieve of Eratosthenes
c. 240 B.C. Archimedean Semi-Regular Polyhedra
225 B.C. Archimedes’ Spiral
c. 180 B.C. Cissoid of Diocles
c. 150 Ptolemy’s Almagest
250 Diophantus’s Arithmetica
c. 340 Pappus’s Hexagon Theorem
c. 350 Bakhshali Manuscript
415 The Death of Hypatia
c. 650 Zero
c. 800 Alcuin’s Propositiones ad Acuendos Juvenes
830 Al-Khwarizmi’s Algebra
834 Borromean Rings
850 Ganita Sara Samgraha
c. 850 Thabit Formula for Amicable Numbers
c. 953 Chapters in Indian Mathematics
1070 Omar Khayyam’s Treatise
c. 1150 Al-Samawal’s The Dazzling
c. 1200 Abacus
1202 Fibonacci’s Liber Abaci
1256 Wheat on a Chessboard
c. 1350 Harmonic Series Diverges
c. 1427 Law of Cosines
1478 Treviso Arithmetic
c. 1500 Discovery of Series Formula for π
1509 Golden Ratio
1518 Polygraphiae Libri Sex
1537 Loxodrome
1545 Cardano’s Ars Magna
1556 Sumario Compendioso
1569 Mercator Projection
1572 Imaginary Numbers
1611 Kepler Conjecture
1614 Logarithms
1621 Slide Rule
1636 Fermat’s Spiral
1637 Fermat’s Last Theorem
1637 Descartes’ La Géométrie
1637 Cardioid
1638 Logarithmic Spiral
1639 Projective Geometry
1641 Torricelli’s Trumpet
1654 Pascal’s Triangle
1657 The Length of Neile’s Semicubical Parabola
1659 Viviani’s Theorem
c. 1665 Discovery of Calculus
1669 Newton’s Method
1673 Tautochrone Problem
1674 Astroid
1696 L’Hôpital’s Analysis of the Infinitely Small
1702 Rope around the Earth Puzzle
1713 Law of Large Numbers
1727 Euler’s Number, e
1730 Stirling’s Formula
1733 Normal Distribution Curve
1735 Euler-Mascheroni Constant
1736 Königsberg Bridges
1738 St. Petersburg Paradox
1742 Goldbach Conjecture
1748 Agnesi’s Instituzioni Analitiche
1751 Euler’s Formula for Polyhedra
1751 Euler’s Polygon Division Problem
1759 Knight’s Tours
1761 Bayes’ Theorem
1769 Franklin Magic Square
1774 Minimal Surface
1777 Buffon’s Needle
1779 Thirty-Six Officers Problem
c. 1789 Sangaku Geometry
1795 Least Squares
1796 Constructing a Regular Heptadecagon
1797 Fundamental Theorem of Algebra
1801 Gauss’s Disquisitiones Arithmeticae
1801 Three-Armed Protractor
1807 Fourier Series
1812 Laplace’s Théorie Analytique des Probabilités
1816 Prince Rupert’s Problem
1817 Bessel Functions
1822 Babbage Mechanical Computer
1823 Cauchy’s Le Calcul Infinitésimal
1827 Barycentric Calculus
1829 Non-Euclidean Geometry
1831 Möbius Function
1832 Group Theory
1834 Pigeonhole Principle
1843 Quaternions
1844 Transcendental Numbers
1844 Catalan Conjecture
1850 The Matrices of Sylvester
1852 Four-Color Theorem
1854 Boolean Algebra