From 0 to Infinity in 26 Centuries (21 page)

The fundamental theories of how the universe works – as discovered by, among others, Newton, Einstein, Feynman and Hawking – have been made through the creation of a mathematical
model and the pursuit of the mathematical conclusions that ensue. These models are then tested by experiments in the real world to check the accuracy of the model.

As time goes by, it seems that in order to generate the best possible rate of advancement in science, we need mathematicians who understand the latest developments in that field, and scientists
who understand the latest developments in mathematics too.

As Galileo said:

Mathematics is the language with which God has written the universe.

Bibliography

50 Mathematical Ideas You Really Need to Know

by Tony Crilly (Quercus)

A History of Mathematics

by Carl Boyer and Uta Merzbach (John Wiley & Sons)

Descartes: Key Philosophical Writings

by Rene Descartes trans. Elizabeth Haldane and G. Ross (Wordsworth Classics)

Elements of Geometry
by Euclid trans. Richard Fitzpatrick

Fermat’s Last Theorem
by Simon Singh (Fourth Estate)

How Mathematics Happened: The First 50,000 Years

by Peter Rudman (Prometheus)

Mathematics: From the Birth of Numbers

by Jan Gullberg (WW Norton & Co.)

Number: From Ancient Civilisations to the Computer

by John McLeish (Flamingo)

The Code Book
by Simon Singh (Fourth Estate)

The History of Mathematics: A Very Short Introduction

by Jacqueline Stedall (OUP)

The Psychology of Learning Mathematics

by Richard Skemp (Pelican)

Index

abacus
ref 1
,
ref 2

abundant numbers
ref 1

accountants, dawn of
ref 1

Al-Khwarizmi
ref 1

Al-Kindi
ref 1

Alcuin of York
ref 1

Alexandria
ref 1

algebra
ref 1
,
ref 2

Boolean
ref 1
,
ref 2

algorithms
ref 1

alien civilizations
ref 1

Analytical Engine
ref 1

Ancient Egypt
ref 1
,
ref 2
,
ref 3
,
ref 4

Ancient Greeks
ref 1

Appel, Kenneth
ref 1

Archimedes
ref 1

Aristotle
ref 1

arithmetic:

Arithmetica
(Diophantus)
ref 1
,
ref 2

Artificial Intelligence
ref 1

astronomy and astrology
ref 1
,
ref 2
,
ref 3

Australian Aboriginals
ref 1

Avogadro’s constant
ref 1

Bede, Venerable
ref 1

Berlin Papyrus
ref 1

Bernoulli, Daniel
ref 1

Bernoulli, Jacob
ref 1
,
ref 2

Bernoulli, Johann
ref 1

Bertrand, Joseph
ref 1

binary numbers
ref 1
,
ref 2

binomial coefficients
ref 1

binomial theorem
ref 1

Birthday problem
ref 1
,
ref 2

Blanusa, Danilo
ref 1

Bletchley Park
ref 1

Bombe
ref 1

Book of Addition and Subtraction
According to the Hindu Calculation
(Al-Khwarizmi)
ref 1

Boole, George
ref 1

Brahmagupta
ref 1

calculus
ref 1

calendars:

Cantor, Georg
ref 1

Cardano, Gerolamo
ref 1

Cartesian graphs
ref 1

catenary curve
ref 1

Chaos Game
ref 1

chaos theory
ref 1

Chaucer, Geoffrey
ref 1

China
ref 1
,
ref 2

Compendious Book on Calculation
. . .,
The
(Al-Khwarizmi)
ref 1

complex numbers
ref 1

compound interest
ref 1

computers:

conic sections
ref 1

continuum hypothesis
ref 1

coordinates
ref 1

Copernicus, Nicolaus
ref 1

cosine
ref 1

counting:

cryptography
ref 1

cubic equations
ref 1

cyclic quadrilateral
ref 1

decimal point
ref 1

decimal system
ref 1
,
ref 2
,
ref 3

deficient numbers
ref 1

Descartes, René
ref 1
,
ref 2

Description of the Wonderful Rule of Logarithms
(Napier)
ref 1

Difference Engine
ref 1

difference of two squares
ref 1
,
ref 2

differential equations
ref 1
,
ref 2

differentiation
ref 1

Diophantus
ref 1
,
ref 2

distributed computing
ref 1

Drake, Frank
ref 1

Dresden Codex
ref 1
,
ref 2

Einstein, Albert
ref 1

Elements
(Euclid)
ref 1
,
ref 2

Enigma
ref 1

equations
ref 1
,
ref 2
,
ref 3
,
ref 4
,
ref 5
,
ref
6

Eratosthenes
ref 1

Euclid
ref 1
,
ref 2
,
ref 3

Euler, Leonhard
ref 1
,
ref 2

Europe, Middle Ages
ref 1

exhaustion, method of
ref 1

Exiguus, Dionysius
ref 1

extraterrestrial intelligence
ref 1

Feynman, Richard
ref 1

Fibonacci
ref 1

fluid mechanics
ref 1

four-colour theorem
ref 1

fractals
ref 1

fractions
ref 1
,
ref 2
,
ref 3
,
ref 4

frequency analysis
ref 1

Gauss, Carl
ref 1

geometry
ref 1
,
ref 2
,
ref 3

Goldbach, Christian
ref 1

Goldbach conjecture
ref 1
,
ref 2

golden mean
ref 1
,
ref 2

Google/Googol
ref 1

gradients
ref 1

graph theory
ref 1

Guthrie, Francis
ref 1

Hall, Monty
ref 1

Hardy, Godfrey
ref 1

Hawking, Stephen
ref 1

Hero
ref 1

hexagrams
ref 1

hieroglyphics and hieratic writing
ref 1

Hilbert, David
ref 1
,
ref 2

Hippasus
ref 1

hunter-gatherers
ref 1

Huygens, Christiaan
ref 1
,
ref 2

Hypatia
ref 1

imaginary numbers
ref 1
,
ref 2

India
ref 1

infinity
ref 1
,
ref 2
,
ref 3

integration
ref 1

irrational numbers
ref 1

Ishango bone
ref 1

Islam
ref 1

iteration
ref 1
,
ref 2

Jia Xian
ref 1

Kasner, Edward
ref 1

Kerckhoff, Auguste
ref 1

Key to Mathematics
,
The
(Oughtred)
ref 1

Khayyám, Omar
ref 1

Koch, Helge von
ref 1

Königsberg bridges
ref 1
,
ref 2

Large Hadron Collider
ref 1

large numbers
ref 1

Leibniz, Gottfried
ref 1
,
ref 2
,
ref 3
,
ref 4
,
ref 5
,
ref 6

Leonardo da Vinci
ref 1

Leonardo of Pisa (Fibonacci)
ref 1

Let’s Make a Deal
ref 1

logarithms
ref 1
,
ref 2

Lorenz, Edward
ref 1

Lovelace, Ada
ref 1

Mandelbrot, Benoit
ref 1

Mandelbrot set
ref 1

mathematics:

Mayans
ref 1
,
ref 2

Meditations on First Philosophy
(Descartes)
ref 1

Mesopotamia
ref 1
,
ref 2
,
ref 3
,
ref 4

Metrodorus
ref 1

Millennium problems
ref 1

Mises, Richard von
ref 1

modular arithmetic
ref 1

Mohammed
ref 1

morphogenesis
ref 1

Moscow Mathematical Papyrus
ref 1

multiplication
ref 1

musical notes and mathematics
ref 1