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Index
Introduction
WHAT IS MATHEMATICS FOR?
An introduction to purposes and prospects
WHERE DO NUMBERS COME FROM?
From notches on bones to hexadecimals
WHY ARE PRIMES THE ATOMS OF MATHEMATICS?
Building blocks and the fundamental theorem of arithmetic
WHICH ARE THE STRANGEST NUMBERS?
Real, irrational and transcendental numbers
ARE IMAGINARY NUMBERS TRULY IMAGINARY?
From the imaginary ‘i’ to octonions
HOW BIG IS INFINITY?
Set theory and the infinity revolution
WHERE DO PARALLEL LINES MEET?
The birth of new geometries
WHAT IS THE MATHEMATICS OF THE UNIVERSE?
The Calculus miracle
ARE STATISTICS LIES?
Data, proof and ‘damned lies’
CAN MATHEMATICS GUARANTEE RICHES?
Uncertainty, chance and probability theory
IS THERE A FORMULA FOR EVERYTHING?
Mathematical recipes and the search for knowledge
WHY ARE THREE DIMENSIONS NOT ENOUGH?
Higher dimensions, monster curves and fractals
CAN A BUTTERFLY’S WINGS REALLY CAUSE A HURRICANE?
Chaos theory, weather equations and strange attractors
CAN WE CREATE AN UNBREAKABLE CODE?
Ciphers, the Enigma machine and quantum computers
IS MATHEMATICS BEAUTIFUL?
Music, art, golden numbers and the Fibonacci sequence
CAN MATHEMATICS PREDICT THE FUTURE?
Mathematical models, simulations and game theory
WHAT SHAPE IS THE UNIVERSE?
Topology, manifolds and the Poincaré conjecture
WHAT IS SYMMETRY?
Patterns, dualities and the fundamental nature of reality
IS MATHEMATICS TRUE?
From Plato’s reality to Gödel’s incompleteness theorems
IS THERE ANYTHING LEFT TO SOLVE?
The great unsolved problems and the future of mathematics
Glossary
Index
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