Something accessible for people who know no maths and something fun for the math literate.
1. The Universe And The Teacup
The mathematics of truth and beauty. An elegant study of the way maths can provide solutions to everyday problems.
Charles Dickens once proclaimed that he was boycotting the train service for the rest of December “on the grounds that the average annual quota of railroad accidents in Britain had not been filled and therefore further disasters were obviously imminent”.
Dickens was not just literate but numerate as well, and he was well aware of the absurdity of his statement. He was trying to make a point about the general public’s poor understanding of statistics, and it is quite likely that many people thought he was being quite serious and followed his advice until the New Year, when presumably a new quota would begin.
A century later we are increasingly bombarded by statistics, probabilities and averages, and yet our understanding of these numbers is still weak. K. C. Cole’s delightful book is an attempt to explain what numbers mean, and how they are used, abused and misunderstood.
(extract from Simon Singh’s review, Sunday Telegraph, 14 March 1998)
2. The Simpsons And Their Mathematical Secrets
Based on interviews with the writers of The Simpsons and accompanied by images from the show, facsimiles of scripts, paintings and drawings and other imagery, this fascinating book reveals the meaningful mathematical concepts behind the most successful show in TV history.
3. Once Upon A Number
What two things could be more different than numbers and stories? Numbers are abstract, certain, and eternal, but to most of us somewhat dry and bloodless. Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections.
4. Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks
Diaconis and Graham tell the stories—and reveal the best tricks—of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick—and much more.
5. Gödel, Escher, Bach: An Eternal Golden Braid
Douglas Hofstadter's book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
6. Euclid in the Rainforest: Discovering Universal Truth in Logic and Math
Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore
logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.
7. The Number Sense
Not a book about mathematics itself, but rather about how the brain deals with numbers.
In 1994 Professor Steven Pinker wrote The Language Instinct, an international best-seller which argued that linguistic ability is a human instinct, hardwired into our brains by evolution. Now Stanislas Dehaene has written
The Number Sense, an attempt to argue the parallel case for numeracy.
In his rigorous (though generally engaging) account, this distinguished mathematician-turned-neuropsychologist explains how we conceptualise numbers, how we learn to count and perform arithmetic, and explores to what extent animals have mathematical talent.
(extract from Simon Singh’s review, Sunday Telegraph, 18 April 1998).
8. The Man Who Knew Infinity: A Life of the Genius Ramanujan
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 and left behind a magical and inspired legacy that is still being plumbed for its secrets today.
9. Mathenauts: Tales of Mathematical Wonder
A collection of 23 science fiction short stories, each of which centres on mathematics. Two are by Martin Gardner, and many of the great writers of SF are represented: Isaac Asimov, Gregory Benford, Larry Niven, Frederik Pohl. The high point is Norman Kagan's utterly hilarious "The Mathenauts", in which only mathematicians can travel through space, because space is mathematical – and, conversely, anything mathematical can be reality. An isomorphomechanism is essential equipment. Between them, these tales cover most of the undergraduate mathematics syllabus, though not in examinable form.
10. The Joy of x: A Guided Tour of Math, from One to Infinity
A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined
Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.
Enjoy your reading!