The Universe and the Teacup: The Mathematics of Truth and Beauty By K C Cole. Little, Brown pound;12.99
I'm a maths missionary," says K C Cole - whose The Universe and the Teacup has been a bestseller in her home town, Los Angeles, for six weeks. "It's amazing that people in LA, which is la-la land, can be keen on maths - but only if you present it in a way that relates to their lives." Using dozens of intriguing examples, the book shows how maths informs the way we think about everyday life.
Some of the book's content is familiar (the use of maths in IQ tests and the statistics in Charles Murray and Richard Herrnstein's The Bell Curve are shown to be "meaningless"), but other aspects are new. Ms Cole shows in fascinating detail how you can use maths to assess the fairness of different voting systems. Other subjects, such as exponential population growth, fear and risk assessment, subatomic physics and the mathematics of prediction, are clearly and fascinatingly set out. The Universe and the Teacup is essential background reading for anyone going to see Good Will Hunting.
Like other popular accounts of science, it feeds a widespread hunger. "The desire to know about science is huge in the US - science museums are more popular than many sporting events. At weekends, they're jammed," says Ms Cole - she hates her first name and is known only by her initials - a journalist for 25 years.
Missionaries are made, not born, and Ms Cole "hated science at high school. Maths was OK, but irrelevant. I wanted to save the world, so I did politics at university." Then in 1972, she ran into Frank Oppenheimer, a physicist, and younger brother of the "father of the atom bomb". "Frank was very political, very left-wing, and saw science as a part of philosophy."
Since then, Ms Cole has won awards for science writing, been a senior editor at Discover magazine, and written six other books, ranging from a collection of her New York Times pieces - "on everything from nuclear war to travel" - to a book on women's issues. She's also taught writing skills to science undergraduates and worked with children in museums.
"One of the difficult things about maths for kids to grasp," Ms Cole says, "is that it's very precise and very abstract." But, as The Universe and the Teacup makes clear, "maths is only really precise about teeny-weeny things - everything else is a bit fuzzy."
Kids "get put off by excessive precision because they feel it doesn't relate to their lives". Teaching maths is "a bit like teaching music", Ms Cole says. "You need to be able to read music and do scales, but just imagine if you never did anything else. When I first played the flute, my teacher started with Bach - which inspired me to keep going."
The Universe and the Teacup sees maths as a way of thinking rather than rote learning. So it has lots of practical examples of how to use its methods when looking at, say, probability, but very few equations. Maths is "basically a critical tool that aims to make sense of information", Ms Cole says.
"For example, people are bad at understanding the mathematics of risk." Probability is always skewed by whether or not we feel in control. "When a plane crashes, everyone feels frightened - but the risk of dying in an air crash is minuscule compared with the risk from eating fatty foods." But since we can control "putting butter on our baked potato", it feels less risky than flying.
Maths always depends on the people using it. While statistics can prove that children with big feet correlate with higher maths scores, there is no causal connection: "The reason for the correlation is that children with bigger feet are older and have had more maths teaching." Scepticism is a valuable tool.
The trouble isn't numbers, it's what you think about them. "Everyone here is in uproar at the moment because of a report in which US children rank near-bottom in international maths tests. But ultimately tests only measure how well you do in tests. There's no shortage of good maths undergraduates in the US - but kids may not be good test-takers."
Once again cultural factors come into play. Such results mean "teachers get the blame". They have to carry the can for "people's worries about scientific illiteracy. Too many Americans believe in UFOs - we even had a president's wife [Nancy Reagan] who consulted a psychic."
Ms Cole says: "I want to show people that they have nothing to fear from science. Too many people think they're stupid because they can't do calculus. But the things in maths that really matter are the big questions, not the technical ways of getting there."
The Universe and the Teacup arose "from conversations with friends - poets, novelists, actors - who don't like maths, but are amazed when I talk about the science of truth and beauty. They are enchanted by the connections between science and the humanities." In the chapter on the mathematics of symmetry, Ms Cole shows how hidden structures hold seemingly dissimilar things together.
By discussing examples as disparate as snowflakes, cubes and circles, planetary orbits, shell patterns and petals, algebra and energy, Ms Cole shows how "the search for symmetry" is an effective tool for looking beyond "superficial differences" to find "more substantive, permanent meanings". On one level, soot and diamonds are both basically carbon. On another, Einstein's theory of relativity is not about "things being relative", but about one thing - the speed of light - being constant. The maths of symmetry gives a concrete feel to "our vague sense" that there is truth in beauty.
She is also keenly aware of gender issues. In one of the most fascinating parts of the book, she shows that when Albert Einstein got into a tricky theoretical corner - energy conservation in curved fourth-dimensional space - it was a German mathematician, Emmy Noether, who helped him out. She discovered the crucial link between symmetry and the fundamental laws of nature. Because she was a woman, she couldn't present her work in her own name. She invented a brilliant theorem, but wasn't interested in calculation - "hers was a maths not of cash registers, but of truth and beauty".
The book argues that "humans as a species are notoriously bad at mathematical reasoning. We're OK on the one-plus-one level, but really bad at imagining big numbers." This is why mathematicians like stories which illustrate what they're talking about. Knowing how many molecules make up a cup of tea is less vivid than being told that, put end to end, they would circle the earth 50 million times. The teacup can be as mysterious as the universe.