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THERE is a great mystery about mathematics. There is also, of course, a great mystique. The Science Masters series from Weidenfeld and Nicolson/BasicBooks aims to breakdown the mystique. The publishers say the series should 鈥渆nable a broad audience to attain scientific literacy鈥� 鈥� a job they are doing wonderfully well in most disciplines. This avenue of inquiry is right in Ian Stewart鈥檚 line. In Nature鈥檚 Numbers he argues that mathematics is perfectly straightforward: it deals with and explores the actual, already present, patterns of nature. Its discourses are abstracted (sucked out) generalities based on experienced connections. Mathematics is, he says, basically and primarily practical. He describes Newton as the last of the 鈥渕agicians鈥�, the last to share a mathematical mystique that stretched from Babylon to the 17th century.

I once asked a mathematician to define the difference between maths and physics. She replied: 鈥淚f it鈥檚 for anything, it isn鈥檛 maths.鈥� Stewart disagrees radically. Ultimately, he claims, all maths is practical, although you may have to wait a while to find out bow it applies. He wants to abolish the division between pure and applied maths by insisting that it is all 鈥渁pplicable maths鈥�.

Consequently, most of the book deals with the maths in connection with problems more often labelled as physics or chemistry. Symmetry for him is about molecular stability. The wave equation is about inventing videos and so on. Nature has patterns and regularities; the 鈥渏ob鈥� of mathematics is to track them down, formulate them and use them.

Even with the mystique taken away, there surely remains a mystery about mathematics. Why does it work? Why does this highly abstract formal game, this 鈥渦nreal鈥� mental construct, deliver accurate descriptions, precise predictions, workable solutions in the 鈥渞eal鈥� world? Or as Stephen Hawking puts it, 鈥渨hat is it that breathes fire into the equations?鈥�

These are the sorts of questions that mathematical illiterates like me want answered. I wish that Stewart had had more space to address them. We would also like to know what mathematicians are up to at the moment, and the nature of their most pressing questions and investigations.

Why do I find the pragmatic approach upsettling? Do I secretly desire the purity of mystical mathematics? I hope this is not the case, although mystery attracts the ignorant. But having encountered the incomprehensibility of Georg Cantor鈥檚 concept of the absolute, the frustrating elegance of Kurt G枚del鈥檚 incompleteness theorems, or the complex, protracted wrestlings with Pierre de Fermat鈥檚 last theorem, I find myself unconvinced by Stewart鈥檚 bouncy common sense.