Imagining Numbers (particularly the square root of minus fifteen) by Barry Mazur, Farrar, Straus and Giroux, $22, ISBN 0374174695 Reviewed by Ben Longstaff
CLOSE your eyes and think of a number. The interesting question is not what is the number that comes into your head, but what image does. The chances are you鈥檙e not picturing an 鈥渋maginary鈥� number 鈥� a multiple of i, the square root of 鈭�1 鈥� because that鈥檚 the funny thing about these objects: the imagination has no ready way to visualise them. Harvard mathematician Barry Mazur sets out to remedy this in Imagining Numbers.
Through anecdotes, poetry and philosophy, Mazur carefully expands the familiar mental confines of the number line into the liberating open spaces of the complex number plane, and along the way he makes a delightful case for the pleasures of abstract thought.
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The mathematics is elementary 鈥� the appeal lies in contemplating what it is to play with these ideas and feel the imagination at work.