ONE TO NINE: THE INNER LIFE OF NUMBERS by Andrew Hodges (Doubleday Canada), 328 pages, $29.95 cloth. Rating: NNNN
Mathematicians have written popular tracts on the enigmatic properties of numbers before, but none before this one have started with a quote from Jane Austen.
In one of the more virtuosic displays of erudition in recent memory, British mathematician and particle physics researcher Andrew Hodges teases out both the elusive and the concrete qualities of the “universal language” of mathematics.
His examination of numbers is also a cultural history, with references to sudoku, quantum physics, existential philosophy, Hindu cosmology, molecular chemistry, reality television, Lewis Carroll and the Pet Shop Boys.
Hopping nimbly from proof to problem to anecdote, Hodges also includes thumbnail biographies of some of the greatest mathematicians, a collection of brainteasers and an accessible tour of the more reality-warping implications of particle physics.
It all begins with a simple question. Since numbers are infinite, how do mathematicians assure themselves that mathematics is indeed a logically consistent system that represents what it purports to represent? How do we prove the unique factorization of prime numbers or, for that matter, truly know that two plus two equals four?
The problematic logical foundations surrounding the number one, the tricky duality of the number two in both computing and quantum physics, the rigorously square logic of four, the mythical and mathematical mysteries surrounding seven – Hodges shows how numbers take part in a sweeping cultural drama while examining mathematics as a symbolic language that’s also a rigorously exact system with universal implications.
This is supposed to be a popular tract, but Hodges has a fairly precise idea of what constitutes a worthwhile math brainteaser. So brace yourself for a mild cerebral sprain and a jolt to your logical faculties as you attempt to follow his rich but surprisingly clear foray into the mystery of number.