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Brief: Prime Time By
Michael Dirda
Mathematics is, paradoxically, among the most romantic of disciplines, replete with unsolved mysteries, unprovable conjectures, and dashing, semi-legendary figures like Ramanujan, David Hilbert and Bernhard Riemann.
In 1859 the young Riemann wondered whether there might be a simple rule for figuring out primes (numbers that can be divided only by themselves or 1).
The problem doesn't seem insurmountable -- just a matter of arithmetic, surely -- and he suggested an answer, but couldn't prove it.
Nor has anybody else, and establishing or disproving Riemann's hypothesis has grown into a kind of Holy Grail, "the greatest unsolved problem in mathematics."
Three new books take a look at the quest to do so: Prime Obsession, by John Derbyshire (Joseph Henry, $27.95);
The Riemann Hypothesis, by Karl Sabbagh (Farrar Straus Giroux, $25); and
The Music of the Primes (HarperCollins, $24.95), by Marcus Du Sautoy.
John Derbyshire is best known for his novel Seeing Calvin Coolidge in a
Dream, yet his book is by far the most mathematically dense of the three, albeit leavened with chapters of biography and history.
Karl Sabbagh, an experienced journalist, focuses largely on the people who have grown obsessed with prime numbers, from Gauss to Louis de Branges.
Du Sautoy, a professor of mathematics at Oxford, presents his account as a historical narrative, interrupted with occasional mathematical examples and illustrations.
Because this prime obsession has been so widespread, all three books end up offering succinct introductions to number theory, as well as intense scrutiny of the various attempts to prove Riemann's hypothesis.
All this is fascinating stuff, but not for the mathematically faint of heart.
Yet like, for example, Charles Rosen's studies of the classical and romantic tradition in music, award-winning works that are replete with specialized terminology and musical notation, these books will reward the effort paid to them, though the most demanding, and for that reason most rewarding, is probably Derbyshire's. |