JANNA LEVIN IS A professor of physics at Columbia University, and this intriguing but flawed debut draws on her love of mathematics and philosophy. Actually, whether it is a novel at all is open to debate.

Based on the brilliant but tragic lives of Kurt Gödel and Alan Turing, two of the last century's leading thinkers in logic and mathematics, A Madman Dreams of Turing Machines is a hotchpotch of big ideas, imaginative biography, novelistic flourishes and occasionally arresting description, all of which is engaging, but doesn't hang together satisfactorily.

Turing, considered the father of modern computers, broke the German Enigma code in the Second World War, while the Austrian Gödel is best known for his incompleteness theorem, which showed that not all mathematical truths are provable.

Although they never met, they led oddly parallel lives, both struggling with personal problems, despite their groundbreaking work. Gödel was paranoid and delusional for much of his life, and starved himself to death, while Turing is portrayed as something akin to a sufferer of high-functioning autism, his travails at the hands of the British courts for homosexuality possibly leading to his suicide by poisoning.

Clearly both could deal more easily with the abstract space of numbers than with the real world and relationships, and Levin uses her novelistic licence well to extrapolate what might have gone on in their minds from her research.

But despite some slightly heavy-handed addressing of the philosophical themes suggested by their work (free will, the nature of the mind, the existence of God), there is nothing to link this all into a coherent narrative.

Occasionally Levin conjures up a wonderfully vivid scene, such as Gödel sitting in a café discussing philosophy with the Vienna Circle, or Turing having his code-breaking revelation while digging in the woods. But ultimately that is not enough to make this web of ideas coalesce into anything more tangible.

A Madman Dreams of Turing Machines by Janna Levin
Weidenfeld, £14.99

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