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WHEN Arthur C. Clarke died earlier this year aged 90, he bequeathed the world a vast library of science fiction, including such classics as Childhood鈥檚 End and, with Stanley Kubrick, 2001: A Space Odyssey. He also pointed out that geosynchronous satellites could be used as communication relays, which is now the basis of much modern telecommunication, and popularised the concept of the space elevator.

The Last Theorem is his aptly titled final novel, and by all accounts . He began it in 2002, but was plagued by ill-health. Worried that the novel might never be finished, he called upon his old friend Frederik Pohl, himself a widely respected science fiction author. Clarke gave Pohl around 100 pages of completed scenes and scribbled notes. Pohl struggled to make sense of the notes, and Clarke was unable to remember what he had meant by many of them. Nevertheless, Pohl went to work. Clarke is said to have seen the final manuscript not long before his death.

It is the story of a Sri Lankan mathematician, Ranjit Subramanian, who is obsessed with Fermat鈥檚 last theorem. Dissatisfied with the unwieldy proof submitted by Andrew Wiles in 1993, Subramanian labours for years to find a simple proof. Eventually he succeeds, and is rewarded with fame, wealth and a beautiful and loving wife. But Subramanian鈥檚 fame also means he has some unusual prospective employers: a group called Pax per Fidem (Peace through Transparency) who use non-lethal weapons to halt wars and bring about international cooperation, but who may have a shady side. Meanwhile, an alien armada is bearing down on Earth, sent to exterminate the human race before we cause trouble.

Disappointingly, the disparate plot threads never mesh. Subramanian鈥檚 mathematical endeavours are irrelevant to the alien-attack plot. He rejects Pax per Fidem鈥檚 job offer, and so takes a back seat as events unfold. His daughter disappears (briefly) when the aliens arrive, but that鈥檚 as involved as he gets. For a book in which the human race is under constant threat, there is a startling lack of urgency and no real climax.

The book only really works as a compendium of Clarke鈥檚 best ideas. Its plot involves a space elevator, spacecraft sailing on the solar wind, the difficulties of interstellar travel, near-omnipotent aliens, and human personalities being uploaded into computers. Sadly, the whole is less than the sum of its parts.

Read all the articles in our Science Fiction Special