Overall, the word I'd use to describe this book is "shallow." Clarke and Pohl, two big names in SF, have managed to take two interesting concepts (Fermat's Last Theorem and alien sterilization of Earth) and turn them into a boring book. It's as if they said one day, "Well, we've succeeded at everything else in literature; now we have to succeed at writing a bad book!"
My major problem with the book is the lack of any consequences, or really, any conflict at all. At points the story threatens to inject a conflict--such as when Ranjit becomes an unwitting accomplice to pirates and subsequently spends two years being tortured in prison. For a moment, I thought that might produce some genuine unhappiness that could mar this otherwise oppressively upbeat book. Unfortunately, that was not the case.
Even toward the end, tragedy loomed on at least three separate occasions, yet somehow everything turned out all right. It's not that I have a problem with happy endings; I loves me a good happy ending. But happiness without struggle against adversity is hollow. I've read much better science fiction than this--this book feels like it was written for a fourteen-year-old as a "My first science fiction novel"--it's patronizing.
Our "protagonist", if indeed we can call him that, Ranjit, stumbles through his life without ever having to make any important decisions. Everything just sort of falls serendipitously into place. Oh, and along the way he discovers a miraculously short proof to Fermat's Last Theorem. Meanwhile, alien overlords have sent alien minions to sterilize Earth of dangerous humanity. But it's OK, because the overlords change their minds and then the minions befriend humanity.
As with the possibilities of tragedy I mentioned above, the book tempts us with the prospect of a meaningful theme when it touches upon the dangerous nature of an EMP-like weapon controlled by "the Big Three"--Russia, China, and the United States. Will this lead to an Orwellian future in which these Big Three control the only military forces on the planet? And will first contact with an alien species ironically lead to all-out planetary war even as the countries of humanity approach global peace?
Nah. It's much easier to just tell us in an epilogue that everything worked out fine, and thirteen thousand years everything was still going fine.
I'd have to say that even The Da Vinci Code better integrated an esoteric academic subject than this book. I understand that not everyone loves math as much as me, so I tolerate the explanations of Fermat's Last Theorem. But it wasn't even interesting. It had no relevance to the plot, because there was no plot. And since this book had Arthur C. Clarke's name on the cover, this has been the cause of severe disappointment for me!