Measuring the World, by Daniel Kehlmann

This novel turns on two very different, and at first glance, antagonistic, approaches to science: one man believes that you have to study everything in creation to understand it, which means suffering every discomfort the unexplored can offer; the other that its secrets can be extrapolated from mathematical laws alone, which means sitting in your room and thinking.

Alexander von Humboldt, a scion of rich but minor aristocracy, has always lived in the shade of his older brother. But this changes after his brother inadvertently gives him his life's mission: to measure the world. Alexander's nascent talents burst into life as he becomes an obsessive annotator of every rock, every cave, every species. He travels to South America, sails the Orinoco, suffers and survives fever, altitude sickness, cannibalism, the loss of a beloved dog, the partial loss of his integrity, all in the cause of mapping and marking the world.

Carl Friedrich Gauss, "prince of mathematics", less favoured by circumstance, but blessed with a prodigious mathematical imagination, stays in Gottingen - as far as his growing fame permits - and, having published his answer to Newton, settles down to watch while mediocrities slave to discover the truths whose unravelling had taken him a moment.

They are, again in their very different ways, violently unsympathetic characters. Grauss has some capacity for love - he certainly loves his mother - but his children are a disappointment, his second wife a torment ("even the sight of her face in the distance made him lonely"), and he shows always, and in every place, a vivid contempt for humanity's limitations. Humboldt, though vaguely progressive, and certainly "correct", loves things, not people. More darkly, both are scarred by the compromises they made during Napoleon's occupation of Germany. Yet they are admirable: their very denial of their own humanity reveals it. They have lived their lives by the tenets of reason, so why do they dream so much, hallucinate so often?

Grauss has set out to prove that the cosmos is curved: Euclid was wrong, parallel lines can converge, and so, as we see by the end, can parallel minds. As time, with its freight of new discovery, overtakes them, and they become sad old men, relics poking at other relics, so telepathy comes to interrupt them. Their waning thoughts criss-cross and bring comfort.

That hunger for fame should coexist with an obsessive passion for the truth is perfectly plausible, but they jar in Humboldt: his desire for recognition wobbles somewhat on top of his sturdily convincing scientific intensity. The elliptical brilliance of the narrative can, on occasion, slip into obscurity: this novel, so concerned with accuracy, leaves a deal of loose threads.

One can easily wilt under the unhealthy glare of another's obsessions, but not here. This is a masterpiece at many levels. In its loving depiction of two men for whom one would feel, at best, cordial dislike in any social context; in the superb use of dialogue, tight, subtle and semi-reported; in its haunting and painful descriptions of mental and physical suffering; in the authenticity of its minor characters. It makes you smile, and sadden, and think.