Soon the housekeeper begins to take her young son to work, and he and the old man become friends. until you see it at last, the oasis of another prime number, a place of rest and cool, clear water. Still, you refuse to give up, staggering on step by step, determined to continue the search. Then you think you see one, a prime number at last, and you go running toward it - only to find that it's just a mirage, nothing but hot wind. The sun shines down mercilessly, your throat is parched, your eyes glaze over. No matter how far you go, you don't find any. At first, the prime numbers are frequent, but 'When you get to much bigger numbers - a million or 10 million - you're venturing into a wasteland where the primes are terribly far apart that's right, a desert. Perhaps the Professor's most splendid speech dramatises prime-hunting as a quest through inhospitable country. We learn about primes, triangular numbers, the invention of zero, and so on, in surprisingly warm-hearted scenes of exposition.

Once he has drawn a picture of her and clipped it to his suit so that he is not altogether surprised to see her every day, he begins to induct her into number theory. He asks for her shoe size and telephone number, and reflects on the mathematical properties of each. 'It's as if he has a single, 80-minute videotape inside his head,' the narrator explains, 'and when he records anything new, he has to record over the existing memories.'

This is the Professor, a brilliant mathematician who suffered brain damage in a car accident in 1975, and since then cannot remember anything for more than an hour and 20 minutes at a time.

He lives in a dingy two-room apartment, and his suit jacket is covered with reminder notes he scribbles to himself. The book is narrated by the housekeeper of the title, a single mother employed by an agency, who is assigned a new client. Its unnamed characters suggest archetype or myth its rapturous concentration on the details of weather and cooking provide a satisfyingly textured foundation.

And yet this novel, with its skilful admixture of tender atmospherics and stealthy education, has sold more than 4 million copies in its native Japan. N umber theory - what Gauss called 'the queen of mathematics', devoted to the study of numbers and their arcane interrelationships - does not perhaps sound like the most fruitful basis for a poignant domestic drama.

Prime first read