The professor is a mathematical genius and a gifted teacher who lives alone in a small cottage on the grounds of his sister-in-law's house. After a car accident in 1975, he has been unable to retain anything in his memory for more than eighty minutes. The suits he wears flutter with pinned notes reminding him of important things in his life. The most important note, which he wakes to every morning, is that his memory only lasts eighty minutes. Many housekeepers have come and gone in his life until the unnamed housekeeper of the title. She must reintroduce herself to the professor every morning offering him numerical tidbits from her life (her birthdate, her phone number, etc.) to help ground him in the immutable, eternal solidity of numbers even while everything else in his life seems new and confusing on a daily basis.
As the housekeeper settles into her own routine, she introduces her ten year old son, nicknamed Root by the professor because of his head's resemblence to the square root sign, into the small cottage. Root's presence pleases and energizes the professor, who takes to teaching both the housekeeper and Root about the beauty he sees in numbers. He explains prime numbers, amicable numbers, and difficult equations. His explanations are elegant and interesting and strike a cord with the housekeeper, who pushes further on her own. The three of them listen to baseball games, the game a statistician's dream. The housekeeper, the professor, and Root form friendships based on mutual interests and genuine caring despite the professor's inability to remember the other two from day to day.
The story itself is quiet, gentle, and lovely. The writing is carefully meticulous and yet elegant in the way that a complicated mathematical proof would be distilled to its simplest rendering. The theme of time and the fleetingness of memory contrast nicely with the eternal strength of numbers and friendship. There are no pyrotechnics here, just the simple beauty of a well-written, enchanting story. Like the concept the professor explains to the housekeper one day, this novel is easily summed up as amicable.