According to Wikipedia, The Professor's Beloved Equation is the title published in Japan in 2003; The Housekeeper and the Professor is the English translation by Stephen Snyder, which was published in 2009. The same article tells us about the characters:
The Professor ~ 64 years old. A former university professor who specializes in number theory. He loves mathematics, children, and the Hanshin Tigers (especially Yutaka Enatsu, who was playing for the Tigers at the time of the Professor's accident and whose uniform number was 28, the second smallest perfect number. After being in an accident at the age of 47, he can retain new memories for only 80 minutes. He keeps important information on memo paper which is attached all over his suits. He keeps baseball cards and another important memento in a cookie tin. He has trouble interacting with other people and has a habit of talking about numbers when he does not know what else to say. He has a talent for reading things backwards and finding the first star in the sky.
The narrator ~ housekeeper and single mother. Initially feels frustration at the Professor, who shows interest only in mathematics, but through observing the Professor's kindness and his passion for mathematics, comes to feel respect and affection for him. She first manages to connect with the Professor when he discovers that her birthday is February 20 (220), which is an amicable number with the number 284, which is imprinted on the underside of his watch, which he received as the University President's Award for a thesis he wrote in university on transcendental number theory. Cannot pronounce the title of the Journal of Mathematics (to which the Professor submits contest entries) very well, so she refers to it as "Jaanaru obu." Gives the Professor a rare baseball card of Yutaka Enatsu as a birthday present.
Root ~ ten years old. The Professor refers to him as "Root" on account of the top of his head being flat like a square root (√) symbol. Is a fan of the Hanshin Tigers, and gets the Professor to repair his radio so that they can listen to baseball broadcasts together. Eventually becomes a junior high school mathematics teacher.
The Widow ~ sister-in-law of the Professor (wife of the Professor's brother). Cannot walk well, as a result of a traffic accident.