Yasuko Hanaoka, a hard-working single mother, kills her ex-husband in self-defense. Shinji Togashi was loathsome and a villain whose death (because it's fictional) we can cheer. What can she and her teenage daughter do now with the dead body in their living room? Yasuko's next-door neighbor, Tetsuyo Ishigami, is a brilliant mathematician, whose academic light has been hidden under a bushel for many years. He will take care of everything, he says. Not to worry, Yasuko.
Detective Kusanagi cannot find any better suspect than Yasuko. It doesn't matter that she has been divorced from Togashi for five years and hasn't seen him at all during that time -- except, as we know, for the fateful night -- and there's really nothing linking her to the victim, whose body, by the way, was found far away on a riverbank. Kusanagi just has finely tuned intuition and that is apparently enough to keep him on Yasuko's trail.
Alas for Ishigami, Kusanagi has asked Manabu Yukawa, an assistant professor of physics at a highly-regarded university -- from which all of them have matriculated -- to help him figure out what's wrong with the murder picture. Kusanagi jokingly calls Yukawa, "Professor Galileo." Yukawa, it turns out, was one of Ishigami's only friends at college and greatly prizes their acquaintance. It is a joyous boon for Yukawa that he has been reunited with Ishigami. Not so much for Ishigami.
It doesn't matter that fiendish Togashi slapped Yasuko's daughter repeatedly on the face and there's no mention of bruising. It doesn't matter that it makes no sense to single out Yasuko when Togashi was a gambler, alcoholic, and general wastrel with, no doubt, plenty of shady characters in his life. It doesn't matter because it's all about the puzzle and how two geniuses respect each other enough not to underestimate the other's intelligence.
Go along for the ride and gasp at the ending. Then you'll see why this book has been nominated for an Edgar Award, and received stars and recommendations from just about every reviewer around.