Colin Singleton is a child prodigy who is fearing he will not grow to become an adult prodigy. After being dumped by his girlfriend, Katherine XIX, Colin is looking for his “missing piece,” longing to feel whole, and longing to matter. He hopes to accomplish his goal of becoming a genius by having a “eureka” moment. Over the span of his life, Colin has dated nineteen girls named Katherine, all spelled in that manner. In these relationships, Colin remembers only the Katherine dumping him.
After graduating from high school, and before college, Colin's best and only friend, Hassan Harbish, convinces him to go on a road trip with him to take his mind off the breakup. Colin goes along with the idea, hoping to find his "eureka" moment on the way. After driving all the way from Chicago to Tennessee, they come across the alleged resting place of the body of Archduke Franz Ferdinand. There, they meet Lindsey Lee Wells. After a short time, Colin and Hassan find themselves employed by Hollis, Lindsey's mother who runs a local factory that is currently producing tampon strings. They live with their employer and her daughter in a rural town called Gutshot, Tennessee. The employment she sends them on is to interview all current adult residents of Gutshot and assemble an oral history of the town.
As time passes, Colin finds himself becoming attracted to Lindsey, though matters are somewhat complicated by her on-again, off-again boyfriend Colin (he and Hassan call him TOC, "the other Colin"). Our Colin, the prodigy, is still chasing his eureka moment, finally finding it in his theorem he created called the Theorem of Underlying Katherine Predictability. It is meant to determine the curve of any relationship based on several factors of the personalities of the two people in a relationship. It would predict the future of any two people. His theorem eventually works for all but one of his past relationships with a Katherine. It is later discovered by Colin that he had dumped this Katherine (Katherine III), rather than the other way around. The graphs all make perfect sense at this juncture.
As Colin’s story is revealed to the reader, we find that K-19 was also the first of the Katherines, “Katherine the Great.” While the back stories of Colin’s life play out, Hassan gets a girlfriend, Katrina, a friend of Lindsey’s. The relationship is cut short when Colin and Hassan catch Katrina having sex with TOC while on a feral hog hunt with Lindsey, her friends and Colin's father. A fight between TOC and all of the surrounding acquaintances begins when Lindsey finds out that he’s been cheating on her. While recovering from a knee whack to the groin, Colin anagrams the Archduke's name while in the grave yard to dull the pain, and realizes that it is actually Lindsey's great-grandfather, named Fred N. Dinzanfar, that is buried in the tomb.
Colin finds Lindsey at her secret hideout in a cave that she had shown him previously, where he tells her the story of every Katherine he has ever loved. Lindsey tells him that she feels so self-centered, claiming that she does not feel sad but instead slightly relieved by TOC's affair. They discuss what it means to them to "matter" and eventually confess their love for each other. As their relationship continues, Colin decides to use his dating formula to determine whether or not he and Lindsey will last. The graph reveals that they will only last for four more days. Lindsey then slips a note under his door, four days later, stating that she cannot be his girlfriend because she is in love with Hassan. But she leaves a P.S. stating that she is joking. Colin realizes that his theorem cannot predict the future of a relationship; it can only shed light on why a relationship failed. Despite this, Colin is content with not “mattering”. Hassan also states that he is applying for two college classes, which Colin has been trying to convince him to do throughout the book. The story ends with the trio driving to a nearby Wendy's. Lindsey states her desire to just "keep going and not stop." Colin takes her advice, as a transcendental and ecstatic feeling of a "connection" with Lindsey, Hassan, and everyone not in the car surges through him. He has finally found peace and happiness via connection with other people, rather than from the pursuit of distinguishing himself from everyone, feeling "non-unique in the very best way possible."