On the same day that child prodigy Colin Singleton graduated from high school, his girlfriend Katherine broke up with him. This next morning, Colin sits in his bathtub and thinks about the Greek philosopher Archimedes, who had a brilliant physics insight while sitting in a tub. Excited, Archimedes supposedly shouted, “Eureka!” meaning, “I have found it!” Colin wishes that, he, too, could have a brilliant insight of some kind. When he comes out of the bathroom, both his parents are sitting on his bed. They tell him Katherine called. She is worried about Colin, and so are they. Colin listens to their expressions of concern for as long as he can before he has to run back into the bathroom to vomit. For the next fourteen hours, he looks through his yearbook. Many of his classmates’ notes to him end with “Stay cool!” which Colin finds absurd, since he is not cool. He spends most of the fourteen hours rereading the inscription from Katherine, with her pledge to be his forever. He makes an anagram of her words, rearranging the letters into a different phrase.
Colin’s friend Hassan Harbish pays a visit. Hassan is hairy and overweight, of Lebanese descent, and a fairly lax Muslim. He enjoys teasing Colin, who is half-Jewish, with Arabic insults like kafir (“infidel”). Hassan is a year older than Colin but is taking a break before starting college. Hassan mocks Colin and brags jokingly about his own, allegedly massive penis, but he listens somewhat sympathetically as Colin pours out his frustrations. All he ever wanted, Colin says, is that Katherine would love him and that he would do something meaningful with his life. Hassan tells Colin, half-seriously, that he needs God. Colin rejects this suggestion. He goes on to say that although he is a prodigy, with a gift for learning things quickly and at a young age, he will never be a genius, one who discovers new things. He wants to matter. Hassan’s retort is that what Colin really wants is to be famous. Hassan announces that Colin has a complicated problem with a simple solution.
Hassan’s proposed solution to Colin’s misery is a road trip. Colin’s parents oppose the plan but relent, perhaps out of guilt, when Colin talks about his wasted potential. Hassan’s parents give their permission after Colin tells them he plans to find Hassan a job. Colin and Hassan leave Chicago’s North Side, where they live, and drive south in Colin’s car, nicknamed Satan’s Hearse. Colin is at the wheel as they pass through Indianapolis after midnight. He thinks of Austrian Archduke Franz Ferdinand, who was neither a prodigy nor a genius but mattered very much, because his assassination triggered World War I. Colin is trying not to think about Katherine. All nineteen of his girlfriends have been named Katherine, and every single one broke up with him.
Colin’s parents first realized he was unusual when he started reading newspaper headlines as a two-year-old. A child psychologist told Colin’s mother that Colin was brilliant, but his parents should not have unreasonable expectations for his future achievements. Colin’s father gave Colin a book to read, Shel Silverstein’s The Missing Piece. Colin read the book quickly and enjoyed it, but he did not understand that he himself was missing a piece, namely the ability to see himself as other saw him. When Colin started attending Kalman, an expensive private school where his mother taught French, he was teased and bullied. In third grade, however, he won the heart of a very pretty girl.
At a rest stop in Kentucky, Hassan alters some carved graffiti to read, “GOD HATES BAGUETTES.” When Colin returns from the bathroom, the updated inscription reminds him of France. The thought of France, in turn, reminds him of his most recent Katherine, Katherine XIX, because she and Colin used to talk of visiting Paris. Later, back on the road, Colin rejects Hassan’s suggestion that they stop to see the World’s Largest Wooden Crucifix. Crucifixes also remind Colin of Katherine. When Hassan objects that she was an atheist, Colin replies that she wasn’t always one. She used to wear a silver crucifix.
Hassan started attending Kalman in tenth grade, after being homeschooled. In calculus class, he watched Colin, a freshman, ask to be excused so he could deal with an eyelash in his pupillary sphincter. Hassan later explained to Colin that a joke about an eyelash in one’s sphincter (any sphincter) does not make a favorable impression on high schoolers. That was when Colin and Hassan became friends. In contrast to Colin, Hassan is lazy, but he is quick-witted enough to keep up with Colin in conversation, and he is much better at reading social situations.
Colin and Hassan see a sign inviting motorists to visit the grave of Archduke Franz Ferdinand. It is unlikely that Franz Ferdinand would really be buried in rural Tennessee. However, Colin was thinking about him just hours before, and the coincidence is too bizarre to ignore. In a town called Gutshot, a dozen or so miles off the highway, the boys stop at a general store painted bright pink. Lindsey Lee Wells sits behind the counter. She is the guide for tours of the archduke’s gravesite. Lindsey is short, skinny, and more interesting-looking than pretty, but she has a smile “that could end wars and cure cancer.” As the boys follow Lindsey to the gravesite, Colin stumbles. He loses his glasses and hits his head on a rock, cutting his forehead. When Hassan refuses to donate his shirt as a bandage because he is self-conscious about his body, Lindsey stops the bleeding with her shirt instead. She tells Hassan to continue applying pressure while she fetches a first-aid kit. As Colin puts his glasses back on, he mumbles “Eureka.”
Lindsey’s bra is bright purple, the same color as Katherine’s on the evening she and Colin broke up. On the night of their graduation, they had gone out to celebrate. Back in his bedroom, however, they argued about Colin’s fear that others were catching up to him intellectually, and about his constantly asking if Katherine still loved him. When she ended their relationship that night, Colin felt as though a piece of his gut had been torn out.
Colin’s “Eureka” after hitting his head is due to a sudden idea. Pulling out a notebook, he sketches x- and y-axes and a curve that rises and then falls. The graph, Colin explains to Lindsey and Hassan, relates to a mathematical formula he has developed for predicting the course of any relationship based on the personality traits of the people involved. Colin classifies people as dumpers, who tend to initiate breakups, and the rest as dumpees. When Lindsey learns that Colin has dated nineteen Katherines, she laughs. She has dated just one boy, another Colin.
Colin’s first Katherine was the pretty girl in third grade. Because he was socially so unskilled, he did much of his schooling away from Kalman under the tutorship of Keith Carter, a friend of his father’s. The tutor had a daughter who was impressed that Colin already knew Latin. She started playing the “why game,” asking him questions and following up every answer of his with “Why?” Eventually, Colin admitted that he did not know why the poet Ovid was born in ancient Rome instead of elsewhere. Then the girl, Katherine I, asked Colin if he wanted to be her boyfriend. When he said yes, she kissed him on the cheek.
At Archduke Ferdinand’s gravesite, Lindsey gives her usual speech. She explains that the owner of the castle where the archduke was originally buried needed money and sold the corpse to the town of Gutshot. Four of Lindsey’s schoolmates approach, including her boyfriend Colin, tall and muscular, and a stunningly attractive girl named Katrina. This Other Colin reacts good-naturedly after Colin and Hassan prank the new arrivals by pretending to be French. Colin and Hassan start referring to The Other Colin as TOC. Back at the store, Lindsey, Colin and Hassan encounter Lindsey’s mother, Hollis. To Colin’s surprise, she recognizes him from a TV quiz show he appeared on a year earlier. Hollis invites the boys to join her and Lindsey for dinner at their home. Driving over in Hollis’s truck and Colin’s car, the four of them pass a factory. Colin learns from Lindsey that it makes something he did not even know existed: tampon strings.
Hollis and Lindsey’s enormous house is bright pink, like the store and Hollis’s truck. While Hollis and Lindsey prepare the meal, Colin works on his formula for predicting the length of a relationship and who will dump whom. (The equation correctly describes his relationship with Katherine I: after he agreed to be her boyfriend, she dumped him within three minutes.) Dinner is pleasant, after a little awkwardness over Hassan’s one-word prayer in Arabic. Hollis, who owns the tampon-string factory, offers the boys a summer job helping her with a project. Lindsey implies that they will stay at the house. The boys accept. Afterward, Colin and Lindsey chat. She used to be ugly and unpopular, she says, but deliberately adopted cool ways in high school. According to her, there is a method to being cool and popular. He tells her about his being a nerd, and his desire to matter.
When the topic of a job came up, Colin imagined a want ad for someone with his peculiar talents: skill at anagramming, fluency in eleven languages, and an encyclopedic memory. The job Hollis actually has for the boys involves taping interviews with people who work for her so she can put together an oral history of Gutshot. Lindsey will accompany the boys to get the interviewees to open up. The first interviewee is an old man named Starnes. The smell of Starnes’s house reminds Colin of the basement in the home of the most recent Katherine. She had taken him down there to watch The Royal Tenenbaums, a comedy about a family of prodigies. He wanted to kiss her, but he had a theory that the girl should make the first move. After the movie, when Katherine asked what Colin was good at besides languages, he answered that he was good with anagrams. For instance, her name could be turned into “their arcane trek.” She asked if he was good at anything else. At that point, he gathered his courage and said he was a good kisser. Katherine XIX and Katherine I are actually the same person: Katherine Carter.
Starnes tells the boys and Lindsey about himself and about Gutshot. The town got its name by being a center for “gutshot boxing,” in which all punches had to land between the belt and shoulders. Looking at Starnes’s old photos of him and his late wife, Colin thinks to himself that he will leave behind something more than just photos. The boys take Lindsey back to the store, for time alone with “the Lyford boy,” as Starnes called TOC. While Colin and Hassan wait outside, Hassan talks Colin out of calling Katherine. When they grow tired of waiting for Lindsey, Hassan fakes an asthma attack. Lindsey quickly leaves with them after Hassan explains that his inhaler is back at the house.
That evening, Colin overhears Hassan explaining to Lindsey and Hollis that Colin is able to remember so much partly because he finds everything interesting, but also partly through hard work. Colin thinks again that his only hope of accomplishing something original is his theory about relationships. He works some more on the formula while Hassan and Lindsey play pool. After Hassan has gone to bed, Lindsey debates with Colin. According to her, mattering is a misguided goal. “The bigger a deal you are, the worse your life is.” Also, she says, Colin needs to learn how to tell stories properly. A story should have a plot, and a moral, and romance. His Theorem about relationships will have romance, Colin retorts.
After Katherine I broke up with Colin, he continued to see her, since her father was his tutor. He was not at all obsessed with her, and yet for some reason he dated no one but Katherines from then on. They all dumped him. The cycle became boring after a while, but never less painful.
The next morning, Colin, Hassan, and Lindsey drive to the factory for more interviews. In a change of plans, Hollis has told them to keep the interviews short. After the first interviewee, Lindsey leaves for the store to be with TOC. In the remaining interviews, Hassan does most of the talking, leaving Colin to think about his Theorem. Afterward, Colin insists on calling Katherine XIX, over Hassan’s objections. While Hassan goes to pick up Lindsey, Colin walks into an open field for better reception. Katherine calls Colin back after he leaves a voicemail, but she confirms that the relationship is over. When Hassan and Lindsey pull up, Colin admits that the call was a bad idea. He cries in the car, humiliated. Back at the house, he decides that his formula will never work and asks Lindsey for matches to burn his notes. She wants a little time to look them over first.
Hassan spends the fifth night in Gutshot cruising with Lindsey and her four friends from the gravesite. He reports to Colin that Katrina is not only gorgeous but also very nice. Hassan is making plans to go pig-hunting with Lindsey and the others. Colin has no desire to go hunting.
Colin’s father believed that given a child of exceptional intelligence, raising a genius was just a matter of “active, results-oriented parenting.” This view is mistaken. Still, Colin’s upbringing paid off sooner than expected when he appeared on the quiz show Hollis had seen, KranialKidz. Colin’s tutor, Keith, had given the show his phone number. As word got out at school that Colin was going to be on TV, he suddenly become popular. He managed to ask a beautiful girl named Marie out for a date. On the afternoon of the date, however, Katherine needed help preparing for a French test. He cancelled his date, pleading that a family emergency had come up. One tutoring session led to another, which was how Katherine I became Katherine XIX.
Hassan has noticed that on Thursdays, Hollis is gone all day, checking on the factory and the warehouse in Memphis. The next Thursday, Hassan claims to have a sinus infection. Since all the people at the factory have been interviewed, Hollis sends Colin and Lindsey to the nursing home in a nearby town to interview factory retirees. Hassan, meanwhile, is back at the house watching TV. During the drive to the nursing home, Lindsey shares an idea she has for fixing Colin’s Theorem: add more variables. Colin listens with enthusiasm. After they settle on a total of five variables, Colin crafts an impressive formula that includes the five variables, powers of x all the way up to x8, and a sine function.
At the nursing home, Lindsey and Colin are greeted warmly. Everyone there has known Lindsey all her life. The women all take Colin to be her boyfriend, which he finds odd but Lindsey does not. Lindsey is dismayed, however, when one of the women mentions that her son is buying some land from Hollis to build a housing subdivision. Lindsey does not understand how that could be. Hollis and she are not in need of money.
The following Sunday and Monday, Hassan again goes cruising with Lindsey and her four friends. On Monday, Hassan kisses Katrina during a game of spin-the-bottle “in the back of Colin’s truck,” as he later tells Colin. Colin describes Katrina as dumb and ditzy. This nearly causes a fistfight between him and Hassan. The next afternoon, Hassan unloads on Colin. He has spent four years putting up with Colin’s self-loathing, and his pining after Katherines, but now Colin can’t be happy for him. Colin replies: “You called him Colin.” Hassan agrees that referring to TOC as Colin was completely out of line, and so the tension between the two friends eases. At the store, Colin accepts TOC’s invitation to join the pig hunt. That evening, while Katrina and Hassan are on a date, Lindsey takes Colin shooting in the forest to get him used to the kick of a ten-gauge shotgun. The land the forest stands on is the land Hollis owns and is selling. Lindsey has a secret hideout there, which she now invites Colin to come see.
Katherine I became Katherine XIX right after Colin’s first, victorious appearance on KranialKidz. At a French café, Katherine used a numeric code to say to Colin, in French, “I think I aimer you.” The word aimer can mean either “love” or “like.”
As night falls, Lindsey and Colin climb up into a small cave deep in the forest. Lindsey has never been there with anyone else before. After they share some moonshine, Lindsey tells Colin her history with TOC. He and her other classmates used to tease Lindsey mercilessly. She responded by making it her goal to be his girlfriend. Now TOC is sweet and protective toward her. Lindsey goes on to explain that Colin, Hassan, TOC, and her other friends all have definite personalities. They are what they are. She, on the other hand, is a chameleon: a thick-accented Southern girl at the nursing home, a math nerd around Colin, and Miss Bubbly Pretty Princess around her boyfriend. Inside, she is nothing.
Colin, however, does not believe she is chameleoning around him. Colin guesses that his being a dork makes her feel safe. The two begin to kiss, but they feel awkward and stop before they get very far. Returning to the house, Lindsey and Colin overhear Hollis talking on the phone with a man named Roy, about how best to dispose of some unnamed materials. Normal waste pickup would be too costly. Hollis suggests burying the materials in “that field back there.” Lindsey, wanting to know what the call was about, tells Colin that a road trip may be in order.
In the early morning, Colin and Hassan meet the rest of the pig-hunting group at a cabin in the woods. Mr. Lyford, TOC’s father, is in charge. After he reviews some basic facts about feral hogs and the use of shotguns, the party splits up. Mr. Lyford takes Colin and Hassan with him. They are soon on a hog’s trail, but Colin and Hassan cannot keep up with Mr. Lyford and sit down to rest. Hassan falls asleep, but Colin puzzles over Katherine III from fourth grade. His formula is apparently wrong because it predicts that he would have broken up with her. When Hassan wakes up, he suggests calling Katherine III to find out where the formula has erred. Colin makes the call and learns from Katherine III that he did, indeed, break up with her. The formula is correct. Colin’s famous memory has failed him.
Suddenly, a feral hog appears. When Colin shoots at the hog but deliberately misses, he unfortunately hits a hornet’s nest. He and Hassan flee blindly from the pursuing hornets and escape with a few stings. Eventually, they stumble out of the woods within sight of Archduke Franz Ferdinand’s grave. There they see Hassan’s new girlfriend, Katrina, having sex with someone, out in the open.
The guy Katrina is having sex with is TOC. Confronted by Colin and Hassan, TOC warns them to say nothing to the others. Colin secretly records TOC with the minirecorder he and Hassan have been using in the oral history interviews. Lindsey arrives with TOC’s two friends, whom Colin and Hassan have named JATT (Jeans are Too Tight) and SOCT (Short One Chewing Tobacco). The group settles down beside the grave memorial to drink beer. The group’s mood is relaxed. When TOC mocks Colin over his hornet stings, however, Colin pulls out the minirecorder and, apologizing to Lindsey, replays the conversation he recorded. Disgusted, Lindsey stands up and stalks away. When TOC tries to embrace her from behind, a prolonged fight breaks out. Everyone gangs up on TOC, including JATT and SOCT, who are tired of seeing TOC cheat on Lindsey with Katrina. TOC is strong enough to be a match for all the others. Colin is out of action after TOC knees him in the groin. When Colin recovers, TOC is gone and Lindsey is giving Hassan first aid. Lindsey calls Colin her hero.
The next morning, Colin and Hassan, aching all over, get an assignment from Hollis to go visit a woman named Mabel. She is at “the other home,” Lindsey says, “the one for when you’re really old.” Lindsey would prefer to skip the visit, but she comes along when Colin remarks that Mabel could probably use the company. The facility is depressing, and during the conversation, Mabel occasionally gets confused about whom she’s talking with. However, she is able to share a fond childhood memory of Dr. Dinzanfar, Lindsey’s great-grandfather. Mabel speaks tenderly to Lindsey, inviting her to visit again soon. After the visit, Lindsey begins sobbing and disappears into a bathroom.
That night, Colin makes a final adjustment to his formula. It now correctly predicts all his Katherine relationships, including the one with Katherine III. Hassan shares Colin’s excitement. Then Lindsey asks what the formula says about her and TOC. After advising her that as far as the formula is concerned, getting cheated on counts as getting dumped, Colin confirms that the formula correctly predicts how Lindsey and TOC’s relationship ended: he dumped her. Lindsey is relieved. “I don’t want to date assholes,” she declares, “and I’m not turned on by muscles.”
Lindsey, Colin, and Hassan drive to the Memphis warehouse to investigate the mystery of Hollis’s late-night phone call. They find Roy and his crew burying boxes in a nearby field. A box breaks open, and its contents flutter into the wind: tampon strings. Hollis arrives and explains what is going on. After she lost almost all her customers to overseas competitors, unsold product started piling up. Rather than lay anyone off, she is continuing production and trying to dispose of the excess product. She can keep going like this for another five years. (The money from the land sale will help.) She will use that time to try to find other ways to make money, but the oral histories the boys are recording will someday tell the next generation what life in the factory’s heyday was like. Lindsey leaves with her mother. As Hassan and Colin drive back together, Hassan speaks admiringly of Hollis’s actions and declares he is done being a lazy “not-doer.” He was already signed up for two college classes in the fall. Now he thinks he may increase his class load to three.
By the time Colin and Hassan arrive back at the house, Lindsey has already left again, supposedly to spend the night at a friend’s house. Realizing that she has gone to her cave hideout, Colin drives out and joins her. They talk about what they have been through. Lindsey has learned that knowing how to make people like her, or make them find her cool, is no substitute for really caring about people, the way Hollis does. Colin has learned that when a breakup with a Katherine leaves a hole in one’s gut, that hole is not filled by getting back together with the Katherine, nor by any other girl, and not by creating a new Theorem, either.
After a time of silent togetherness, Colin announces that the man in the tomb near the store is Lindsey’s great-grandfather Fred N. Dinzanfar, whose name is an anagram for Franz Ferdinand. Lindsey confirms this. Colin then shares that he broke up with Katherine III. He remembered wrong because his story about himself was that he always got dumped. At Lindsey’s request, Colin tells the story of all nineteen Katherines, start to finish. When he is done, the hole in his gut has started to heal. Colin and Lindsey confess that they like each other. They drive back to the house in their separate vehicles, kiss in the driveway, and sneak inside.
The next morning, Lindsey goes to visit Mabel. Colin’s formula predicts Lindsey will dump him within a few days. On the expected day, however, a breakup note from her ends with “P.S. Just kidding.” They are still together. Colin makes one last attempt to fix his formula, but as he listens to Lindsey and Hassan play poker, he realizes that the formula is unfixable. It can explain the past, but it cannot predict the future, any more than a formula could predict future poker hands. The formula is a kind of story. Stories are how we make sense of the past, and how we are able to matter, a little bit, in the infinite sea of time. The unknowable future comes at us and resists our efforts to make sense of it.
Ready for lunch, the trio jump into Colin’s car. Passing up their usual burger stop, they drive onto the interstate, with plans to “just keep driving for a while.” Colin is getting used to being not-unique. His future, like everyone else’s, is wide open.