Two years ago, a subway train operator reports that he hit a kid after someone pushed the boy onto the tracks.
The FBI take DNA samples from Reese and the three mercenaries captured with him at the bank. Donnelly and Carter watch through a one-way mirror and Donnelly assures the warden that one of them is the man he's been hunting for over a year. Despite the warden's misgivings, Donnelly plans to hold all four of them up the 72 hours that he's permitted without charges. Once they're alone, Donnelly assures Carter that he has enough forensic evidence to identify the man in the suit and put him away for a long good.
Once Reese is taken to his cell, a cell phone beneath the bunk rings. It's Finch, who managed to plant the cell there, and he tells Reese that he'll soon have him out. Reese worries that they'll have another Number come up and Finch admits that they never stop. He assures Reese that he'll deal with it and then goes into a Brooklyn high school where he's working as a substitute teacher. He informs his math that the substitute teacher, Mrs. Bentham, received an all-expense paid trip to Hawaii. The students explain that they're doing addition as punishment, Finch insists that math shouldn't be punishment and challenges their Number, Caleb Phipps, to make up a formula to do the work. Caleb isn't interested and before Finch can start teaching, the bell rings. As he leaves, Caleb tosses away a piece of paper that he was doodling on.
Finch calls to have Fusco check Caleb's police record. The detective confirms that Caleb has had a few minor run-ins with the police but nothing significant. Finch checks the piece of paper and finds the formula he asked Caleb to do on it. Fusco digs a little deeper and discovers that Caleb's older brother, Ryan, died in a subway accident two years ago. Caleb now lives with his mother Lori, who is employed as an administrative access. Finch follows Caleb down the hallway and hears him mention to a girl, Julia, that he's going out of town that weekend. As he follows the student, Finch notices two students dealing drugs and sends photos of them to Fusco to check on.
Carter meets Finch outside the school and he says that he doesn't want her involved given her new position with the FBI. Carter admits that she already is involved and that she's erased the FBI records with Reese's fingerprints. The FBI is keeping Reese's DNA samples at their local lab and Carter tells Finch that he needs to get her a couple of things so she can handle it.
As Finch goes back inside, Principal Lawton complains to him that he's trying to teach the students. She insists that this job is simply to make sure that Bentham's punishment is carrying out. Computer science teacher Chris Beckner overhears and, once Lawton leaves, tells Finch not to sweat it. Once Beckner goes, Finch breaks into Lawton's office and accesses Caleb's records. Fusco calls to tell him that according to the files, Caleb was there when Ryan died in the subway accident. Also, the transit cop, Murphy, who saw the incident initially called for police backup. However, a few minutes later he cancelled the request. Fusco tells Finch that he'll check out Lori while Finch discovers that Caleb scored exactly 50% on his tests. He figures that Caleb did so deliberately and actually knew all of the answers.
The next day, Finch talks to Caleb as he comes to and asks him about the formula. Caleb accuses him of digging through the trash and avoids the question. Once everyone is seated, a student asks Finch what good knowing things like the value of pi is. He explains that pi contains every number and number sequence in existence, and thus every word when the numbers are translated into letters. Finch tells them what they do with those possibilities is up to them.
Fusco goes to the Phipps apartment claiming to be investigating a string of robberies. Lori has the shakes and is running late for work. Once she leaves, Fusco calls Finch and tells him that Lori is an alcoholic and that he confirmed that the two students dealing drugs are Diego Velasquez and Ronnie Samms. After working for a thug named Lorenzo, they've switched to a new employer that Narcotics hasn't been able to identify.
At the school, Caleb passes Diego, Ronnie, and another boy in the stairwell. They threaten Caleb not to say anything and he starts to go, but then turns around and warns them that their customer is likely to panic. They come after Caleb but Finch arrives and orders them away. Once they leave, Caleb tells Finch that he doesn't need help and walks away. Finch notices a piece of paper that Caleb dropped in the scuffle and discovers that it has computer coding on it.
Beckner is giving a lecture in his computer lab about the history of hacking. Finch hacks the security camera in the room and listens as Caleb defends hackers. Beckner talks about the hacker who freed up the Internet for the world and was never caught, catching Caleb's interest. Fusco checks in with Finch, who tells him that the piece of code that Caleb dropped is a program that the teenager has been writing in longhand at home and then bringing to the school to enter into the computers. Impressed, Finch tells the detective that Caleb's work is groundbreaking, and tells Fusco to follow Ronnie and Diego.
That night, Fusco follows the two students, who hand off some money to a homeless man. Meanwhile, Finch parks down the street from Caleb's apartment and watches on the webcam that Fusco planted earlier. Carter calls Finch to tell him that she got his package but will need accurate specs. Finch sends them to her electronically and Carter then leaves the restroom and goes into the nearby bar. Looking around, Carter spots the man she's looking for and approaches him.
Finch watches as Caleb comes home and tucks his mother in after she passes out from drinking. He then leaves and Finch calls Fusco and tells him that their Number is on the move and then follows the teenager.
Carter chats with the man at the bar and asks a number of medical questions. He wonders what's up but she leads him outside, flirting with him. However, when he gets into the car, he passes out from the drugged drink she got him. Once he's unconscious, Carter takes a DNA sample from him.
Fusco tracks the payoff bag across the city and calls to tell Finch that he's at a PO Box. Finch is there as well and they realize that Caleb is the new drug lord that Ronnie and Diego are working for.
The next morning, Beckner returns student tests and tells Caleb that he expected better from him. Meanwhile, Finch monitors Caleb's computer and sees the student receive an e-mail from his supplier asking for a two o'clock meeting. Once the ends and Caleb and the other students leave, Beckner logs onto Caleb's computer and downloads a file. After watching Beckner, Finch goes outside and gives Caleb back the coding he dropped. Much to Caleb's surprise, Finch compliments him on the coding and then gives him a suggestion to implement his program.
Once Caleb leaves, Finch meets Fusco outside and they tail Caleb. He goes to an alleyway to meet with his supplier, Roman, but discovers the man lying on the ground. The local drug dealer, Lorenzo, steps out with two of his men and demands to know why Caleb is selling drugs on his turf. While Finch and Fusco move in, Lorenzo tells Caleb that he's heard he's planning to leave town and agrees to let him if he pays back all of the money he made from Lorenzo's customers. The drug lord gives Caleb until 8 that night to pay off and lets him off with a warning... for the moment.
That night, Fusco and Finch watch the Phipps apartment again and Fusco wonders why Caleb is picking a fight with Lorenzo. He then gives Finch the police transcripts from the night of Ryan's death. On them, Caleb initially reported that Ryan was fighting with two kids. However, later, Caleb retracted his story and said it was an accident. Fusco figures that Caleb is getting revenge on Diego and Ronnie, who must be the kids that killed Ryan, by setting them up to take the fall for dealing drugs. Meanwhile, Finch monitors Beckner and confirms that he's still accessing Caleb's computer. Finch listens in as Beckner calls an old college ate, Howard Glazer, and asks for a meeting to sell him something valuable. Finch tells Fusco to keep watching Caleb while he follows Beckner.
Beckner goes to a restaurant and meets with Howard. Much to Howard's surprise, Beckner has an advanced compression algorithm to sell him that he claims is his. The teacher wants Howard to provide startup money to fund development, and a skeptical Howard points out that Beckner wasn't that good a programmer in college. Beckner insists that he wrote it and that no one else knows about it, and Howard agrees to have his company provide the development money.
The next day, Fusco calls Finch and tells him that he's going to meet with the transit cop, Murphy, who called in Ryan's death. Meanwhile, Finch checks Caleb's computer and discovers that the teenager is shifting his money into a trust fun. Beckner texts Caleb and asks for an 8 p.m. meeting that night, the same time that Lorenzo wants his money. Fusco suggests that they leave Caleb to his fate and help get Reese out of prison, and Finch tells him that he already has someone on it.
That night, Carter breaks into the lab and replaces Reese's DNA with that of the man from the bar.
Finch continues watching on the webcam as Caleb comes home and deals with his mother. She tells him that she'll be better the next day and he agrees. Since he doesn't know which appointment Caleb will keep at 8, Finch calls Fusco at the station. The detective says that he'll be there shortly and then interviews Murphy. When he realizes that Murphy isn't telling the whole story, Fusco calls the transit cop on it and Murphy explains that Caleb lied when he said there were two other kids who shoved Ryan. He explains that Ryan and Caleb were the only people there. They had been drinking and dared each other to cross the subway tracks. Ryan lost and was killed. When Murphy realized the truth, he told Caleb that he'd write it off as an accident. The transit cop admits that he's not sure if Caleb came out of it for the better and tells Fusco that some things can't be fixed .
Once he's done, Fusco checks with Finch, who admits that he lost Caleb when he took a city bus. Fusco goes to stake out Lorenzo, returning to the alleyway where he met Caleb earlier. Finch goes to the high school and runs into Beckner coming out. Beckner finally admits that Caleb approached him about the compression algorithm. The student asked for some money, saying he was going to take a trip, and offered the algorithm in exchange. Caleb didn't want any credit but Beckner shows Finch the paperwork proving that he was going to give Caleb full credit for the work as well as all of the money. He only told Howard it was his own idea to convince the man to invest. When Beckner explains that he's placing Caleb's money into a trust fund for his mother, number 17-6-21, Finch realizes what the number means and tells Beckner that Caleb won't live to see the money.
Finch finds Caleb in the subway station where Ryan died two years ago. He talks to the student about making mistakes and how they're part of what someone is and there's no moving beyond them. Caleb isn't interested but Finch explains that he knows the significance of the trust fund number: Ryan was 17 years, 7 months, and 21 days old when he died. Caleb is now the exact same age and plans to end his life the same way that his brother died. Finch says that he understands because they're both reckless people. Caleb doesn't see the point on going on, figuring that he'll just keep breaking things, but Finch insists that the world is better off with both of them in. Speaking from personal experience, Finch tells Caleb that leaving doesn't make things better on anyone.
After taking care of Lorenzo, Fusco arrives at the station. Caleb looks at the train as it approaches the station, braces himself... and then stays seated as it passes. Finch puts a comforting hand on the teenager's shoulder.
Later, a lab tech gives Donnelly a report on the DNA. None of their prisoners' DNA matches the sample they have on file. The FBI agent figures that someone tampered with the samples and orders them sent out for examination, and then tells the tech to get Carter back in.
Caleb finds Finch waiting for him outside of the high school. He thanks Finch for his help and Finch talks about how a kid with a homemade computer changed the world by revealing the Internet to the world during the Cold War. Finch tells Caleb to keep his code close and be careful when choosing friends, and gives him a sheet with pi carried out to three thousand digits. When Caleb wonders what it means, Finch tells him that his phone number is in there somewhere, and he's sure that Caleb will find it eventually. As Finch walks away, Caleb asks him how he knew that the Internet hacker used a homemade computer. Finch claims that he must have heard it somewhere and leaves.
At Rikers, the warden prepares to release Reese. However, Donnelly and Carter arrive and Donnelly informs the warden that he's keeping all four men in prison after having them refied as unlawful combatants. As the guards take Reese back to his cell, Donnelly tells Carter that since someone tampered with the evidence, there's only one person he knows he can trust: her. He wants her to use her expertise as an Army interrogator to question all four prisoners... starting with Reese.