It is 1987, and Shawn and his father are playing chess. Henry tells him if he wants to play the game, he has to learn the pieces, how they move and what they are called. Shawn gets up and leaves, after checkmating his father.
In present day, two teenagers, Shockley and Goddard, come to the Psych office to hire Shawn and Gus for a case. They need help and the police won't take them seriously since they are kids. One of their teachers at the Meitner School for Gifted Students has killed someone and in two days, he'll kill again. The problem is, they don't know which teacher it is, who he killed or who his next victim will be. When they broke into school late one night to pull a prank, they accidentally hacked into a cell phone call being made from the campus. The only other information they could get is that the killer has a deep voice and a cousin named Muriel.
At the police station, Juliet tells Lassiter that it's time for her to take the lead on a case. Lassiter decides to give her an easy one her first time out - a couple of kids came in to complain about their teacher. Despite it being such a low priority case, Juliet decides to give it her all.
When Shawn and Gus arrive at the school to investigate, Shockley and Goddard have their cover story worked out for them already. They are going to be guest lecturers on paranormal studies. While the headmaster shows them around, Gus asks if it's possible to see records of past applicants. Shawn figures out Gus applied there when they were kids and didn't get in. While in the office, Lassiter and Juliet show up and tell them to stay away from their case. Ignoring this, Shawn and Gus decide to start by questioning the custodian, the eyes and ears of any high school, who tells them that on the night in question he found a gold pin on his rounds and put it in lost and found. They find the pin, which has an integral sign on it, and figure their guy must be a math teacher. In the teacher's lounge, they learn that the calculus teacher is Professor Hahn who is also in a carpool, which Shawn and Gus worm their way into. On the ride home, they confirm that not only did Hahn stay late at school that night, he also has a deep voice.
Shawn invites Hahn to their lecture the next day, planning to grill him in front of the class in the hopes of getting a confession. But all he succeeds in doing is getting a few 'readings' on the students. The last one questions his ability, and after Shawn touches his face and gets a negativity vibe, he kicks him out of class, later commenting to Gus he had weird zit cream on.
Since the guys were unable to get anything out of Hahn in the classroom, they ask Shockley and Goddard for more information on him. All they know is that he gets a coffee every day from the school espresso bar and that five years ago he got a student expelled who attacked him. They check the school records and find out Hahn caught the student cheating and then tried to extort his scholarship money from him to keep quiet. While in the records room, Gus finds his file and is surprised to discover he actually got into the school.
The next day, the day the murder is supposed to take place, it's Gus' turn to drive carpool, but they arrive at Hahn's house to find the place has burnt to the ground. The cops are already there and tell them that there was a slight gas leak in the stove, which ignited a spark from faulty wiring in the coffee maker as it switched on in the morning. But since Shawn knows that Hahn got his coffee at school, he has a 'vision' that the killer brought the coffee maker over to use as a detonator after he created the gas leak. Among the ruins, Shawn sees a notice of foreclosure on Hahn's house. Hahn was broke and the due date for payment is today. He also sees a partly burnt file folder and puts together it's a record from Muriel Juvenile Hall from 1991.
Shawn and Gus hack into Muriel's records but all they can find is a photo from 1991 of the student Shawn kicked out of class, Kirk Gidel, looking exactly the same as he does now. Shawn goes to the police station to get Juliet to do a background check on Kirk. She finds out that Kirk apparently died in a car crash along with his parents but there is no death certificate on record. They go back to the school, and during their lecture, Shawn exposes Kirk to be an imposter. He stole the real Kirk's identity to get into the school and then went online to delete the death certificate. He did time in juvenile hall for causing someone's death 15 years ago and Meitner doesn't accept anyone with a record. The weird zit cream was actually make-up he used to help disguise his real age. Hahn discovered his secret and blackmailed him, but he couldn't pay up and called his cousin to vent - the call that Shockley and Goddard overheard. He then killed Hahn and deleted all records of him being at Muriel. Juliet gets an arrest in her first big case and Gus finally gets a hold of his parents to ask why he didn't go to Meitner only to be told that they thought it was too far to drive.
- A variation on the 'Argumentam ad crumenam' or 'Argument to the purse' which in modern English often manifests as "If you’re so smart, why aren’t you rich?", the title obviously somewhat subverts a long-standing trope. The 'Argumentam' can be found explicitly as far back in English literature as 'Tristram Shandy'. This particular version is probably linked to the "If you're so smart, how come you're only (age)?" concept occasionally resorted to by adults dealing with precocious youngsters.
- Lassiter's line, "Lesson number One, O'Hara - there are no small cases, only small detectives" is a distortion of the famous quotation from the Russian actor and founder of 'method acting' Constantin Stanslavski, who famously declared that "there are no small roles, only small actors."
- Many of the characters are named after famous scientists. William Shockley was an American physicist and inventor who won the Nobel prize in 1956. Dr. Robert Goddard was an American engineer, professor, physicist, and inventor who is credited with creating and building the world's first liquid-fueled rocket. Otto Hahn is a German chemist who is credited with the discovery of nuclear fission and won the Nobel prize in 1944, and is known as "the father of nuclear chemistry"; also, Hans Hahn was a mathematician known for the Hahn–Banach theorem. The Meitner School itself is named for Hahn's colleague, Swedish chemist Lise Meitner. Mae Jemison is an American physician and NASA astronaut who was the first African-American woman to travel in space. Kurt Gödel was a logician, mathematician, and philosopher known for his incompleteness theorems and Gödel numbering technique.
- The number Kirk writes on the board is Avogadro's number.
- In the end, Shawn reveals that the real name of the student posing as Kirk Gödel was Jay Macendale. Jason Macendale was the name of the Spiderman nemesis Jack O' Lantern, later Hobgoblin, a former CIA agent recruited out of college turned costumed terrorist.
[Henry and Young Shawn are playing chess]
Young Shawn: I'm gonna take your pointy sad-faced guy for my horsey guy.
Henry: Stop. What is this piece called? [He points to the knight]
Young Shawn: I call him Dwight.
Shawn [after previously calling an umlad "omelette"]: Circle your horses, Jules - we're about to crack your case like an egg. And then, we'll make some umlads - with shallots....and justice.
The gallery for If You're So Smart, Then Why Are You Dead? can be found here.