Harlan Emple is one of Sherlock Holmes' "Irregulars." He helps Holmes with cases that require advanced mathematics knowledge and, he likes to work with his shirt off. In 1999, Emple devised a formula for predicting crime patterns in NYC which brought him to Holmes' attention. He is Professor for Applied Mathematics at Columbia University, and holder of the Smithfield Endowed Chair of Algebraic Geometry at the Huntington Institute.
|After Holmes finds math equations at a murder scene that are written in ink that only UV light can reveal, he calls Emple to examine the equations. Reproductions are put on a wall in The Brownstone which Emple identifies as "P versus NP". He explains that solving the problem is not only worth $1M but could also be used to render computer security useless. ("Solve for X")
|While playing a puzzle hunt in which math problems need to be solved to identify locations, Emple comes upon a dead body. Agitated, Harlan is questioned at the 11th Precinct by Detective Bell and Captain Gregson where he explains the math game. He becomes frustrated and won't talk more until Holmes and Watson arrive. Cleared of committing the crime, Harlan accompanies Sherlock and Watson to the crime scene. Holmes finds the next clue in the game and deduces that the killing was done by someone playing the game who tortured the victim. Harlan surprises everyone by mentioning that the game prize is over $1.7M. Harlan brings Holmes to a woman who is playing the game who identifies the dead body and knows all the other players. At the Brownstone, Harlan discovers from Kitty that Sherlock used another math expert on a case, which hurts his feelings.
|Harlan finds that the game controller changed the clues after the murder, giving a different location. At the new location another tortured, murdered body is found. Sherlock deduces that the game is a trap to kill mathematicians. Watson finds Paul Ladesma who claims that a mysterious blogger, "Mo Shellshocker", is the likely killer. Paul is also looking for him. Sherlock realizes that Mo is actually Harlan as the blogger name is an anagram for "Sherlock Holmes". Harlan admits he is Mo and that the blog reveals those abusing math which also includes secret military data. Harlan expresses his frustration with Sherlock using another math expert. Sherlock explains that Harlan had become too needy, they aren't friends which Harlan takes that he's a loser.
|After Kitty encourages Sherlock to look at the Mo blog, he calls Ladesma using a fake voice and reveals that Mo is Harlan. Sherlock meets an annoyed Harlan at his place and tells him that Ladesma is the killer and Harlan is his target. Harlan's blog revealed lottery weaknesses which made Ladesma rich prompting Ladesma to find "Mo" and kill him. Sherlock sends Ladesma into a trap where he is arrested by the police. Sherlock also misleads the FBI that Mo is a cyber-terrorist Holmes became aware of when working for MI6. Having saved Harlan's life, Sherlock gives Harlan an apology of sorts by telling him that he is a tremendous asset that he looks forward to working with again. ("Just a Regular Irregular")
|Emple asks Holmes and Watson to find a missing PhD student, Lily Zavala, who he has had a crush on for several years. Harlan realizes this makes a suspect which is confirmed when the FBI visit him and report that Lily has been kidnapped. Holmes and Watson vouch for Emple with the FBI, however Holmes confides to Watson that he's annoyed with Emple as he's had to listen to Harlan's desire for Lily for two years and that Emple hasn't taken any of Holmes' advice to take action. Holmes and Watson visit a site where Lily was held captive and one of the kidnappers was killed and, believes she was kidnapped to work on a math problem. He discusses this with Emple who confirms Lily is a genius but he is worried sick that Lily may have been exposed to the killing. Holmes has kept the FBI at bay from arresting Emple by pointing out that Emple's math skills are greater than Lily's so he isn't a likely kidnapping accomplice.
|After continually calling Holmes for progress in finding Lily, Emple reports that Lily escaped and is with him. At the 11th Precinct, Lily discusses the kidnappers and that the math she was forced to perform was on FEMA flood maps of Brooklyn. Emple explains the complexities involved in creating the maps which he contributed to. Lily independently sought out copies from the Floodplain Office after hearing Harlan discuss them in class. Later, Harlan sees Holmes at the Brownstone, hugs him and says he told Lily about his feelings for her which she reciprocated. He credits following Holmes' advice for the success. Holmes is somewhat jealous and still smarting from criticism from Watson for comparing all women to Moriarty. This leads him to ask one of his long time paramours Athena out on a date. ("The Geek Interpreter")
- After a note with a mathematical formula is found on the body of Henry Wilseck, Holmes texts a picture of the formula to Harlan who identifies it as being used in victim compensation. ("When Your Number's Up")
- Holmes has Harlan provide mathematical evidence that Everett Keck is spreading bee mites by demonstrating that the occurrences of Keck finding hives with mites is too great statistically compared to his fellow workers at the USDA for it not to be sabotage. ("Absconded")
- Holmes uses Harlan's identity when questioning Tim Bledsoe's mother, Elise, with Watson. ("Gutshot")