Harlan Emple is a professor of Applied Mathematics at Columbia University, and one of Sherlock Holmes' "irregulars" - the collection of experts Holmes occasionally consults with for some specialized aspect of a case.
The two men first met when Emple theorized that it was possible to create a mathematical formula to predict crime rates in New York City. Although his theory was ultimately disproved, Holmes was highly intrigued by his methods, and the two continued to correspond.
Holmes called Emple in to decipher the mathematical formulas found on the walls of a murder victim's apartment.
One of Emple's quirks, according to Holmes, was that, "like any great thinker, he has a process," and Emple's was that "he doesn't like anything between him and the numbers," which is why Emple often goes shirtless, or disrobes completely, when contemplating maths.