How Mathematics Solves Murder Mysteries: From Galois to Network Theory

Galois Solves a Murder

We travel back to 19th‑century France to meet the brilliant mathematician Evariste Galois , founder of Galois theory, who applies his mathematical insight to a homicide case. His friend Lupin is murdered, and Galois notices the victim clutched a half‑eaten apple pie. Recognizing that “pie” sounds like the mathematical constant π (3.14), he suggests that room 314 may be linked to the killer. Police investigate, find the suspect in that room, and arrest him.

This anecdote highlights the role of luck and probability in solving crimes.

Serial Crimes and Radian Angles

In a more complex scenario, a series of murders in California are linked by a mysterious letter containing a circle with five crosses, indicating five planned killings. Linguist Goris Payne discovers the word “radian” in the letter. Since one radian equals 57.3°, detectives associate the angle between crime scenes with this value, predicting the next murder at Lake Tahoe. The perpetrator turns out to be a mathematics professor.

Criminologist Rossney combines environmental criminology with a distance‑decay function , which models the probability of a criminal choosing a location based on its distance from their home area. Using this model, police successfully predict and prevent further attacks, demonstrating the power of mathematical modeling in crime analysis.

Mathematics in Counter‑Terrorism Networks

Traditional investigative methods struggle against the complex connections among terrorists. Caltech mathematician Jonathan Farley proposes a “grid theory” that treats terrorist relationships as a network, where each node represents an individual and edges represent connections. By identifying and removing critical nodes, entire networks can collapse.

Farley’s team applied this approach to dismantle a drug‑and‑weapon smuggling ring in Jamaica, showing how network analysis can efficiently target key actors and reduce risk.

Beyond these examples, mathematics underpins many aspects of criminal justice, from trial analysis to dynamic crime‑rate forecasting. With growing data, machine‑learning algorithms are increasingly used to predict and prevent crimes.

For instance, a study from Shandong Police Academy used a machine‑learning model to rank risk features for telecom‑fraud victims, illustrating how predictive analytics can guide law‑enforcement strategies.

References:

[1] A. Bi. "Mathematics Chasing Criminals". Prosecutor Cloud , 2011, (18):62‑64.

[2] L. Xuemei. "Insights and Evolution: Predictive Analysis of Telecom Fraud Victims". Journal of Fujian Police Academy , 2023, 37(01):83‑90.