Math for Crime Fighting

Credit: Tony Webster/Wikimedia Commons

On New Year’s Eve 2019, abc13 News posted a story about using mathematics to tease out the details of a crash that killed a father and two young boys. The driver who hit them was sentenced to 60 years in prison for their deaths.

“We were able to clearly show that (he was) driving almost double the speed limit and being intoxicated. Remove either one of those and I don’t think this crash happens,” Lt. Paul Adkins of the Texas Department of Public Safety told article author Marla Carter.

Reading about this case made me think about the different ways mathematics can be used to analyze or solve solve crimes. Here are just a few of the pieces available on the topic.

If you haven’t already, check out Anna Haensch’s “Some Math About Guns,” which she wrote in 2018 for this blog.

“Catching criminals with maths” by Hugo Castillo Sánchez, David Pérez Esparza, Rafael Prieto Curiel and Sanaz Zolghadriha.

This post for the Chalkdust Magazine blog covers the mathematics of organized crime networks and gang rivalry, bloodstain pattern analysis, how Newton’s law of cooling can be used to calculate time of death and more.

Plus Magazine articles

Plus Magazine, “an online magazine which aims to introduce readers to the beauty and the practical applications of mathematics,” has some interesting articles about math and crime:

“Crime fighting maths” by Chris Budd

This post describes how math can help law enforcement catch getaway cars, determine the origin of contaminants illegal dumped into water, and more.

There is also a section of that post that discusses solving inverse problems pertaining to crime scenes and accidents, a topic that is covered further in “Inverse problems save the day” by Chris Budd and Cathryn Mitchell.

“Police and thieves” and “Police and thieves continued” by Marianne Freiberger

These articles describe Andrea Bertozzi’s research on modeling home burglary patterns and “what we can learn” from her model.

This model “consists of two interlinked equations (partial differential equations to be precise) which describe how the attractiveness value of a location and the density of burglars at a location change over time (depending on a number of parameters),” Freiberger wrote.

“Interestingly, the equations you get have the same form as those describing reaction-diffusion processes you see in chemistry or biology: here two substances spread out (diffuse) through space and react with each other when they meet…The way to think about reaction-diffusion in a crime context is this. Both the risk of crime (given by the attractiveness value of a location) and the density of burglars diffuse through space — they are like the two chemical substances. And when risk meets burglar the two can interact, causing a crime. Using this idea, Bertozzi and her colleagues built a more sophisticated model in which targets can also move around. This means they can represent, not just houses, but also cars or people. So a wider range of crimes, not just burglaries, can be represented,” Freiberger added.

“Law and Order: MVT” by Evelyn Lamb (published on her Roots of Unity blog and posted to her website)

This post is definitely more lighthearted than the other ones I’m mentioning here.

Come for the amusing opening lines (“In the criminal justice system, velocity-based offenses are considered especially unimportant. In New York, the dedicated detectives who investigate these minor misdemeanors are members of an elite squad known as the Moving Violation Team. These are their stories.“), stay for the plot twist ending in this post where Law and Order meets the Mean Value Theorem.

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