Math on Trial: How Numbers Get Used and Abused in the Courtroom

One doesn’t expect to see math at the center of grizzly trials involving murdered children, academic sex discrimination claims or financial pyramid schemes. However, mathematicians Leila Schneps and Coralie Colmez argue in Math on Trial that in at least 10 instances over the past century, innocent or wrongly accused defendants have been imprisoned or publicly harassed in part due to simple mathematical errors at trial, such as believing two events are independent (when they are not) or under appreciating the power of exponential growth.

The authors sprinkle their narrative with both sensationalism and academic nuance. The highlighted trials are ripped directly from tabloid headlines, including the salacious Amanda Knox trial and the now infamous Charles Ponzi trial. These efforts to mainstream the usually staid subject matter places Math on Trial in line with such books as Steven Levitt and Stephen Dubner’s Freakonomics or Dan Ariely’s Predictably Irrational. Although Freakonomics and Predictably Irrational provide stronger academic support for their positions, Math on Trial rivals either book in its narrative style and ability to explain abstract social science to a wider audience.

Schneps and Colmez evoke sympathy for the accused before focusing on the mathematical errors at trial. For example, the pair details how an “expert’s” retroactive misapplication of the probabilities of events that have already occurred led to the six-year imprisonment of the so-called “Angel of Death,” Dutch nurse Lucia de Berk, for the death of seven babies in a hospital nursery. Similarly, Schneps and Colmez document how a prosecution’s unsupported estimates of the number of yellow cars and men with beards, among other identifying features, convicted Malcolm Collins of theft. 

Additionally, in one case, Schneps and Colmez describe the late-1800s trial of Hetty Green, who was accused of forging the signature of her dying aunt in order to invalidate a will removing her as the sole beneficiary of the aunt’s vast wealth. While Green used a battery of forensic experts — including Oliver Wendell Holmes — the aunt’s estate relied on mathematicians to deny the future “Witch of Wall Street” complete access to the estate. 

Criticizing the mathematicians’ reliance on the binominal formula to postulate that the likelihood Green had not forged the signature to be infinitesimally small, Schneps and Colmez note that the mathematicians inexplicably disregarded common reasons why signatures of the same person may change (i.e., as people get older, as they switch pens, etc.). Had they properly reasoned through the issues and corrected their math, the experts would have seen that it is far more common for the same person to have variances in his signature over time. While the authors admit to not knowing if Green actually had forged the signature or not, the authors’ primary concern is that the faulty math had an undue influence during the trial, thereby ensuring an unfair trial for Green.

Readers, thankfully, only need a limited understanding of math in order to understand the authors’ dissection of the errors produced at trial. Such accessibility elevates Math on Trial from college-syllabus fodder to a bookstore true-crime story. The authors’ postscripts for each case aid the narrative and provide some resolution from the drama of trial. In most instances, the accused are rescued from their persecution either by gallant mathematicians or the introduction of new evidence leading to the overturning of these faulty lower-court opinions. These efforts lead to larger questions about the ability of lower courts around the world to handle complexities of all types in their criminal trials.

Despite Schneps and Colmez’s engrossing narratives and mathematical explanations, Math on Trial does suffer some limitations that are hard to ignore. The authors do not suggest who might ultimately be responsible for the misuse of numbers in the courtroom. The case studies cast a wide net, alternatively identifying incompetent judges, conniving prosecutors, terrible defense attorneys, inadequate experts and uneducated lay juries as sources of the problem. Ultimately, the authors assign blame to everyone who touches the legal system.

As a result, Math on Trial neglects to provide any solutions for ending the misuse of math in criminal trials. Schneps and Colmez appear to endorse either severely limiting, if not prohibiting, the use of math courtrooms (as advocated by Lawrence Tribe of Gore v. Bush and Obama administration fame) or allowing only complex criteria and special analytic tools for its use in courtrooms (as conceived by the authors’ own Bayes in Law Research Consortium). Both ideas have little support (at least in the United States) and fail to assist accused defendants in the short term.

Despite Math on Trial’s limitations, Schneps and Colmez’s clever use of headline-grabbing case studies and digestible explanations of mathematical problems combine to argue for the careful use of numbers by advocates and lay juries alike. Their warnings remain relevant today as courtrooms face greater use of DNA evidence and other sophisticated forensic technologies.

A mix of academic primer and crime blotter, Math on Trial mainstreams the conversation about the appropriate use of math in our courtrooms and the real-life impact it has on the freedoms of the criminally accused. Legal practitioners and arm-chair advocates alike should enjoy this book.

Bharath Parthasarathy is an attorney and lives in Atlanta, Georgia.

 

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