Math on Trial

Most lawyers hate math. If we'd been any good at math, the joke goes, we would have gone to medical school. But math is hard to avoid in modern courtrooms. Expert witnesses are constantly using numbers to say things that lawyers and jurors struggle to follow, and that's where problems start.

In Math on Trial, a mother-daughter team of mathematicians tries to cast light on the matter. Leila Schneps and Coralie Colmez offer highly readable accounts of ten famous legal cases in which mathematical evidence was used - or rather, misused - drawing an important lesson from each about how mathematical proof (and the experts who present it) can go awry.

Most of the lessons are commonsensical warnings about the importance of basing mathematical estimates on valid data, verifying the accuracy of underlying assumptions, and considering all relevant factors. But some are eye-opening and counterintuitive. The authors use a sex discrimination case filed in 1989 by a UC Berkeley math professor to explain Simpson's paradox, which accounts for the mind-bending fact that, overall, a higher percentage of male than female applicants are admitted to Berkeley even though there is no evidence that any particular department at Berkeley admits men at a higher rate than women.

The book provides compelling accounts of several famous miscarriages of justice, including the 19th-century prosecution of French army Captain Alfred Dreyfus, who was a victim of virulent anti-Semitism and fabricated evidence as well as flawed mathematical proof. It also offers fascinating reviews of the more recent case of Dutch nurse Lucia de Berk, who was convicted of murder after it appeared that patients were dying on her watch in numbers far too high (or so an expert claimed) to be due to coincidence; and the tragic case of British lawyer Sally Clark, who was convicted of infanticide based on flawed mathematical estimates of the improbability that her two children would both succumb to "crib death."

There is an engaging account of the fraudulent financial machinations of the notorious Charles Ponzi, perpetrator of the Ponzi scheme, and a nice explanation of why such schemes are doomed to fail.

The book also offers a fresh perspective on the case of People v. Collins, known to every law student, in which the California Supreme Court overturned a conviction that had been based on a flawed mathematical estimate of the probability of finding in Los Angeles another couple, besides the defendants, consisting of a black man with a beard and mustache and a blond woman with a ponytail, who drove a yellow convertible.

The authors' primary goal is to explain potential weaknesses in mathematical evidence, but there is a disturbing subtext to the stories they tell. Again and again, experts who should have known better, and in some cases did know better, presented misleading mathematical testimony. What led them astray? The authors spoke with one of these wayward experts, mathematician Edward O. Thorp, who presented a misleading "mathematical proof of guilt" in a New Mexico murder case. Thorp is no fool. Author of the best-selling blackjack guide Beat the Dealer, he made a small fortune using card-counting to beat casinos at their own game before making a much larger fortune managing a hedge fund. Thorp told the authors that he recognized the logical defects in the testimony that the prosecutor had asked him to present, but he went ahead with the testimony because the prosecutor had convinced him that the defendant was guilty and because he was "always amenable to an interesting experience." Even mathematicians, it seems, can get caught up in adversarial zeal and seduced into partisanship by the enticement of playing the game.

In that light, we note as a weakness of the book its one-sided account of two cases on which the authors clearly have strong opinions: Amanda Knox, the American college student who was convicted of murder in 2009 in Perugia, Italy; and John Puckett, a California man who was convicted in 2008 of the 1972 murder of a San Francisco nurse. Schneps and Colmez think Knox is guilty as sin, and they offer their own calculation of the chances of Puckett's innocence - which they peg at 1 in 70. In both instances, their misunderstanding of some of the technical details of the forensic DNA evidence central to these cases undermines their analyses. In advocating for a particular point of view, they fall victim to some of the same analytic errors that they condemn in other mathematicians.

Despite these quibbles, we found the book both intellectually engaging and fun to read - worthwhile even for lawyers who hate math. Using the drama of courtroom battles, Math on Trial illustrates the difficulties of using numbers to guide us through an uncertain world.

William C. Thompson is a professor in the Department of Criminology, Law and Society at UC Irvine with a joint appointment in the School of Law. Joelle Vuille, a Swiss criminologist, is completing a two-year post-doctoral fellowship at UC Irvine.

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