# Examples of Mathematics in Court

In court trials, natural sciences such as physics and biology routinely make an appearance, e.g. when estimating the speed of a vehicle based on impact damage or trying to deduce from the condition of a corpse how long ago the person died.

Pure mathematics is found in courtrooms much more rarely (perhaps because of the difficulty of convincing a judge – or worse, a jury – with mathematical arguments). I am currently aware of the following two broad categories of mathematics being invoked in a trial:

1. Probability and conditional probability, especially the misunderstanding thereof. One instance of this is known as the Prosecutor's fallacy and basically involves a confusion of prior and posterior in Bayesian inference. The Wikipedia page mentions the infamous "Sally Clark case" as a possible example of this fallacy resulting in a wrongful conviction. BBC News also has an article according to which mathematical reasoning about test results played a role in the Knox/Sollecito murder trial.

2. Benford's First-Digit Law which predicts the approximate frequency distribution of digits in real-life data, is not only used as a heuristic for the detection of possible fraud, but shockingly even accepted as evidence of the same by some jurisdictions.

Are there examples of other branches of mathematics that have played a role (for the better or worse) in the courtroom?

As a side note, is is interesting that much of the key courtroom vocabulary like "trial", "case", "law" etc. is also part of standard mathematics lingo, which makes meaningful web searches for such material quite challenging.

• matheducators.stackexchange.com/questions/5676/… – JP McCarthy Nov 14 '14 at 12:10
• There's a section in Salvadori's Why Buildings Fall Down in which he describes testifying as an expert witness in a case involving a building collapse, explaining to the jury the equations that govern the maximum loading of a dome, and being cross-examined about that. – MJD Nov 14 '14 at 14:28
• The infamous Indiana pi Bill comes to mind. :) – David H Nov 21 '14 at 10:23
• "Objection, your honor! The counselor is assuming the continuum hypothesis, which is clearly unprovable from the axioms of $\sf ZFC$ as shown by Goedel and Cohen!!!" $\tag*{}$ "Sustained." – Asaf Karagila Nov 23 '14 at 23:54

• "The paper was awarded a special prize of $400 that the author did not have to pay to the state of California." :) – user139000 Nov 14 '14 at 11:31 The book Math on Trial: How Numbers Get Used and Abused in the Courtroom by Leila Schneps and Coralie Colmez has many examples. B. Grofman and H. Scarrow, ‘Iannucci and Its Aftermath: The Application of the Banzhaf Index to Weighted Voting in the State of New York’, in Steven Brams, Andrew Schotter and Gerhard Schwodiauer (Eds.), Applied Game Theory, Physica-Verlag, Vienna,$1979$,$168$-$183\$, discusses the use and misuse of the Banzhaf power index by the courts; a PDF is available here.