Season 7 Episode 4
Lawyers have, on occasion, tried to use somewhat dubious mathematical arguments in a court of law. In this episode, author and mathematician Coralie Colmez is on the show to discuss this with us!
Further Reading
Coralie Colmez
We were discussing cases from Coralie's book Math on Trial. Her website is here, and the books page has a link to buy Math on Trial and also has a free PDF of The Irrational Diary of Clara Valentine.
The Irrational Diary of Clara Valentine was Chalkdust Book of the Year 2022, which gives me an excuse to link to Chalkdust, a maths magazine with articles, interviews, puzzles, activities, and occasionally a quiz like "which integral are you?". I really like Chalkdust.
Coralie's website also links to her art and music projects, and to her company Unifrog. Whenever someone asks me what you can do with a maths degree, I think about how people like Coralie make it hard to answer that briefly!
Sally Clark
For more on the case, see this Wikipedia page. The case was, naturally, covered in the national press throughout.
The prosecutor's fallacy was mentioned; you can read more about that in this article from Oxford's Centre for Evidence-Based Medicine. This is the difference between the probability of "cause given effect" and "effect given cause". It's sometimes called base rate fallacy.
DNA Fingerprinting
This article in Nature Education gives more detail about the "13 loci" on DNA that Coralie talked about.
From that article, I've learned that there are parts of DNA which don't code for any protein (as far as we know), and that those parts sometimes include a repeating section which varies in length from person to person. The length of each of13 particular repeating sections is used by the FBI as a DNA fingerprint. I think this helps to answer a question from chat; when the DNA is degraded and only five of the 13 signals are present, I think that the FBI probably know which five they've got.
The article lists a probability of 1 in 575 trillion which might raise an eyebrow, but they also list some assumptions, which you might like to think about.
This article on PubMed Central gives more information on the repeating sections of DNA.
If you want to get in touch with us about any of the mathematics in the video or the further reading, feel free to email us on oomc [at] maths.ox.ac.uk.