Mathematics has a habit of infiltrating all areas of life and this includes the realm of law and justice. Whether it's the use of statistics in court, assessing DNA evidence, or the potential role of AI in the criminal justice system, a mathematical understanding of the issues involved can be useful, if not essential. Here is a collection of articles exploring some of these issues.

AI be the judge: The use of algorithms in the criminal justice system — Could AI help judges deliver fair and transparent sentences? A recent study group involving law experts and mathematicians explored the question and the challenges it poses.

Maths in a minute: The prosecutor's fallacy — If someone's DNA is found at the scene of a crime it's tempting to deduce the person is guilty — but that conclusion may be a little bit too rash. Here's why.

It's a match! — What exactly is a DNA match and how should we use it as evidence? Here's a more detailed look at the issues involved.

Beyond reasonable doubt — A lack of understanding of probabilities can lead to miscarriages of justice. Here is an example, involving a woman falsely convicted of murdering two of her children.

### Background reading

Maths in a minute: Conditional probability — When you think about the likelihood of someone being guilty, it can be useful to think in terms of conditional probability: the probability the person is guilty given the evidence. Here is a quick introduction to the concept.

Maths in a minute: Bayes' theorem — An important role in the mathematics of justice is played by Bayes' theorem, which allows you to update the probability of something (a person being guilty) in the light of new evidence (a DNA match being found). Here's a look at the theorem, using an example from medicine.

Maths in a minute: Odds ratios — When comparing the outcome for different population groups passing through the criminal justice system people often use the concept of odds ratios. Here is a quick introduction.

Maths in a minute: Algorithms — When we talk about using algorithms in the criminal justice system, what do we actually mean by an algorithm? Find out with this easy introduction.

Maths in a minute: Gödel's incompleteness theorems — The concept of consistency, that everybody should be treated equally by the law, is central in justice. But it also has a meaning in maths. Find out more here.

*This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here. *

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The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more. *