Abstract

As artificial intelligence, large language models, and interactive theorem proving improve in their mathematical abilities and usefulness, prominent mathematicians are predicting that computational tools will soon have even bigger impacts on how mathematics is done. For example, the centuries-old dream of gap-free and error-free mathematics might finally be within reach. In this paper, we will examine about how these kinds of changes to the infrastructure of mathematical knowledge will bring about new dangers. Specifically, we will argue that the move to AI-assisted “mass-produced” mathematics will leave mathematics vulnerable to hacking in ways that it has not been previously. We will give some simple examples of what hacking mathematics might look like and why it might be done, then consider the options for the cybersecurity of mathematical knowledge. While the potential changes to mathematical practice might reduce the dangers of gaps and errors, we will argue that they also add a new category of danger: deliberate subversion.