Abstract

We can do very little mathematics without the aid of cognitive tools and artefacts. In that sense, mathematics is a tool-driven practice, and many of the disputes we have seen in the history of mathematics about which objects and theorems to accept have in effect been disputes about the acceptability of certain tools. AI is a new and powerful cognitive tool, and the discussions we are having today about AI can be seen as a modern iteration of the millennia-old discussion about which tools to accept. This does not make the discussion trivial. On the contrary. Tools are not neutral, and the debate about which tools to accept in mathematics is always also a discussion about what mathematics to accept. That goes for AI tools as well. In my presentation, I will situate current debates about AI within the broader history of debates about cognitive tools, and I will explore how the introduction of AI might shape mathematics in the future.