Mathematical insights as novel connections: Evidence from expert mathematicians
Where do mathematical insights come from? According to classic accounts, creativity is a multi-stage process that involves combining ideas in novel ways. Evidence for these accounts, however, is drawn from artificial lab-based settings or is zoomed out from the messy, moment-to-moment details of discovery. Here, we examine a video corpus of expert mathematicians generating proofs in an ecologically valid setting. We find that mathematicians begin by creating a variety of inscriptions. They then interact with these inscriptions through gaze, speech, gesture, and writing. When they experience an insight, however, their interactions become unpredictable, and they begin to connect inscriptions in novel ways (quantified by an information-theoretic measure, surprisal). Expert mathematical discovery, we conclude, exhibits the stages and combinatorial processing that have been proposed to characterize creativity. Even at the pinnacle of abstraction, at the highest levels of expertise, new ideas are born when the body discovers unexpected affinities among ideas.