The complex system of mathematical creativity: Modularity, burstiness, and the network structure of how experts use inscriptions

AbstractOne of the pinnacles of human cognition is the creative insight of expert mathematics. While its concepts are abstract, the actual practice of mathematics is undeniably material and embodied. Mathematicians draw, sketch, write; having created these inscriptions, they interact with them. This iterated process of inscription is the engine of mathematical discovery. But how does this engine work? Here, using a new video corpus of mathematical experts working on proofs, and deploying tools from network and complexity science, we characterize the structure and temporal dynamics of how mathematical experts create and interact with blackboard inscriptions. We find regularities in the structure of this activity (e.g., emergent ‘communities’ of inscriptions) and its temporal dynamics (e.g., ‘bursty’ shifts in attention). By characterizing this activity, we gain a better understanding of the distributed ecosystem in which mathematical creativity occurs — including the ways that mathematicians actively construct their own notational niches.

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