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Human and Artificial Understanding in Mathematics - A comparative study of informal, but functionally valuable moves performed by mathematical agents. (FWOTM822)
Computers are only fairly recently being used in the practice of mathematics. As mathematics has a reputation for being the formal, deductive science, it was hoped that its automation would quickly lead to impressive results. Not so. Mathematics proved to be much more dependent on the undefined quality of informal understanding than formal deduction. This lack of understanding in computer systems gets criticized, but the critique is vague and little seems to be done to investigate what this (informal) understanding might actually or preferably entail as well as how and how successfully or poorly automated mathematics is attempting to alleviate that deficiency. Starting from accounts of mathematical practice, I will investigate how and which informal moves augment mathematical abilities, focusing on two activities in particular: social dynamics and concept formation. I will then look into the available literature regarding its attempted automation and conduct an extensive investigation of multiple case studies to interpret their results and recognise its prospects and flaws. The results of my analysis will furthermore be used to reassess the general discussion on mathematical understanding and its informal moves.
Date:1 Oct 2016 → 30 Dec 2020