Visualizing in Mathematics
Visual thinking in mathematics (thinking with representations in visual imagination or external diagrams) has a plurality of uses. This chapter assesses the epistemic standing of major uses of visual thinking, concentrating on proving (and following a proof), and discovering, i.e. coming to believe a truth by one's own lights in a way that is reliable and involves no violation of epistemic rationality. Taking into account the sorts of error to which visual thinking is especially vulnerable, it is argued that visual thinking can have a non-superfluous role in proving. The chapter then discusses and illustrates the possibility of discovering mathematical truths visually. Finally, other uses of visual thinking in mathematics are surveyed.
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