Mathematicians and visuo-spatial thinking

Do mathematicians only think in formulas? We surveyed mathematicians’ use of mental imagery via the OSIVQ test (n=232) and four open questions (n=222). Combining expert judgement and text mining count of the number of diagrams in 3799 arXiv articles, we investigated whether the amount of visuo-spatial thinking (if any) is related to an article’s subdiscipline (as defined by the MSC2020 classification1). Finally, we explored the role of visuo-spatial thinking in mathematical research. We conclude that mathematicians are highly visual as measured by their OSIVQ spatial imagery scores. Roughly one third of the mathematicians in our survey used visuo-spatial thinking regularly and one-third frequently. This is not connected to their subdiscipline. Visual representations are important in mathematical practice. As one expert expressed: “images and even movies are continuously running in our minds”.