Luke Wolcott is a recent PhD graduate and previous member of the editorial board of this blog. He is currently working on a postdoc project and could use our help. Please see Luke’s note below.

As a side project during my research postdoc, I’ve been collaborating with a philosopher of mathematics, Alexandra Van Quynh, on mathematical phenomenology. We’re looking for help from math PhD students (or postdocs, or professors). We’ve decided to look at the mathematician’s lived experience of groups (the abstract algebra kind). We’re mainly interested in the mental imagery, metaphors, and narratives that mathematicians use to understand and work with groups. Our working assumption is that this internal experience differs significantly from the formal manifestations of groups that appear in math literature, that it is subjective but that there are commonalities among mathematicians. The motivation came in part from this MathOverflow post (started by the late Bill Thurston), in part from Lakoff and Nunez’s Where Mathematics Comes From, in part from a survey of working mathematicians that (mathematician!) Jacques Hadamard used in the 1950s as data to conjecture patterns of mathematical intuition. I think groups are a great test object, because they’re basic enough that all mathematicians are familiar with them, they show up in so many different places in mathematics, and they’re perhaps the first step into abstract algebra. Groups are one of the first, most basic math objects that are (relatively) severed from the real world, and in particular visual or spacial intuition. Well, I don’t want to give away our hypotheses too much. **We’ve made a survey, asking questions about the lived experience of groups, and we’re distributing it to mathematicians. Would you consider completing the survey?** The survey is below. Spend as much or little time on it as you feel like. It’s not necessary to overthink your answers; sometimes the first, spontaneous response is the more revealing. We may get back to you and ask some follow-up questions about your responses. We’ll keep your responses confidential, or we’ll ask your permission if we decide it would be nice to quote you. Enjoy!