Perelman's *proof* of the conjecture uses this concept called Ricci flow, which is kind of about a structure in the manifold that allows the concept of "distance" to change over time. The quantum-gravity people and other mathematical physicists do some things with Ricci flow, but Perelman just used it as a tool to show "this hypothetical object can't exist, because when you apply a Ricci flow to it it would do something impossible". It's a rather elegant approach to the problem but it doesn't say anything about the "real" universe (whatever that means).
My thesis advisor, after retiring from academia, took up sculpture in a serious way (http://www.sieradskistudios.com/). His work isn't explicitly mathematical, but I can see where it reflects a lot of time spent visualizing low-dimensional topology. It's an interesting question---how can one bring that sort of inspiration into the photographic world?
Man Ray's answer seems largely to have been to construct mathematically-inspired objects and photograph them, which is fair enough but seems more about "mathematical sculpture, followed by photography". I'm not sure how to bring geometric content directly into the photographic process, but it's an interesting concept.