Virtual Reality and the Perception of Non-Euclidean Geometry: How Expert Mathematicians Evaluate Its Research Potential

Abstract

Virtual reality (vr) offers a promising approach to visualize Thurston’s non-Euclidean geometries which are notoriously difficult to represent using traditional methods. This study evaluates the pedagogical and research potential of a vr application designed for experts to explore S2 × E. Through immersive tasks, semi-structured interviews, and pre/post-immersion drawings with 20 researchers in low-dimensional manifold geometry, we assess whether vr can provide intuitive yet rigorous geometric representations. Results show that participants identified vr’s potential to foster geometric intuition. Many noted that vr could help generate new questions or provide fresh perspectives in mathematical research, and enhance conceptual understanding in pedagogy by making abstract geometries more tangible. Participants also cited practical barriers for both research (e.g., technical adaptation) and pedagogy (e.g., logistical constraints). This work contributes to the field of mathematical visualization in vr, documenting expert feedback on its opportunities and limitations for advanced research and teaching.