Emphasis on speed and the no-control-panel, direct manipulation philosophy characterizing the last several systems becomes very important when trying to produce workable mathematical visualizations in virtual reality environments. Demonstrations from both the Illinois and Indiana groups now run in the duplicatable room-size CAVE environment pioneered by the Electronic Visualization Laboratory of the University of Illinois at Chicago. If it is possible to induce new mathematical perceptions by immersing the user in intuition-building interactive worlds of this sort, then these developments are potentially of great importance.