Phase shifting interferometry (PSI) is one of the more common techniques for interpolation between interference fringes. A surface-profiling PSI instrument stores CCD image frames of fringe patterns for a series of reference phases; then applies a mathematical algorithm to recover phase information.1 Because the wavefront phase itself is a linear function of the surface profile, PSI provides a high-resolution measurement of the surface figure. In the early days, computational limits restricted the number of image frames to three or four, which does not leave much room for variation. As demands for precision have increased, so have the length and variety of phase-shifting algorithms. The state of the art has advanced to 5, 7 and even 15 frame varieties. At the same time, the level of sophistication in deriving these algorithms has risen dramatically.234 This paper explores the limits of these trends, while reviewing some of the mathematical techniques that we at Zygo use to analyze PSI performance. Finally, in an attempt to predict far into the future, I present a 101-frame algorithm that is highly resistant to error sources. This somewhat extreme example highlights the practical limits on algorithm length, which are actually more relaxed than one might think, provided that we loosen the definition of PSI.