  A major breakthrough in the theory of topological algorithms occurred in 1992
when Hyam Rubinstein introduced the idea of an almost normal surface. We
explain how almost normal surfaces emerged naturally from the study of
geodesics and minimal surfaces. Patterns of stable and unstable geodesics can
be used to characterize the 2-sphere among surfaces, and similar patterns
characterize the 3-sphere among 3-manifolds. Analogous patterns of normal and
almost normal surfaces led Rubinstein to an algorithm for recognizing the
3-sphere.
