Following postdoctoral work at the University of California, Berkeley, Max joined the scientific staff of the Lawrence Livermore National Laboratory in 1974, working on problems in plasma physics relating to fusion technology. In 1984, she became the founding Director of the Livermore branch of the UC Institute of Geophysics and Planetary Physics, and in 1995 she became the Director of University Relations. She joined the faculty at UC Santa Cruz in 2001.
Max is best known for her contributions to the theory of adaptive optics as a technique for reducing the optical distortions of images taken through the turbulent atmosphere. This work began at the JASON Defense Advisory Group, which she joined in 1983 as its first female member. With her colleagues in JASON, she developed the idea of using an artificial laser guide star to correct astronomical images. In addition to continuing to develop this technology at the Center for Adaptive Optics, she now uses adaptive optics to study active galactic nuclei as well as planets in the Solar System.