Gary Froyland has significantly influenced the fields of dynamical systems and ergodic theory and has made major contributions to discrete optimisation. He is a world authority on the application of transfer operator methods to geophysical fluid flow, and his imaginative program of mathematics has reshaped scientific views on how to characterise complex fluid flow. Froyland has led multidisciplinary teams to solve pressing scientific problems in physical oceanography and atmospheric science, and to make port operations more efficient. His research on open-pit mine optimisation has had a profound impact on the scheduling of base metal mines internationally and will make cancer radiation therapy safer.