Professor J H Rubinstein is Australia's leading topologist, and one of the country's most outstanding mathematicians. He has made important progress towards the resolution of the spherical space form problem and the recognition problem for the three-sphere, and made important contributions to our understanding of how general three-manifolds can be made up of polyhedra and other pieces. He has also made important contributions to the theory of minimal surfaces and to operations research, by introducing combinatorial techniques and minimax methods to the construction of minimal surfaces, and by introducing techniques from calculus into the combinatorial theory of shortest networks.