Survey of the mathematical theory of fish locomotion

In this paper an attempt is made to give a survey of the mathematical approach to the description of the swimming of fish. This type of investigation is of interest because it gives insight in the fundamentals of the interaction of the body of the fish and the fluid. Sir James Lighthill considered this problem in a very lively way by showing that simple ideas can be the nucleus of deep mathematical investigations. He and, besides him, T.Y. Wu can most probably be regarded as the founders of the hydrodynamical description of fish locomotion. They have stimulated many capable theoreticians to contribute to this rich field of beautiful problems. Of course, the mathematical investigations were stimulated by the many experimental discoveries already made earlier by prominent biologists.