Summary: Mathematics plays a major role in contemporary fisheries management. Stock assessments often depend on elaborate models used to set catch levels and address other policy objectives. In recent years, the collapse of various important fish stocks has caused some critics to suggest that mathematical models actually obscure the truth by narrowing scientific understanding to the realm of quantifiable events. In the words of one fisherman, "Mathematics has highjacked the definition and position of real science." In this paper, I present a number of typical fishery models, examine their limitations, discuss controversies about their use, and explore possible alternatives. I draw on examples from economics and investment theory to illustrate the problem of making credible predictions about an uncertain future. The constraints of the real world, where people care deeply about policy consequences, have altered my scientific perspective as an applied mathematician. This paper reflects the evolution of thought that has accompanied my experience working for 28 years at the Pacific Biological Station in Nanaimo, B.C., the host city for this conference.