This paper uses a case study of a 1970s controversy in artificial-intelligence research to explore how scientists understand the relationships between research and practical applications. It is part of a project that seeks to map such relationships in order to enable better policy recommendations to be grounded empirically through historical evidence. In 1972 the mathematician James Lighthill submitted a report, published in 1973, on the state of artificial-intelligence research under way in the United Kingdom. The criticisms made in the report (...) have been held to be a major cause behind the dramatic slowing down of such research. This paper has two aims, one narrow and one broad. The narrow aim is to inquire into the causes, motivations and content of the Lighthill report. I argue that behind James Lighthill's criticisms of a central part of artificial intelligence was a principle he held throughout his career – that the best research was tightly coupled to practical problem solving. I also show that the Science Research Council provided a preliminary steer to the direction of this apparently independent report. The broader aim of the paper is to map some of the ways that scientists have articulated and justified relationships between research and practical, real-world problems, an issue previously identified as central to historical analysis of modern science. The paper therefore offers some deepened historical case studies of the processes identified in Agar's ‘working-worlds’ model. (shrink)