In the history of science, the concept of ‘institution builder’ would not be related only with the physical establishment or institutional development related to scientific research or education but also cover the consolidation of the boundary of a certain scientific field. Then it is possible to find some aspects of the institution builder from Augustus De Morgan who has been remembered only as a researcher of mathematical logic or a mathematics teacher. This paper explains how the academic status of ‘pure mathematics’ could be firmly established as an independent scientific field through the research and education of mathematics by De Morgan at University College London. The development and boundary of mathematics and physics in the twentieth century suggest that De Morgan can be regarded as an institution builder of modern mathematics in England.