ArgumentThis paper aims to show how a nineteenth-century Korean scholarʼs mathematical study reflects the Korean intellectual environment of his time by focusing on the rule of false double position and the method of root extraction. There were two major trends in Korean mathematics of the early nineteenth century: the first was “Tongsan,” literally “Eastern Mathematics,” which largely depended on Chinese mathematics of the Song and Yuan period adopting counting rod calculation; the second trend was Western mathematics, which was transmitted by the Jesuits and their Chinese collaborators from the late sixteenth century. There was also an intellectual transition in late eighteenth-century Korea when mathematics, which had been of only minor interest for Confucian scholars, became an important part of Confucian pursuits. We can gain an insight into the history of mathematics in Korea by examining and understanding Hong Kil-chuʼs (1786–1841) mathematical studies and the context of the academic world of his time.