Cahit Arf (1910-1997), a famous Turkish scientist whose picture is depicted in one of the Turkish banknotes, is a well-known figure in mathematics with his discoveries named after him (e.g., Arf invariant, Arf rings, the Hasse-Arf theorem). Although Arf may not be considered as a prolific scientist in terms of number of papers (he authored a total of 23 papers), his influence on mathematics and related disciplines was profound. As he was active before, during, and after World War II, Arf's contributions are not properly listed in citation indexes, and thus did not generate many citations even though several papers with "Arf" in their titles appeared in literature. This paper traces influence of Arf in scientific world using citation analysis techniques first. It reviews scientific impact of Arf by analyzing both; the papers authored by Arf and papers whose titles or keywords containing various combinations of "Arf invariant," "Arf rings," and so on. The paper then goes on to study Arf's contributions using social network analysis (SNA) and author co-citation analysis (ACA) techniques. CiteSpace and pennant diagrams are used to explore scientific impact of Arf by mapping his cited references derived from Thomson Reuters' Web of Science (WoS) database. The direct and indirect influences of Arf's highly cited paper on Arf invariant are assessed through ACA and single publication h index, respectively. The paper ends with a discussion of whether data analysis techniques used in this study can be useful to study scientific impact of researchers retrospectively.