Arf was born in Thessaloniki in 1910. He graduated from St. Louis High School in Paris (in two years instead of three) in 1932. He graduated from École Normale Supérieure, again in two years, and returned to Turkey. After teaching at Galatasaray High School, he worked at İstanbul University’s Department of Mathematics. He commenced his doctoral studies in 1937 at Göttingen University in Germany, under the tutelage of renowned mathematician Herman Hasse. He completed his dissertation in one and a half years. After returning to İstanbul University in 1938, he became professor in 1943, and distinguished professor in 1955. He undertook research at the University of Maryland in the 1950-1951 academic year. As a Fulbright grantee from 1964 to 1966, he conducted research in the fields of algebra and theory of numbers at Princeton University’s Institute for Advanced Study. After working as a lecturer at the University of California Berkeley, he started teaching at Middle East Technical University’s Mathematics Department in 1967. He is known for the Arf Invariant, Arf Ring and Hasse-Arf Theorem. He passed away in 1997 in İstanbul.