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cahit Arf was born on 18 February 1910 in Selanik (Thessaloniki), which was then a part of the Ottoman Empire. His family migrated to Istanbul with the outbreak of the Balkan War in 1912. The family finally settled in izmir where Cahit Arf received his primary education. Upon receiving a scholarship from the Turkish Ministry of Education he continued his education in Paris and graduated from École Normale Supérieure.

Returning to Turkey, he taught mathematics at Galatasaray Lisesi. In 1933 he joined the Mathematics Department of Istanbul University. In 1937 he went to züttingen, where he received his PhD from the University of züttingen and he worked with Helmut Hasse and Josue Cruz de Munoz. He returned to Istanbul University and worked there until his involvement with the foundation work of Scientific and Technological Research Council (TÜBiTAK) upon President Cemal Gursel's appointment in 1962. After serving as the founding director of the council in 1963, he joined the Mathematics Department of Robert College in Istanbul. Arf spent the period of 1964–1966 working at the Institute for Advanced Study in Princeton, New Jersey. He later visited University of California, Berkeley for one year.

Upon his final return to Turkey, he joined the Mathematics Department of the Middle East Technical University and continued his studies there until his retirement in 1980. Arf received numerous awards for his contributions to mathematics, among them are: Inonu Award in 1948, Scientific and Technological Research Council of Turkey (TÜBiTAK) Science Award in 1974, and Commandeur des Palmes Academiques (France) in 1994. Arf was a member of the Mainz Academy and the Turkish Academy of Sciences. He was the president of the Turkish Mathematical Society from 1985 until 1989. Arf died on December 26, 1997 in Bebek, Istanbul, at the age of 87. His collected works were published, in 1988, by the Turkish Mathematical Society.