CAHİT ARF

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2 Mar 2024

Cahit Arf was born on October 11, 1910 in Thessaloniki, which was then part of the Ottoman Empire. He moved to Istanbul with his family due to the Balkan Wars that started in 1912. He started his education life in Istanbul in 1914, first in Beşiktaş Sultanisi, now Kabataş Boys' High School, when he was four years old, but after the big fire in Cihangir and Tophane, which consisted mostly of wooden buildings, in 1915, he moved to Süleymaniye and continued his education in Istanbul Sultanisi (now Istanbul Boys' High School). . In 1919, Arf's family moved again, this time to Ankara, but after returning to Istanbul for a short time, they finally settled in Izmir.

Cahit Arf's interest in mathematics was noticed and encouraged by a teacher who encouraged him to solve Euclidean geometry problems when he was a fifth grade student during his school years in Izmir. When he reached the middle of high school, Cahit Arf was able to solve mathematics problems that his schoolmates could not solve. This talent attracted the attention of his family and teachers, and he went to St. Petersburg in Paris. He was sent to France by his family in 1926 to study at St. Louis High School. Cahit Arf, who completed his three-year high school education in two years and returned to Turkey in 1928, was among the candidate students to be sent to Europe by the Turkish government for higher education at that time. He completed his higher education at Ecole Normale Superieure in France in 1932. When he returned to Istanbul, after working as a mathematics teacher at Galatasaray High School for about a year, he worked as an associate professor candidate at Istanbul University, Faculty of Science.

Arf, who had been asking himself since his high school years which geometric problems could be solved with the help of rulers and compasses and which could not, was planning to make a list of algebraic equations or Galois algebraic equations that could be solved in those years. Since he thought that he could not cope with this project he designed in Istanbul, he took leave from Istanbul University and went to Göttingen University in 1937. He completed his doctoral studies under the supervision of Helmut Hasse in 1938, obtaining, among other results, the theorem now known as the Hasse-Arf Theorem. Cahit Arf II. He studied in Göttingen during a very difficult period leading up to World War II, but Hasse asked him to stay there for another year to continue his studies, and during this time Arf's work introduced concepts that are today called Arf Invariants in the world of mathematics.

Arf returned to Istanbul University from Germany in 1940. He was promoted to full professor in 1943, and to ordinary professor in 1955. In 1949 he spent a year as a visiting professor at the University of Maryland, and in 1956 he was honored by being elected a corresponding member of the Mainz Academy. He left Istanbul University in 1962. In 1963 Arf taught at Robert College in Istanbul. Later, between 1964 and 1966, Arf worked at the Institute for Advanced Study in Princeton in the United States. After staying in the United States for another year and visiting the University of California at Berkeley, he returned to Turkey in 1967 and attended the Middle East Technical University in Ankara. Arf retired in 1980 and continued his work at the Gebze Research Center affiliated with TÜBİTAK during his retirement.

He was one of the founding members of the Turkish Mathematical Association, established in 1948, and served as the president of the Turkish Mathematical Association between 1976-1982 and 1986-1989. Cahit Arf, who made a great contribution to the establishment and development of TÜBİTAK, which was established in 1963, also served as the Chairman of the Scientific Board of this institution for years.

Cahit Arf received the İnönü Award in 1948, the TÜBİTAK Science Award in 1974, honorary doctorates from Istanbul Technical University in 1979, from Karadeniz Technical University in 1980, from the Middle East Technical University in 1981, December 1993. He was honored with the Honorary Membership of the Turkish Academy of Sciences and the "Commandeur des Palmes Academiques" award from France on February 4, 1994.

Cahit Arf did most of his most important work in the field of algebraic number theory. He invented Arf invariants, which have many applications in algebraic and differential topology. His first works were on quadratic forms on objects, especially on quadratic forms on an object with characteristic 2. The name Cahit Arf is mentioned in the mathematical literature not only with the Arf Invariants, but also with the Hasse-Arf Theorem, which plays an important role in Class Field theory and Artin's L-functions theory. In ring theory, the Arf Rings are also named after him. In addition, Arf worked in applied mathematics, writing several papers on elastic plane bodies bounded by free boundaries and a paper on the algebraic structure of set expansion in statistical mechanics.

Cahit Arf, who died as a result of a heart attack on December 26, 1997, was buried in Zincirlikuyu Cemetery after the ceremony held at Istanbul University.

The silver coins printed by the General Directorate of Mint in 2001 within the scope of the Turks of the Millennium Commemorative Coin Series have Cahit Arf's portrait on one side and a section from the formula known as the Arf Invariant on the other side. Later, a portrait of Cahit Arf and a section from the formula known as the Arf Invariant were printed on the back of the 10 Turkish Lira banknotes put into circulation by the Central Bank of the Republic of Turkey as of January 1, 2009.

Doctoral Students

: Altıntaş Güleç Büke, Istanbul University, 1949
: Selma Soysal, Istanbul University, 1949
: Hilal Pamir, Istanbul University, 1953
: Nakibe Topuz, Istanbul University, 1953
: Kemal Özden, Istanbul University, 1954
: Bediz Asral, Istanbul University, 1955
:Şükufe Yamantürk, Istanbul University, 1955
:Bahattin Şamlı, Istanbul University, 1957
:Neşet Ayırtman, Istanbul University, 1961
:Özdem Çelik, Istanbul University, 1961
:Gültekin Büyükyenerel, Middle East Technical University, 1972
:Halil İbrahim Karakas, Middle East Technical University, 1974
: Mehmet Yenigül, Ege University, 1977
: Murat Kirezci, Middle East Technical University, 1981
: Azize Hayfavi, Middle East Technical University, 1983

Articles and Books

[1] C. Arf. ''Untersuchungen uber reinverzweigte Erweiterungen discret bewerteter perfecter Körper''. J. Reine Angew. Math., 181:1-44, 1940.
[2] C. Arf. ''Untersuchungen uber quadratische Formen in Körpern der Charakteristik 2. I''. J. Reine Angew. Math., 183:148-167, 1941.
[3] C. Arf. ''Untersuchungen uber quadratische Formen in Körper der Charakteristik 2. II''. Über aritmetische Aequivalenz quadratischer Formen in Potenzreihenkörpern über einem vollkommenen Korper der Charakteristik 2. Rev. Fac. Sci. Univ. Istanbul (A), 8:297-327, 1943.
[4] C. Arf. ''Un theoreme de geometrie elementaire''. Rev. Fac. Sci. Univ. Istanbul (A), 12:153-160, 1947.
[5] C. Arf. ''Sur les zones de Brillouin''. Rev. Fac. Sci. Univ. Istanbul, Ser. A, 12:161-163, 1947.
[6] C. Arf. ''Sur la determination des etats d'equilibre d'un milieu elastique plan admettant des frontieres libres a tensions constantes''. Rev. Fac. Sci. Univ. Istanbul (A), 12:309-344, 1947.
[7] C. Arf. ''Cebir Dersleri [Lectures on Algebra]'', Ankara University Faculty of Science Publications, No: 46 general, 9 mathematics, Ibrahim Horoz Publishing House, 442 pages, Istanbul, 1947.
[8] C. Arf. ''Sur la definition des determinants''. In Universite d'Istanbul. Faculte des Sciences. Collection of memoirs commemorating the laying of the first stone of the New Institutes of the Faculty of Sciences, pages 9-20. Istanbul, 1948.
[9] C.Arf. ''An algebraic interpretation of the sequence of multiplicity orders of an algebraic branch''. Proc. London Math. Soc. (2), 50:256-287, 1948.
[10] C. Arf. ''On the existence of the solution to an elasticity problem''. Rev. Fac. Sci. Univ. Istanbul (A), 14:75-85, 1949.
[11] C. Arf. ''On the identity of an elasticity free boundary problem with a flow problem''. Bull. Tech. Univ. Istanbul, 4(1):1-4 (1952), 1951.
[12] C. Arf. ''On the methods of Rayleigh-Ritz-Weinstein''. Proc. Bitter. Math. Soc., 3:223-232, 1952.
[13] C. Arf. ''On the determination of multiply connected domains of an elastic plane body, bounded by free boundaries with constant tangential stresses''. Bitter. J. Math., 74:797-820, 1952.
[14] C. Arf. ''On a free boundary problem of two-dimensional elasticity''. Bull. Tech. Univ. Istanbul, 5:13-16 (1953), 1952.
[15] C. Arf. ''Remarks about a memoir by K. Erim''. Rev. Fac. Sci. Univ. Istanbul (A), 19:45-54, 1954.
[16] C. Arf. ''On a generalization of Green's formula and its application to the Cauchy problem for a hyperbolic equation''. In Studies in mathematics and mechanics presented to Richard von Mises, pages 69-78. Academic Press Inc., New York, 1954.
[17] C. Arf. ''On the free boundaries at constant tensions of a plane elastic medium in equilibrium''. Rev. Fac Sci. Univ. Istanbul. Ser. A., 19:119-132, 1954.
[18] C. Arf. ''On Reiss's theorem''. Returns. Mast. e Appl. (5), 14:181-191, 1954.
[19] C. Arf. ''Eine explizite Konstruktion der separablen Hulle eines Potenzreihenkörpers''. Abh. Math. Week. Univ. Hamburg, 19:117-126, 1955.
[20] C. Arf. ''Uber den Satz von Dubourdieu''. Abh. Math. Week. Univ. Hamburg, 20:112-114, 1955.
[21] C. Arf. ''Uber ein Analogon des Riemann-Rochschen Satzes in Zahlkörpern''. Akad. Wis. Mainz. Abh. Math.-Nat. Kl., 1957:293-328, 1957.
[22] C. Arf, K. Imre, and E. Ozizmir. ''On the algebraic structure of the cluster expansion in statistical mechanics''. J. Mathematical Phys., 6:1179-1188, 1965.
[23] C. Arf and G. Saban.''Due dimostrazioni elementari del teorema di Cartan e Dieudonne''. Riv. Mast. Univ. Parma (2), 6:169-223, 1965.
[24] C. Arf. ''On the structure of the Galois group of the algebraic closure of a field of power series on a finite field and the Artin conductors''. In Les Tendances Geom. in Algebra and Number Theory, pages 27-35. Editions du Center National de la Recherche Scientifique, Paris, 1966.
[25] C. Arf. ''The advantage of geometric concepts in mathematics''. In Rings and geometry (Istanbul, 1984), pages 553-556.

Views

* Cahit Arf saw mathematics not as a profession but as a lifestyle. He constantly tells his students: "Don't memorize mathematics, do it yourself and understand it." he said.

* "Mathematics is essentially a matter of patience. It is necessary to understand by discovering, not by memorizing." he said.

* He emphasized the artistic aspect of mathematics by saying, "Mathematics is an art like painting, music and sculpture."

* "Mathematics is an inductive science, and this inductive science is valid for infinite sets. We grasp these infinities in an inductive way, and when we grasp it, we feel that infinity. Infinity... And this gives us happiness because we forget about death... Everyone is immortal. He wants to work in the field he feels. I also felt immortal in mathematics.