Turkish mathematical genius: Who is Cahit Arf?

He was born on 11 October 1910 in Thessaloniki.

“My family was a class-changing family. So he had complexes that are in this type of family. For example, there was the concept of a neighborhood boy in my family. They wouldn't let me out on the street. Because I would be a neighborhood kid, and that wasn't something to envy. In this atmosphere, a child turns into himself. He sets up his own game. When I was a kid, I used to make paper toys all the time. This has been helpful in a way. I was inventing toys and constantly trying to observe my surroundings.”

Cahit Arf (24 October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasse–Arf theorem in ramification theory, Arf semigroups, and Arf rings.

“First we moved to Istanbul, then to Izmir. I met a teacher in the fifth grade in Izmir Sultanisi. Actually, he wasn't a teacher. He finished high school and went to Istanbul to become a dentist, for this he needs money; He teaches to save money. This young man took an interest in me because my grammar was very good, and I could also solve problems with linear systems. He made me prove the first theorems of Euclidean geometry. The last one was the Pythagorean theorem. I couldn't do it and I told him. Then he told me. Thanks to this man, I became interested in mathematics. At that time, I was not very enthusiastic about mathematics. My strength was grammar. Another of my interests is painting, reading articles on Vatan-Nation-Sakarya… I think every young child who lived through the War of Independence was like that then.”

“When I went to high school, I would not study mathematics from any book. I would listen to the lecture, but I would not take notes. Again, I didn't need to study at all in the exams, because my friends would always come and ask me questions. So I spent the middle part of high school answering the questions of my friends and my family heard about my talent from the teachers.”

Thus, his father had the opportunity to send Cahit Arf to France to attend high school. Cahit Arf graduated from St. Louis High School in Paris in two years instead of three and returned to Turkey. At that time, the Turkish government was sending students to Europe to study for higher education. The Sultan of Izmir also nominated Cahit Arf. Cahit Arf passed the exam and went to France again, and after attending the preparatory classes for the "special" colleges for two years, he took the exams of both École Normale Supérieure and École Politéchnique. The first is a school where many famous scientists in France are educated, while the other is a military engineering school that also receives civilians. Cahit Arf, who passed the exams of both. However, he gave up Politéchniqué and enrolled in the École Normale Supérieure and finished there in two years.

“When we were in Adana when the weather was very hot, we would go out at night. There was something like a casino in front of our house; they played a movie there one day. We were watching from the roof. But movies were always spoken in foreign languages. I knew a little French at the time, but I did not understand what was being said. There was a young lady with us who spoke French and she was translating the film to the group gathered on our roof. My parents were trying to encourage me by saying, "Look, if you learn French like this, you can do it too." I told them, “I will not learn a foreign language”. When I asked why, I replied, “Because we will work in such a way that they will learn from us and we will make the discoveries”. These were the feelings of a nine-year-old boy suffering from the weakness of society.”

After teaching at Galatasaray High School for a while, he moved to Istanbul University Mathematics Department as an associate professor candidate. 1937, the year Cahit Arf went to Göttingen to do his doctorate. Arf's doctoral work in Göttingen is not only a focus that has earned him worldwide recognition, but also a good indication of his approach to mathematics. Cahit Arf returns to Turkey at the end of 1938 and continues his duty at Istanbul University.

During the war years, an English mathematician named Patrick Du Val came to Istanbul University. While Du Val is explaining a theory, Cahit Arf is also in the audience. Du Val mentioned his theory in 1942 which states the properties of singularities around a point on an algebraic curve. Cahit Arf, who was in the audience while describing Du Val's findings, claims that there are effective algebraic concepts behind these geometric arguments. When Du Val asks him to express this claim openly, Cahit Arf stays at home for a week.

“Something came out at the end of the week, and it spread around the world. There were some loops in this business. O-rings are called Arf Rings, and closures are called Arf Closures. So that's how I became famous because of someone else. But the work I wanted to do never really introduced me…”

Cahit Arf received the title of professor in 1943.

“After that, I did a bad job: I sought applause from the environment. For this reason, I talked to engineers around and tried to understand their work. I thought if I solved a problem for them, they would applaud me. I also won the applause. In fact, the İnönü Award was given to me for this. But doing business for such applause is not a good thing. I think that if a person tries to take his own problem as far as he can with all his strength, he will make a much greater contribution to science…”

After leaving Istanbul University, he has been teaching at Robert College for about a year. In 1960, he was commissioned to establish the Cessation Nuclear Research Center. 1964-1966 covers the period when Cahit Arf continued his research at the Institute for Advanced Study at Princeton. Cahit Arf, who later became a visiting professor at the University of California, returned to Turkey in 1967 and started working at the Department of Mathematics at the Middle East Technical University.

Of course, the scientific activities of an idealist scientist like Cahit Arf could not be limited to research only. Cahit Arf, who contributed greatly to the establishment and development of TÜBİTAK, which was founded in 1963, also served as the Chairman of the Science Board of this institution for years.

METU Department of Mathematics Faculty Member Prof Dr. Şafak Alpay says the following about Cahit Arf:

“… We loved and respected Cahit Hodja, who loved wood carving, cherry liqueur, Sabahattin Ali stories, and his grandchildren very much. The smell of tobacco and the sound of thunder in the department corridors, the chalkboards filled with elegant writing will never leave our minds and will always be a source of inspiration for us.”

“Mathematics is an inductive science, and this inductive science is valid for infinite sets. These infinities

We grasp it inductively, and when we grasp it, we feel that infinity, infinity. And this gives us happiness because we forget about death… Everyone wants to work in a field where they feel immortal. I also felt immortal in mathematics…”

In his article titled The Basis of Freedom, published in the journal Özgür Insan, he wrote in June 1976:

“In 1932, when I finished my mathematics education and returned home, I was talking to an old friend of mine, who was at the Ministry of National Education at that time, when I was talking to him, with the naive idealism of the youth, that I wanted to be a mathematics teacher in an Anatolian town and that I wanted to deal with my students by being a mathematics teacher there. I said that I would read Marx and Nietzsche, and argue as much as I could. My old friend, who was an enthusiastic history teacher at the time, pointed in astonishment at the incompatibility between mathematics, Marx, and Nietzsche. My response to this was: “My aim is not to inculcate this or that view in my students, but to raise free people”. What I meant then was freedom from the prejudices that I think are, in a way, most essential to our happiness today. In my opinion, the basic principle of national education is not raising future generations conditioned in one way or another; On the contrary, future generations should be brought up to be unconditioned, to see things as they are, to ask why in every event, in every behavior, and to give natural and logical answers to this question.”

Since 1938, Cahit Arf has made fundamental contributions to mathematics with his studies in various fields such as algebra, number theory, elasticity theory, analysis, geometry, and engineering mathematics, and has achieved structural and permanent results. He passed away on 26 December 1997 due to heart disease.