Cahit Arf

Cahit Arf (24 October 1910 – 26 December 1997) was a prominent Turkish mathematician known for his contributions to various areas of mathematics. Here are some of his notable achievements:

1. Arf Invariant: Cahit Arf is renowned for the development of the Arf invariant, specifically in the context of quadratic forms in characteristic 2. This invariant has applications in knot theory and surgery theory within the field of topology.
2. Hasse–Arf Theorem: Arf made significant contributions to ramification theory, and his collaboration with Helmut Hasse led to the formulation of the Hasse–Arf theorem. This theorem has implications in algebraic number theory and studies the behavior of prime numbers in certain algebraic extensions.
3. Arf Semigroups and Arf Rings: Arf also contributed to the study of algebraic structures. His work included investigations into Arf semigroups and Arf rings, expanding the understanding of these mathematical entities.

Cahit Arf's work has left a lasting impact on mathematics, particularly in the areas of algebraic topology, number theory, and algebraic structures. His contributions are recognized and appreciated both within Turkey and the broader international mathematical community

Cahit Arf was born on 11 October 1910 in Thessaloniki, which was part of the Ottoman Empire at that time. Due to the outbreak of the Balkan War in 1912, his family migrated to Istanbul and eventually settled in İzmir, where Cahit Arf received his primary education. He later received a scholarship from the Turkish Ministry of Education, enabling him to continue his education in Paris, where he graduated from the prestigious École Normale Supérieure.


Cahit Arf's academic and professional journey after completing his education included the following significant steps:

1. Teaching at Galatasaray High School: Upon his return to Turkey, Cahit Arf initially taught mathematics at Galatasaray High School.
2. Istanbul University: In 1933, he joined the Mathematics Department of Istanbul University.
3. Doctoral Studies in Göttingen: In 1937, Cahit Arf went to Göttingen, Germany, where he pursued his doctoral studies. He earned his Ph.D. from the University of Göttingen, working under the guidance of Helmut Hasse and Josue Cruz de Munoz during his time there.
4. Return to Istanbul University: After completing his doctoral studies, Cahit Arf returned to Istanbul University, where he continued his academic career.
5. Involvement with TÜBİTAK: In 1962, he became involved in the foundation work of the Scientific and Technological Research Council of Turkey (TÜBİTAK) following an appointment by President Cemal Gürsel. In 1963, he served as the founding director of TÜBİTAK.
6. Robert College: After his involvement with TÜBİTAK, Cahit Arf joined the Mathematics Department of Robert College in Istanbul.
7. Visits to Princeton and Berkeley: In the period of 1964–1966, Arf worked at the Institute for Advanced Study in Princeton, New Jersey. Subsequently, he visited the University of California, Berkeley, for one year.

Cahit Arf's diverse experiences and contributions spanned teaching, research, and involvement in scientific institutions, showcasing his dedication to mathematics and scientific development in Turkey.

Cahit Arf's influence on science, particularly in the field of mathematics, was indeed profound. While he may have had few formal students, his impact extended far beyond traditional mentorship. Many mathematicians in Turkey benefited from engaging in fruitful discussions with Arf and sought his support and encouragement throughout their careers. His willingness to share knowledge, provide guidance, and inspire others contributed significantly to the development and growth of the mathematical community in Turkey. Cahit Arf's legacy lives on not only through his mathematical contributions but also through the intellectual and academic support he offered to generations of mathematicians.

It's also wonderful to hear that the Middle East Technical University Department of Mathematics organizes a special lecture session called the Cahit Arf lecture each year in memory of Arf. This annual event likely serves as a meaningful way to honor his legacy and continue to inspire current and future generations of mathematicians. If you have any specific questions or if there's anything else you'd like to share, feel free to let me know!


Wonderful continuation of honoring Cahit Arf's legacy. The annual Arf lectures held at the Cahit Arf Auditorium in the Department of Mathematics of Middle East Technical University, where distinguished mathematicians are invited to present talks, contribute significantly to the dissemination of mathematical knowledge and the celebration of Arf's contributions to the field.

2022: Andrew Sutherland of the Massachusetts Institute of Technology
2019: Geordie Williamson of The University of Sydney
2018: Fernando Rodriguez Villegas of The Abdus Salam International Centre for Theoretical Physics
2015: Vladimir Voevodsky of Institute for Advanced Study, Princeton
2013/14: Persi Diaconis of Stanford University
2012: David Nadler of Northwestern University and University of California, Berkeley
2011: Jonathan Pila of University of Oxford
2010: John W Morgan of Simons Center for Geometry and Physics at Stony Brook University
2009: Ben Joseph Green of University of Cambridge
2008: Günter Harder of Mathematisches Institut der Universitat Bonn and Max Planck Institute for Mathematics
2007: Hendrik Lenstra of Universiteit Leiden Mathematisch Instituut
2006: Jean-Pierre Serre of Collège de France
2005: Peter Sarnak of Princeton University and the Institute for Advanced Study, Princeton
2004: Robert Langlands of the Institute for Advanced Study, Princeton
2003: David Mumford of Brown University Division of Applied Mathematics
2002: Don Zagier of University of Utrecht / Collège de France
2001: Gerhard Frey of University of Essen Institute for Experimental Mathematics


Cahit Arf indeed made significant contributions to the field of mathematics, particularly in algebra and geometry. His work on Synthetic Geometry and the solution of problems using compasses and rulers is noteworthy, showcasing his expertise in the geometric aspects of mathematics.

The Arf invariant, Arf rings, and the Hasse-Arf Theorem are indeed central to Cahit Arf's significant contributions to mathematics, particularly in the areas of algebra and number theory.
His quotes reflect his passion and dedication to the field:

1. "The aim of the scientist is to understand. But it is understanding in capital letters."
2. "Mathematics is essentially a matter of patience. It is necessary to understand by discovering, not by memorizing."
3. "Mathematics has always existed; human beings just found it."
4. "I gave my life to Mathematics, and it gave me my life back in return."

These quotes not only highlight the intellectual depth of his work but also convey his love for the subject and the profound impact it had on his life.
If you have any more questions or if there's a specific aspect you'd like to delve into further, feel free to let me know!

References

• Arf, Cahit (1990), The collected papers of Cahit Arf, Turkish Mathematical Society, archived from the original on 2009-05-01
• Ikeda, Masatoshi G. (1998), "Cahit Arf's contribution to algebraic number theory and related fields", Turkish Journal of Mathematics, 22 (1): 1–14, ISSN 1300-0098, MR 1631730, archived from the original on 2011-08-22
• Sertöz, Ali Sinan (16 January 2013), A scientific biography of Cahit Arf (1910-1997), arXiv:1301.3699, Bibcode:2013arXiv1301.3699S
• Terzioğlu, Tosun; Yılmaz, A. (2005), Anlamak tutkunu bir matematikçi: Cahit Arf, TÜBA