Cahit Arf (; 24 October 1910 – 26 December 1997) was a Turkish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He is known for the

Arf invariant In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf i ...

of a

quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a ...

in characteristic 2 (applied in

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

and

surgery theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by . Milnor called this technique ''surgery'', while An ...

) in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

, the Hasse–Arf theorem in

ramification theory In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two ''branches'' differing in sign. The term is also used from the opposite perspective (branches coming together) as ...

, Arf semigroups and Arf rings.

Biography

Cahit Arf was born on 11 October 1910 in

Selanik Thessaloniki (; el, Θεσσαλονίκη, , also known as Thessalonica (), Saloniki, or Salonica (), is the second-largest city in Greece, with over one million inhabitants in its Thessaloniki metropolitan area, metropolitan area, and the capi ...

(

Thessaloniki Thessaloniki (; el, Θεσσαλονίκη, , also known as Thessalonica (), Saloniki, or Salonica (), is the second-largest city in Greece, with over one million inhabitants in its Thessaloniki metropolitan area, metropolitan area, and the capi ...

), which was then a part of the

Ottoman Empire The Ottoman Empire, * ; is an archaic version. The definite article forms and were synonymous * and el, Оθωμανική Αυτοκρατορία, Othōmanikē Avtokratoria, label=none * info page on book at Martin Luther University) ...

. His family migrated to

Istanbul Istanbul ( , ; tr, İstanbul ), formerly known as Constantinople ( grc-gre, Κωνσταντινούπολις; la, Constantinopolis), is the List of largest cities and towns in Turkey, largest city in Turkey, serving as the country's economic, ...

with the outbreak of the

Balkan War The Balkan Wars refers to a series of two conflicts that took place in the Balkan States in 1912 and 1913. In the First Balkan War, the four Balkan States of Greece, Serbia, Montenegro and Bulgaria declared war upon the Ottoman Empire and defea ...

in 1912. The family finally settled in

İzmir İzmir ( , ; ), also spelled Izmir, is a metropolitan city in the western extremity of Anatolia, capital of the province of the same name. It is the third most populous city in Turkey, after Istanbul and Ankara and the second largest urban agglo ...

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 École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

. Returning to Turkey, he taught

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Galatasaray High School Galatasaray High School ( tr, Galatasaray Lisesi, french: Lycée de Galatasaray), established in what was then Constantinople and is now Istanbul, in 1481, is the oldest high school in Turkey. It is also the second-oldest Turkish educational in ...

. In 1933 he joined the Mathematics Department of

Istanbul University , image = Istanbul_University_logo.svg , image_size = 200px , latin_name = Universitas Istanbulensis , motto = tr, Tarihten Geleceğe Bilim Köprüsü , mottoeng = Science Bridge from Past to the Future , established = 1453 1846 1933 ...

. In 1937 he went to

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

, where he received his PhD from the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

and he worked with

Helmut Hasse Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ...

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 (TÜBİTAK) upon President

Cemal Gürsel Cemal Gürsel (; 13 October 1895 – 14 September 1966) was a Turkish army general who became the List of Presidents of Turkey, fourth President of Turkey after a coup. Early life He was born in the city of Erzurum as the son of an Ottoman A ...

's appointment in 1962. After serving as the founding director of the council in 1963, he joined the Mathematics Department of

Robert College The American Robert College of Istanbul ( tr, İstanbul Özel Amerikan Robert Lisesi or ), often shortened to Robert, or RC, is a Selective school, highly selective, Independent school, independent, mixed-sex education, co-educational Secondary ...

in Istanbul. Arf spent the period of 1964–1966 working at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. He later visited

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

for one year. Upon his final return to Turkey, he joined the Mathematics Department of the

Middle East Technical University Middle East Technical University (commonly referred to as METU; in Turkish language, Turkish, ''Orta Doğu Teknik Üniversitesi'', ODTÜ) is a public university, public Institute of technology, technical university located in Ankara, Turkey. The ...

and continued his studies there until his retirement in 1980. Arf received numerous awards for his contributions to mathematics, among them are: İnönü Award in 1948, Scientific and Technological Research Council of Turkey (TÜBİTAK) 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 The Turkish Academy of Sciences ( tr, Türkiye Bilimler Akademisi – TÜBA) is an autonomous scholarly association aimed at promoting scientific activities in Turkey. Although it is attached to the office of the Prime Minister and is largely fund ...

. 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.

Influence

Arf's influence on science in general and mathematics in particular was profound. Although he had very few formal students, many of the mathematicians of Turkey, at some time of their careers, had fruitful discussions on their field of interest with him and had received support and encouragement. He facilitated the now-celebrated visit of

Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...

Turkey Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a list of transcontinental countries, transcontinental country located mainly on the Anatolia, Anatolian Peninsula in Western Asia, with ...

(now famous for the

Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...

, among many other things); during which Langlands worked out some arduous calculations on the epsilon factors of

Artin L-function In mathematics, an Artin ''L''-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group ''G''. These functions were introduced in 1923 by Emil Artin, in connection with his research into class field theory. T ...

s. Arf's portrait is depicted on the

reverse Reverse or reversing may refer to: Arts and media * ''Reverse'' (Eldritch album), 2001 * ''Reverse'' (2009 film), a Polish comedy-drama film * ''Reverse'' (2019 film), an Iranian crime-drama film * ''Reverse'' (Morandi album), 2005 * ''Reverse'' ...

of the Turkish 10

lira Lira is the name of several currency units. It is the current currency of Turkey and also the local name of the currencies of Lebanon and of Syria. It is also the name of several former currencies, including those of Italy, Malta and Israe ...

banknote issued in 2009.

br>Department of Mathematics
organizes a special lecture session called the Cahit Arf lecture each year in memory of Arf.

Arf Lectures

Since 2001 the Arf lectures in honor of Cahit Arf have been held annually at the Cahit Arf Auditorium in the Department of Mathematics of

. Each lecture is presented by a distinguished mathematician selected by the advisory board. Since 2006, the Arf Lecturers are invited to deliver their talks at IMBM (Istanbul Center for Mathematical Sciences) too. * 2022: Andrew Sutherland of the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

* 2019:

Geordie Williamson Geordie Williamson (born 1981 in Bowral, Australia) is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36. Education Educated at Che ...

The University of Sydney The University of Sydney (USYD), also known as Sydney University, or informally Sydney Uni, is a public research university located in Sydney, Australia. Founded in 1850, it is the oldest university in Australia and is one of the country's si ...

* 2018: Fernando Rodriguez Villegas of The Abdus Salam

International Centre for Theoretical Physics The Abdus Salam International Centre for Theoretical Physics (ICTP) is an international research institute for physical and mathematical sciences that operates under a tripartite agreement between the Italian Government, United Nations Education ...

* 2015:

Vladimir Voevodsky Vladimir Alexandrovich Voevodsky (, russian: Влади́мир Алекса́ндрович Воево́дский; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic var ...

Institute for Advanced Study, Princeton The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

* 2013/14:

Persi Diaconis Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known f ...

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

* 2012: David Nadler of

Northwestern University Northwestern University is a private research university in Evanston, Illinois. Founded in 1851, Northwestern is the oldest chartered university in Illinois and is ranked among the most prestigious academic institutions in the world. Charte ...

and

* 2011:

Jonathan Pila Jonathan Solomon Pila (born 1962) FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: is an Australian mathematician at the University of Oxford. Education Pila earned his bachelor's degree at ...

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

* 2010: John W Morgan of

Simons Center for Geometry and Physics The Simons Center for Geometry and Physics is a center for theoretical physics and mathematics at Stony Brook University in New York. The focus of the center is mathematical physics and the interface of geometry and physics. It was founded in 2 ...

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...

* 2009: Ben Joseph Green of

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

* 2008:

Günter Harder Günter Harder (born 14 March 1938 in Ratzeburg) is a German mathematician, specializing in arithmetic geometry and number theory. Education and career Harder studied mathematics and physics in Hamburg und Göttingen. Simultaneously with the St ...

of Mathematisches Institut der Universitat Bonn and

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck S ...

* 2007:

Hendrik Lenstra Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician. Biography Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987 he was appointed to the faculty of ...

Universiteit Leiden Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...

Mathematisch Instituut * 2006:

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment (''grand établissement'') in France. It is located in Paris ne ...

* 2005:

Peter Sarnak Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced St ...

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

and the

* 2004:

of the

* 2003:

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded t ...

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

Division of Applied Mathematics * 2002:

Don Zagier Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the ''Col ...

University of Utrecht Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

* 2001:

Gerhard Frey Gerhard Frey (; born 1 June 1944) is a German mathematician, known for his work in number theory. Following an original idea of Hellegouarch, he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a pur ...

University of Essen The University of Duisburg-Essen (german: link=no, Universität Duisburg-Essen) is a public research university in North Rhine-Westphalia, Germany. In the 2019 ''Times Higher Education World University Rankings'', the university was awarded ...

Institute for Experimental Mathematics

Notes

References

* * * *

External links

Cahit Arf Lectures homepage

Page and links on Cahit Arf

A documentary on Cahit Arf
* *
Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...

{{DEFAULTSORT:Arf, Cahit 1910 births 1997 deaths Scientists from Thessaloniki People from Salonica vilayet Macedonian Turks 20th-century Turkish mathematicians Topologists École Normale Supérieure alumni Istanbul University faculty Institute for Advanced Study visiting scholars University of Göttingen alumni Middle East Technical University faculty Commandeurs of the Ordre des Palmes Académiques Recipients of TÜBİTAK Science Award METU Mustafa Parlar Foundation Science Award winners