Cahit Arf
Encyclopedia
Cahit Arf 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 semigroup
s, and Arf ring
s.
), 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 İzmir
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 High School. In 1933 he joined the Mathematics Department of Istanbul University
. In 1937 he went to Göttingen
, where he received his PhD from the University of Göttingen 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 (TÜBİTAK)
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 (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
. 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.
Arf's influence on Turkish Mathematics 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
to Turkey
(now famous for the Langlands program
, among many other things); during which Langlands worked out some arduous calculations on the epsilon factors of Artin L-function
s.
Arf's portrait is depicted on the reverse
of the Turkish 10 lira
banknote issued in 2009.
Middle East Technical University
Department of Mathematics organizes a special lecture session called the Cahit Arf lecture each year in memory of Arf.
include:
Turkic peoples
The Turkic peoples are peoples residing in northern, central and western Asia, southern Siberia and northwestern China and parts of eastern Europe. They speak languages belonging to the Turkic language family. They share, to varying degrees, certain cultural traits and historical backgrounds...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is known for the Arf invariant
Arf invariant
In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by when he started the systematic study of quadratic forms over arbitrary fields of characteristic2. The Arf invariant is the substitute, in...
of a quadratic form
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
in characteristic
Characteristic
Characteristic may refer to:In physics and engineering, any characteristic curve that shows the relationship between certain input and output parameters, for example:...
2 (applied in knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
and surgery theory
Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way, introduced by . Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along...
) in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, the Hasse–Arf theorem in ramification theory, Arf semigroup
Arf semigroup
In mathematics, Arf semigroups are certain subsets of the positive integers closed under addition, that were studied by . They appeared as the semigroups of values of Arf rings.A subsemigroup of the positive integers, with elements ρ1...
s, and Arf ring
Arf ring
In mathematics, an Arf ring was defined by to be a 1-dimensional commutative semi-local Macaulay ring satisfying some extra conditions studied by ....
s.
Biography
Cahit Arf was born on 11 October 1910 in Selanik (ThessalonikiThessaloniki
Thessaloniki , historically also known as Thessalonica, Salonika or Salonica, is the second-largest city in Greece and the capital of the region of Central Macedonia as well as the capital of the Decentralized Administration of Macedonia and Thrace...
), which was then a part of the Ottoman Empire
Ottoman Empire
The Ottoman EmpireIt was usually referred to as the "Ottoman Empire", the "Turkish Empire", the "Ottoman Caliphate" or more commonly "Turkey" by its contemporaries...
. His family migrated to Istanbul
Istanbul
Istanbul , historically known as Byzantium and Constantinople , is the largest city of Turkey. Istanbul metropolitan province had 13.26 million people living in it as of December, 2010, which is 18% of Turkey's population and the 3rd largest metropolitan area in Europe after London and...
with the outbreak of the Balkan War in 1912. The family finally settled in İzmir
Izmir
Izmir is a large metropolis in the western extremity of Anatolia. The metropolitan area in the entire Izmir Province had a population of 3.35 million as of 2010, making the city third most populous in Turkey...
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 Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
.
Returning to Turkey, he taught mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Galatasaray High School. In 1933 he joined the Mathematics Department of Istanbul University
Istanbul University
Istanbul University is a Turkish university located in Istanbul. The main campus is adjacent to Beyazıt Square.- Synopsis :A madrasa, a religious school, was established sometime in the 15th century after the Ottoman conquest of Constantinople. An institution of higher education named the...
. In 1937 he went to Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, where he received his PhD from the University of Göttingen and he worked with Helmut Hasse
Helmut Hasse
Helmut Hasse 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 classfield theory and diophantine geometry , and to local zeta functions.-Life:He was born in Kassel, and died in...
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)
TÜBITAK
The Scientific and Technological Research Council of Turkey is the main body responsible for organizing research and development activities on the national level in Turkey, with headquarters located in Ankara.-History:...
upon President Cemal Gursel
Cemal Gürsel
Cemal Gürsel , was a Turkish army officer, and the fourth President of Turkey.- Early life :He was born in the city of Erzurum to the Turkish parents as the son of an Ottoman Army officer, Abidin Bey, the grandson of Ibrahim and the great-grandson of Haci Ahmad...
's appointment in 1962. After serving as the founding director of the council in 1963, he joined the Mathematics Department of Robert College
Robert College
Robert College of Istanbul , is one of the most selective independent private high schools in Turkey. Robert College is a co-educational, boarding school with a wooded campus on the European side of Istanbul between the two bridges on the Bosphorus, with the Arnavutköy district to the east, and...
in Istanbul. Arf spent the period of 1964–1966 working at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. He later visited University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
for one year.
Upon his final return to Turkey, he joined the Mathematics Department of the Middle East Technical University
Middle East Technical University
Middle East Technical University is a public technical university located in Ankara, Turkey...
and continued his studies there until his retirement in 1980. Arf received numerous awards for his contributions to mathematics, among them are: Inonu
Inonu
-Person:* Erdal İnönü was a Turkish physicist and politician.* İsmet İnönü was a Turkish soldier, statesman and the second President of Turkey.-Districts and towns:* İnönü, Eskişehir a town and district in Eskişehir Province....
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
Turkish Academy of Sciences
The Turkish Academy of Sciences is an autonomous scholarly society acting to promote scientific activities in Turkey. Although it is attached to the office of the Prime Minister and is largely funded by the government, it maintains financial and administrative autonomy...
. 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
He facilitated the now-celebrated visit of Robert Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
to Turkey
Turkey
Turkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...
(now famous for the Langlands program
Langlands program
The Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by ....
, among many other things); during which Langlands worked out some arduous calculations on the epsilon factors of Artin L-function
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 the 1923 by Emil Artin, in connection with his research into class field theory. Their fundamental properties, in particular the Artin...
s.
Arf's portrait is depicted on the reverse
Obverse and reverse
Obverse and its opposite, reverse, refer to the two flat faces of coins and some other two-sided objects, including paper money, flags , seals, medals, drawings, old master prints and other works of art, and printed fabrics. In this usage, obverse means the front face of the object and reverse...
of the Turkish 10 lira
Turkish lira
The Turkish lira is the currency of Turkey and the de facto independent state of the Turkish Republic of Northern Cyprus. The lira is subdivided into 100 kuruş...
banknote issued in 2009.
Middle East Technical University
Middle East Technical University
Middle East Technical University is a public technical university located in Ankara, Turkey...
Department of Mathematics organizes a special lecture session called the Cahit Arf lecture each year in memory of Arf.
Cahit Arf Lectures
Previous Cahit Arf lectures held at Middle East Technical UniversityMiddle East Technical University
Middle East Technical University is a public technical university located in Ankara, Turkey...
include:
- 2011: Jonathan PilaJonathan PilaJonathan S. Pila is an Australian mathematician at the University of Oxford. He won the 2011 Clay Research Award for his resolution of the André–Oort conjecture in the case of products of modular curves. In June of 2011, he was awarded the Senior Whitehead Prize by the London Mathematical Society...
of University of OxfordUniversity of OxfordThe University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
: Diophantine Geometry via O-minimality - 2010: John W. MorganJohn W. MorganJohn W. Morgan, , is a Canadian lawyer, politician, and businessman. He is the current mayor of the Cape Breton Regional Municipality in Nova Scotia....
of Stony Brook University, Simons Center for Geometry and Physics - 2009: Ben Joseph Green of University of CambridgeUniversity of CambridgeThe University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
- 2008: Gunter Harder of Mathematisches Institut der Universitat Bonn
- 2007: Hendrik LenstraHendrik LenstraHendrik Willem Lenstra, Jr. is a Dutch mathematician.-Biography:Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978...
of Universiteit Leiden Mathematisch Instituut - 2006: Jean-Pierre SerreJean-Pierre SerreJean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
of Collège de FranceCollège de FranceThe Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles... - 2005: Peter SarnakPeter SarnakPeter Clive Sarnak is a South African-born mathematician. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics...
of Princeton UniversityPrinceton UniversityPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and the Institute for Advanced StudyInstitute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner... - 2004: Robert LanglandsRobert LanglandsRobert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
of the Institute for Advanced StudyInstitute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner... - 2003: David MumfordDavid MumfordDavid Bryant Mumford is an American mathematician known for distinguished 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 the National Medal of Science...
of Brown UniversityBrown UniversityBrown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
Division of Applied Mathematics - 2002: Don ZagierDon ZagierDon Bernard Zagier is an American 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, and a professor at the Collège de France in Paris, France.He was born in Heidelberg, Germany...
of University of Utrecht / Collège de FranceCollège de FranceThe Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles... - 2001: Gerhard FreyGerhard FreyGerhard Frey is a German mathematician, known for his work in number theory. His Frey curve, a construction of an elliptic curve from a purported solution to the Fermat equation, was central to Wiles' proof of Fermat's Last Theorem....
of University of Essen Institute for Experimental Mathematics