Gerd Faltings (; born 28 July 1954) is a German

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 ...

known for his work in

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic variety, alg ...

Education

From 1972 to 1978, Faltings studied

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 ...

and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

at the

University of Münster The University of Münster (german: Westfälische Wilhelms-Universität Münster, WWU) is a public university, public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over ...

. In 1978 he received his PhD in mathematics.

Career and research

In 1981 he obtained the ''venia legendi'' (

Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

) in mathematics, from the

. During this time he was an assistant professor at the University of Münster. From 1982 to 1984, he was

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

at the

University of Wuppertal The University of Wuppertal (''Universität Wuppertal'') is a German scientific institution, located in Wuppertal, in the state of North Rhine-Westphalia, Germany. The university's official name in German is ''Bergische Universität Wuppertal'' ...

. From 1985 to 1994, he was professor at

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 ...

. In the fall of 1988 and in the academic year 1992–1993 he was a visiting scholar 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 ...

. In 1986 he was awarded the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

at the ICM at Berkeley for proving the

Tate conjecture In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conje ...

for abelian varieties over number fields, the Shafarevich conjecture for abelian varieties over number fields and the

Mordell conjecture Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

, which states that any non-singular projective curve of genus ''g'' > 1 defined over a number field ''K'' contains only finitely many ''K''-rational points. As a Fields Medalist he gave an ICM plenary talk ''Recent progress in arithmetic algebraic geometry''. In 1994 as an ICM invited speaker in Zurich he gave a talk ''Mumford-Stabilität in der algebraischen Geometrie.'' Extending methods of

Paul Vojta Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation. Contributions In formulating Vojta's conjecture, he pointed out the possible existe ...

, he proved the

Mordell–Lang conjecture This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of pr ...

, which is a generalization of the Mordell conjecture. Together with

Gisbert Wüstholz Gisbert Wüstholz (born June 4, 1948, in Tuttlingen, Germany) is a German mathematician internationally known for his fundamental contributions to number theory (in the field of transcendental number theory, Diophantine approximation) and arithmet ...

, he reproved

Roth's theorem In mathematics, Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational number approximations that are 'very good'. Over half ...

, for which Roth had been awarded the Fields medal in 1958. In 1994, he returned to Germany and from 1994 to 2018, he was a director of the

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 ...

Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ruhr r ...

. In 1996, he received the

Gottfried Wilhelm Leibniz Prize The Gottfried Wilhelm Leibniz Prize (german: link=no, Förderpreis für deutsche Wissenschaftler im Gottfried Wilhelm Leibniz-Programm der Deutschen Forschungsgemeinschaft), in short Leibniz Prize, is awarded by the German Research Foundation to ...

of the

Deutsche Forschungsgemeinschaft The German Research Foundation (german: Deutsche Forschungsgemeinschaft ; DFG ) is a German research funding organization, which functions as a self-governing institution for the promotion of science and research in the Federal Republic of Germ ...

, which is the highest honour awarded in German research. Faltings was the formal supervisor of

Shinichi Mochizuki is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperboli ...

, Wieslawa Niziol, Nikolai Dourov.

Awards and honours

(1986) *

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

(1988/89) *

(1996) *

King Faisal International Prize The King Faisal Prize ( ar, جائزة الملك فيصل, formerly King Faisal International Prize), is an annual award sponsored by King Faisal Foundation presented to "dedicated men and women whose contributions make a positive difference". T ...

(2014) *

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

(2015) *

Foreign Member of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics ...

(2016) *

Cantor Medal The Cantor medal of the Deutsche Mathematiker-Vereinigung is named in honor of Georg Cantor, the first president of the society. It is awarded at most every second year during the yearly meetings of the society. The prize winners are mathematician ...

(2017) *

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

International Member (2018)

References

External links

{{DEFAULTSORT:Faltings, Gerd 1954 births Living people People from Gelsenkirchen Studienstiftung alumni University of Münster alumni Princeton University faculty Institute for Advanced Study visiting scholars 20th-century German mathematicians 21st-century German mathematicians Fields Medalists Gottfried Wilhelm Leibniz Prize winners Arithmetic geometers University of Bonn faculty Foreign Members of the Royal Society Foreign associates of the National Academy of Sciences Max Planck Institute directors