Günther Hans Frei (born 19 May 1942 in St. Gallen) is a Swiss mathematician and historian of mathematics.

Education and career

Frei studied mathematics, physics and languages at the University of Zurich. There he received his doctoral degree in 1968 with advisor

Bartel Leendert van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amste ...

and dissertation on geometry (''Beiträge zur axiomatischen Inhaltstheorie''). He became an instructor in 1968 at the

University of Notre Dame The University of Notre Dame du Lac (known simply as Notre Dame; ; ND) is a Private university, private Catholic research university in Notre Dame, Indiana, United States. Founded in 1842 by members of the Congregation of Holy Cross, a Cathol ...

and in 1970 at Quebec's

Université Laval (; English: ''Laval University)'' is a public research university in Quebec City, Quebec, Canada. The university traces its roots to the Séminaire de Québec, founded by François de Montmorency-Laval in 1663, making it the oldest institutio ...

, where he became in 1971 a professor. He remained there until he retired as professor emeritus and returned to Switzerland to live in

Hombrechtikon Hombrechtikon is a municipality in the district of Meilen in the canton of Zürich in Switzerland. History Hombrechtikon is first mentioned in 1200 as ''Humbrechtigkon''. In 1217 it was mentioned as ''Hunbrechticon''. Geography Hombrech ...

. Frei's research deals with

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and the history of mathematics, especially the history of number theory in the 19th and 20th centuries and Swiss mathematics. He has written extensively on the life and work of

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 ...

. Frei is a member of the Euler Committee of the Swiss Academy of Sciences.

Selected publications

* ''Felix Klein. A biographical sketch.'' In: ''Jahrbuch Überblicke Mathematik.'' 1984, pp. 229–254 (and ''Felix Klein.'' In: ''Collection Mathématique.'' Université Laval, vol. 40, 1981). * ''Leben und Werk von Helmut Hasse.'' In: ''Collection Mathématique.'' Université Laval, 1977 (and ''Helmut Hasse.'' In: ''Collection Math.'' vol. 38, 1981). * ''Helmut Hasse.'' In: ''Expositiones Mathematicae.'' vol. 3. 1985, pp. 55–69. * with Urs Stammbach: ''

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

und die Mathematik an der ETH Zürich 1913–1930.'' Birkhäuser 1992. * with Urs Stammbach: ''Die Mathematik an den Zürcher Hochschulen.'' Birkhäuser 1994. * with Urs Stammbach: ''Mathematicians and Mathematics in Zürich, at the university and the ETH.'' Schriftenreihe der ETH-Bibliothek 2007. * as editor with

Peter Roquette Peter Jaques Roquette (8 October 1927 – 24 February 2023) was a German mathematician working in algebraic geometry, algebra, and number theory. Biography Roquette was born in Königsberg on 8 October 1927. He studied in Erlangen, Berlin, and H ...

: ''

Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number t ...

und

– die Korrespondenz 1923–1934.'' Universitätsverlag Göttingen 2008 (originally published in 1981 in ''Collection Mathématique.'' Universität Laval). ** 2014 hbk translation;''Emil and Helmut Hasse: The Correspondence 1923–1958'', 2014 ebook
* as editor: ''Der Briefwechsel

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

–

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

1886–1918.'' Vandenhoeck und Ruprecht 1985. * with Urs Stammbach: ''

Heinz Hopf Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. Early life and education Hopf was born in Gräbschen, German Empire (now , part of Wrocław, Poland) ...

.'' In:

Ioan James Ioan Mackenzie James FRS (23 May 1928 – 21 February 2025) was a British mathematician working in the field of topology, particularly in homotopy theory. Life and career James was born in Croydon, Surrey, England, and was educated at St Paul ...

(ed.): ''History of Topology.'' Elsevier 1999. * ''The unpublished section eight: on the way to function fields over finite fields.'' In:

Catherine Goldstein : Catherine Goldstein (born July 5, 1958 in Paris) is a French number theorist and historian of mathematics who works as a director of research at the (IMJ). She was president of L'association femmes et mathématiques in 1991. Education and car ...

Joachim Schwermer Joachim Schwermer (26 May 1950, Kulmbach) is a German mathematician, specializing in number theory. Education Schwermer received his ''Abitur'' in 1969 at Aloisiuskolleg in Bad Godesberg and then studied mathematics at the University of Bonn. Af ...

, Norbert Schappacher (eds.) ''The shaping of arithmetic – after C. F. Gauss´s

Disquisitiones Arithmeticae (Latin for ''Arithmetical Investigations'') is a textbook on number theory written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24. It had a revolutionary impact on number theory by making the f ...

.'' Springer 2007 (also in ''Nachrichten Akad. Wiss.'' Göttingen 2006). * ''Heinrich Weber and the emergence of class field theory.'' in David Rowe, John McCleary (eds.) ''History of modern mathematics.'' Academic Press, 1989, pp. 424–450. (See

Heinrich Martin Weber Heinrich Martin Weber (5 March 1842, Heidelberg, German Confederation, Germany – 17 May 1913, Straßburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician. Weber's main work was in algebra, number theory, ...

.) * ''Chapter 6. Developments in the theory of algebra over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory.'' in

Jeremy Gray Jeremy John Gray (born 25 April 1947) is an English mathematician primarily interested in the history of mathematics. Biography Gray studied mathematics at the University of Oxford from 1966 to 1969, and then at Warwick University, obtaining h ...

Karen Parshall Karen Hunger Parshall (born 1955, Virginia; ''née'' Karen Virginia Hunger) is an American historian of mathematics. She is the Commonwealth Professor of History and Mathematics at the University of Virginia with a joint appointment in the Corcora ...

(eds.): ''Episodes in the history of modern algebra 1800–1950.'' American Mathematical Society 2007, pp. 117–151
Chapter 6, 2011 pbk edition
* ''The reciprocity law from Euler to Eisenstein.'' in C. Sasaki, M. Sugiura,

Joseph Dauben Joseph Warren Dauben (born December 29, 1944, Santa Monica) is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York. He obtained his PhD from Harvard University in 1972. His PhD thesis ' ...

: ''The intersection of history and mathematics.'' Birkhäuser 1994.

References

External links

* {{DEFAULTSORT:Frei, Gunther Swiss historians of mathematics 20th-century Swiss mathematicians University of Zurich alumni Academic staff of Université Laval 1942 births Living people