Friedrich Bachmann (born 11 February 1909 in

Wernigerode Wernigerode () is a town in the district of Harz, Saxony-Anhalt, Germany. Until 2007, it was the capital of the district of Wernigerode. Its population was 35,041 in 2012. Wernigerode is located southwest of Halberstadt, and is picturesquely s ...

, died 1 October 1982 in

Kiel Kiel () is the capital and most populous city in the northern Germany, German state of Schleswig-Holstein, with a population of 246,243 (2021). Kiel lies approximately north of Hamburg. Due to its geographic location in the southeast of the J ...

.) was a German mathematician who specialised in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

Life

Bachmann was the son of a

Lutheran Lutheranism is one of the largest branches of Protestantism, identifying primarily with the theology of Martin Luther, the 16th-century German monk and reformer whose efforts to reform the theology and practice of the Catholic Church launched th ...

minister Hans Bachmann. Bachmann came from an intellectual family, his paternal grandfather was the

number theorist Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

Paul Gustav Heinrich Bachmann Paul Gustav Heinrich Bachmann (22 June 1837 – 31 March 1920) was a German mathematician. Life Bachmann studied mathematics at the university of his native city of Berlin and received his doctorate in 1862 for his thesis on group theory. He th ...

. Bachmann took his early education at the Gymnasium in

Münster Münster (; nds, Mönster) is an independent city (''Kreisfreie Stadt'') in North Rhine-Westphalia, Germany. It is in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also a state distr ...

. After attending the Gymnasium, he attended 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 ...

and the

Humboldt University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

and graduated in 1927. While there he was a member of the Münster Wingolfs. In 1933, Bachmann was promoted to

D.Phil A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

with a thesis titled, ''Studies on the foundation of arithmetic with special reference to

Dedekind Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the Peano axioms, axiomatic foundations of ari ...

Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philo ...

, and Russell'' (german: Untersuchungen zur Grundlegung der Arithmetik mit besonderer Beziehung auf Dedekind, Frege, und Russell). His advisor was

Heinrich Scholz Heinrich Scholz (; 17 December 1884 – 30 December 1956) was a German logician, philosopher, and Protestant theologian. He was a peer of Alan Turing who mentioned Scholz when writing with regard to the reception of "On Computable Numbers, wit ...

. His doctoral students include

Andreas Dress Andreas Dress (born 26 August 1938) is a German mathematician specializing in geometry, combinatorics and mathematical biology. Dress earned his PhD from the University of Kiel in 1962, under the supervision of Friedrich Bachmann and Karl-Heinr ...

and Rolf Lingenberg. Bachmann was married to a great-granddaughter of

Otto von Bismarck Otto, Prince of Bismarck, Count of Bismarck-Schönhausen, Duke of Lauenburg (, ; 1 April 1815 – 30 July 1898), born Otto Eduard Leopold von Bismarck, was a conservative German statesman and diplomat. From his origins in the upper class of J ...

, Alexandra von Bredow. They had a son together, Sebastian

Career

In 1935, Bachmann moved to the

University of Marburg The Philipps University of Marburg (german: Philipps-Universität Marburg) was founded in 1527 by Philip I, Landgrave of Hesse, which makes it one of Germany's oldest universities and the oldest still operating Protestant university in the wor ...

where assisted

Kurt Reidemeister Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Göttinge ...

. Bachman

habilitated 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 ...

at Marburg before becoming a

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

in 1939. From 1941 Bachmann became a private lecturer at

University of Königsberg The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Prussi ...

and from 1943 at the

. On 1 March 1949, he was promoted to full professor (

Ordentlicher Professor Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

) at the

University of Kiel Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in ...

. He became known for his work on geometry, especially for his axiomatic justification of elementary geometry with mirroring operations, previously begun by

Johannes Hjelmslev Johannes Trolle Hjelmslev (; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for mapp ...

and others. After the war, Bachmann worked with the mathematician

Karl-Heinrich Weise Karl Heinrich Weise (24 May 1909, Gera – 15 April 1990, Kiel) was a German mathematician. In 1956 he was the president of the German Mathematical Society (''Deutsche-Mathematiker Vereinigung'', DMV). Biography Karl-Heinrich Weise, the son of a ...

to rebuild the mathematics department at the

. From 1960 Bachman was editor of the series titled, ''Grundzüge der Mathematik für Lehrer an Gymnasien sowie für Mathematiker in Industrie und Wirtschaft'' (Basic features of mathematics for teachers at grammar schools as well as for mathematicians in industry and business). In 1962–1963, Bachmann was elected

Dean Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * ...

of the mathematics department of the Faculty of Philosophy of Kiel University. Bachmann retired on 31 March 1977.

Bibliography

The following are articles, written or co-authored by Bachmann. * * * * * * The following is books or monographs written by Bachmann * *> *

Literature

* *

References

{{DEFAULTSORT:Bachmann, Friedrich 1909 births 1982 deaths People from Wernigerode 20th-century German mathematicians Group theorists