Paul Bachmann
Encyclopedia
Paul Gustav Heinrich Bachmann (22 June 1837 – 31 March 1920) was a German
mathematician
.
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 then went to Breslau to study for his habilitation, which he received in 1864 for his thesis on Complex Units.
Bachmann was a professor at Breslau and later at Münster
.
His major works include
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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....
.
Bachmann studied 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 the University of his native city of Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
and
received his doctorate in 1862 for his thesis on group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
. He then went to Breslau to study for his habilitation, which he received in 1864 for his thesis on Complex Units.
Bachmann was a professor at Breslau and later at Münster
Münster
Münster is an independent city in North Rhine-Westphalia, Germany. It is located in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also capital of the local government region Münsterland...
.
His major works include
- Analytische Zahlentheorie, a work on analytic number theoryAnalytic number theoryIn mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
in which Big O notationBig O notationIn mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...
was first introduced - Die Lehre von der Kreistheilung und ihre Beziehungen zur Zahlentheorie, Teubner, Leipzig, 1872
- Niedere Zahlentheorie, a two-volume work on elementary number theoryNumber theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
- Das Fermat-Problem in seiner bisherigen Entwicklung, a work about Fermat's Last TheoremFermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....