Paul Gustav Heinrich Bachmann (22 June 1837 – 31 March 1920) was 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
O ...
.
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
In 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 ...
. 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.
Works
*''Zahlentheorie'', Bachmann's work on
number theory
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, "Mathe ...
in five volumes (1872-1923):
**Vol. I:
Die Elemente der Zahlentheorie' (1892)
**Vol. II:
Analytische Zahlentheorie' (1894), a work on
analytic number theory
In 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 Peter Gustav Lejeune Dirichlet's 1837 introduction of Diri ...
in which
Big O notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Land ...
was first introduced
**Vol. III:
Die Lehre von der Kreistheilung und ihre Beziehungen zur Zahlentheorie' (first published in 1872)
**Vol. IV (Part 1):
Die Arithmetik der quadratischen Formen' (1898)
**Vol. IV (Part 2):
Die Arithmetik der quadratischen Formen' (posthumously published in 1923)
**Vol. V:
Allgemeine Arithmetik der Zahlenkörper' (1905)
*''Niedere Zahlentheorie''
First part(1902)
Second part(1910),
a two-volume work on elementary
number theory
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, "Mathe ...
*''Das Fermat-Problem in seiner bisherigen Entwicklung'', a work about
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...
References
External links
*
*
Author profilein the database
zbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructu ...
Further reading
*
1837 births
1920 deaths
Scientists from Berlin
19th-century German mathematicians
20th-century German mathematicians
Group theorists
Number theorists
University of Münster faculty
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