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Paul Gustav Heinrich Bachmann (22 June 1837 – 31 March 1920) was a German
Die Elemente der Zahlentheorie
' (1892) **Vol. II:
Analytische Zahlentheorie
' (1894), a work on
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
Author profile
in the database
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 ...
.
Life
Bachmann studiedmathematics
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 ...
at the university of his native city of Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
and
received his doctorate in 1862 for his thesis on 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 ...
. He then went to Breslau to study for his habilitation, which he received in 1864 for his thesis on Complex Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and ...
s.
Bachmann was a professor at Breslau and later at 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 ...
.
Works
*''Zahlentheorie'', Bachmann's work onnumber 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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
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 Diric ...
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 Lan ...
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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
*''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 profile
in the database
zbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ...
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 {{germany-mathematician-stub