Albrecht Dold (5 August 1928 – 26 September 2011) 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 On ...

specializing in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

who proved the

Dold–Thom theorem In algebraic topology, the Dold-Thom theorem states that the homotopy groups of the infinite symmetric product of a connected CW complex are the same as its reduced homology groups. The most common version of its proof consists of showing that the ...

, the

Dold–Kan correspondence In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence (named after Albrecht Dold and Daniel Kan) states that there is an equivalence between the category of (nonnegatively graded) chain complexes and the ...

, and introduced

Dold manifold In mathematics, a Dold manifold is one of the manifolds P(m,n) = (S^m \times \mathbb^n)/\tau, where \tau is the involution that acts as −1 on the n-sphere, ''m''-sphere S^m and as complex conjugation on the complex projective space \mathbb^n. ...

s, Dold–Puppe stabilization, and

Dold fibration The surname Dold may refer to *Albrecht Dold (1928–2011), German mathematician *Bob Dold (born 1969), American politician *Brian Dold (1930–1976), South African cricketer *Chris Dold (born 1987), Canadian sailor *Douglas Dold (1895–1980), So ...

Life

Albrecht Dold was born in Triberg, and studied mathematics and physics at

Heidelberg University } Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...

, earning a

Ph.D. 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 ...

degree in 1954 under the direction of

Herbert Seifert Herbert Karl Johannes Seifert (; 27 May 1897, Bernstadt – 1 October 1996, Heidelberg) was a German mathematician known for his work in topology. Biography Seifert was born in Bernstadt auf dem Eigen, but soon moved to Bautzen, where he attend ...

. He visited the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

in Princeton in 1956–58, and taught at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

in 1960–62 and at the

University of Zürich The University of Zürich (UZH, german: Universität Zürich) is a public research university located in the city of Zürich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 f ...

in 1962–63. In 1963 he returned to Heidelberg, where he stayed most of his career, till his retirement in 1996. Dold's work in

, in particular, his work on

fixed-point theory Fixed point may refer to: * Fixed point (mathematics), a value that does not change under a given transformation * Fixed-point arithmetic, a manner of doing arithmetic on computers * Fixed point, a benchmark (surveying) used by geodesists * Fixed p ...

has made him known in economics as well as mathematics. His book "Lectures on Algebraic Topology" is a standard reference among economists as well as mathematicians. He had 19 doctoral students, including

Mónica Clapp Mónica Alicia Clapp Jiménez Labora is a mathematician at the Universidad Nacional Autónoma de México (UNAM) known for her work in nonlinear partial differential equations and algebraic topology. Life and work Clapp was born in Mexico City. S ...

Eberhard Freitag Eberhard Freitag (born 19 May 1942, in Mühlacker) is a German mathematician, specializing in complex analysis and especially modular forms. Education and career Freitag studied from 1961 mathematics, physics and astronomy at Heidelberg Univer ...

, Volker Puppe, and Carl-Friedrich Bödigheimer, as well as 58 descendants. Dold was married to Yvonne Dold-Samplonius, a distinguished historian of mathematics.

References

* * * {{DEFAULTSORT:Dold, Albrecht 1928 births 2011 deaths 20th-century German mathematicians 21st-century German mathematicians Topologists Heidelberg University alumni Heidelberg University faculty People from Schwarzwald-Baar-Kreis