Heinrich Brandt (8 November 1886, in Feudingen – 9 October 1954, in

Halle, Saxony-Anhalt Halle (Saale), or simply Halle (; from the 15th to the 17th century: ''Hall in Sachsen''; until the beginning of the 20th century: ''Halle an der Saale'' ; from 1965 to 1995: ''Halle/Saale'') is the largest city of the German state of Saxony-Anh ...

) 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 ...

who was the first to develop the concept of a

groupoid In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: *''Group'' with a partial functi ...

. Brandt studied at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

and, from 1910 to 1913, at the

University of Strasbourg The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the ea ...

. In 1912 he attained his doctorate; he was a student of

Heinrich Martin Weber Heinrich Martin Weber (5 March 1842, Heidelberg, Germany – 17 May 1913, Straßburg, Alsace-Lorraine, German Empire, now Strasbourg, France) was a German mathematician. Weber's main work was in algebra, number theory, and analysis. He is ...

. From 1913 he was assistant at the

University of Karlsruhe (TH) The Karlsruhe Institute of Technology (KIT; german: Karlsruher Institut für Technologie) is a public research university in Karlsruhe, Germany. The institute is a national research center of the Helmholtz Association. KIT was created in 2009 w ...

. He taught

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

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

from 1921 at

RWTH Aachen RWTH Aachen University (), also known as North Rhine-Westphalia Technical University of Aachen, Rhine-Westphalia Technical University of Aachen, Technical University of Aachen, University of Aachen, or ''Rheinisch-Westfälische Technische Hoch ...

. From 1930 he was the chair for mathematics at the

University of Halle Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university i ...

. A

Brandt matrix In mathematics, Brandt matrices are matrices, introduced by , that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra. calcu ...

is a computational way of describing the

Hecke operator In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by , is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic repr ...

action on

theta series In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theo ...

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

s. The theory was developed in part by Brandt's student

Martin Eichler Martin Maximilian Emil Eichler (29 March 1912 – 7 October 1992) was a German number theorist. Eichler received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936. Eichler and Goro Shimura developed a method to constr ...

. It offers an algorithmic approach for machine computation (in that theta series span spaces of modular forms); the theory is now considered by means of

Brandt module Brandt may refer to: Places United States * Brandt, Ohio, an unincorporated community * Brandt, South Dakota, a town * Brandt Township, Polk County, Minnesota Elsewhere * Mount Brandt, Queen Maud Land, Antarctica * Brandt Cove, South Georgia Is ...

External links

* H.-J. Hoehnke and M.-A. Knus (2004
A Tribute to (the work of) Heinrich Brandt on the 50 anniversary of his death
link from

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

Heinrich Brandt
from

Martin Luther University of Halle-Wittenberg Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university i ...

* 1886 births 1954 deaths 20th-century German mathematicians University of Göttingen alumni University of Strasbourg alumni Academic staff of the Karlsruhe Institute of Technology Academic staff of the Martin Luther University of Halle-Wittenberg {{Germany-mathematician-stub

See also

External links