Ludwig Otto Hesse (22 April 1811 – 4 August 1874) 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 ...

. Hesse was born in Königsberg,

Prussia Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an ...

, and died in

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and Ha ...

Bavaria Bavaria ( ; ), officially the Free State of Bavaria (german: Freistaat Bayern, link=no ), is a state in the south-east of Germany. With an area of , Bavaria is the largest German state by land area, comprising roughly a fifth of the total lan ...

. He worked mainly on

algebraic invariant Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descrip ...

s, and

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 ...

. The

Hessian matrix In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed ...

, the

Hesse normal form The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in \mathbb^2 or a plane in Euclidean space \mathbb^3 or a hyperplane in higher dimensions.John Vince: ''Geometry for Computer Graphics''. ...

, the

Hesse configuration In geometry, the Hesse configuration, introduced by Colin Maclaurin and studied by , is a configuration of 9 points and 12 lines with three points per line and four lines through each point. It can be realized in the complex projective plane as t ...

, the Hessian group, Hessian pairs,

Hesse's theorem In geometry, Hesse's theorem, named for Otto Hesse, states that if two pairs of opposite vertices of a quadrilateral are conjugate with respect to some conic, then so is the third pair. A quadrilateral with this property is called a Hesse quadrilat ...

Hesse pencil In mathematics, the syzygetic pencil or Hesse pencil, named for Otto Hesse, is a pencil (one-dimensional family) of cubic plane elliptic curves in the complex projective plane, defined by the equation :\lambda(x^3+y^3+z^3) + \mu xyz =0. Each curve ...

, and the

Hesse transfer principle In geometry, Hesse's principle of transfer (german: Übertragungsprinzip) states that if the points of the projective line P1 are depicted by a rational normal curve in P''n'', then the group of the projective transformations of P''n'' that preserv ...

are named after him. Many of Hesse's research findings were presented for the first time in '' Crelle's Journal'' or Hesse's textbooks. MacTutor History of Mathematics archive and

Complete Dictionary of Scientific Biography The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It consi ...

Life

Hesse was born in Königsberg (today Kaliningrad) as the son of Johann Gottlieb Hesse, a businessman and brewery owner and his wife Anna Karoline Reiter (1788–1865). He studied in his hometown at the

Albertina The Albertina is a museum in the Innere Stadt (First District) of Vienna, Austria. It houses one of the largest and most important print rooms in the world with approximately 65,000 drawings and approximately 1 million old master prints, as well ...

under

Carl Gustav Jacob Jacobi Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasiona ...

. Among his teachers were count

Friedrich Wilhelm Bessel Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...

and Friedrich Julius Richelot. He earned his doctorate in 1840 at the

University of Königsberg The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Pruss ...

with the dissertation ''De octo punctis intersectionis trium superficium secundi ordinis''. In 1841, Hesse completed his habilitation thesis. In the same year he married Sophie Marie Emilie Dulk, the daughter of pharmacists and chemistry professor Friedrich Philipp Dulk (1788–1852). The couple had a son and five daughters. Hesse taught for some time physics and chemistry at the Vocational School in Königsberg and lectured at the Albertina. In 1845 he was appointed associate professor in Königsberg. In 1855 he moved to Halle and in 1856 to Heidelberg until 1868, when he finally moved to

to the newly established

Polytechnic School Polytechnic School, often referred to simply as Poly, is a college preparatory private day school located in Pasadena, California with approximately 850 students enrolled in grades Kindergarten through 12. The school is a former member of the ...

. In 1869 he joined the

Bavarian Academy of Sciences The Bavarian Academy of Sciences and Humanities (german: Bayerische Akademie der Wissenschaften) is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledg ...

. His doctoral students include Olaus Henrici,

Gustav Kirchhoff Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He ...

Jacob Lüroth Jacob Lüroth (18 February 1844, Mannheim, Germany – 14 September 1910, Munich, Germany) was a German mathematician who proved Lüroth's theorem and introduced Lüroth quartics. His name is sometimes written Lueroth, following the common pr ...

, Adolph Mayer, Carl Neumann,

Max Noether Max Noether (24 September 1844 – 13 December 1921) was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the f ...

, Ernst Schröder, and Heinrich Martin Weber.

Works

* ''Vorlesungen über analytische Geometrie des Raumes.'' (Lectures on analytic geometry of space) Leipzig (3. A. 1876)
Internet Archive
* ''Vorlesungen aus der analytischen Geometrie der geraden Linie, des Punktes und des Kreises.'' (Lectures from the analytical geometry of the straight line, the point and the circle) Leipzig (1881). Hrsg. A. Gundelfinger
Internet Archive
* ''Die Determinanten elementar behandelt.'' (Determinants elementary treated) Leipzig (2. A. 1872)
Göttinger Digitalisierungszentrum
* ''Die vier Species.'' (The four Species) Leipzig (1872)
Internet Archive
His collected works were published in 1897 by Bavarian Academy of Sciences and Humanities. *
Internet Archive

References

External links

* *
Vorlesungen über analytische Geometrie des Raumes, insbesondere über Oberflächen zweiter Ordnung
*

:
Hesse, Ludwig Otto
1811 births 1874 deaths 19th-century German mathematicians Algebraists Geometers Scientists from Königsberg University of Königsberg alumni University of Königsberg faculty Martin Luther University of Halle-Wittenberg faculty Heidelberg University faculty Technical University of Munich faculty German textbook writers Members of the Göttingen Academy of Sciences and Humanities {{Germany-mathematician-stub