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, mathematical structure, structure, space, Mathematica ...

. Hesse was born in

Königsberg Königsberg (; ; ; ; ; ; , ) is the historic Germany, German and Prussian name of the city now called Kaliningrad, Russia. The city was founded in 1255 on the site of the small Old Prussians, Old Prussian settlement ''Twangste'' by the Teuton ...

Prussia Prussia (; ; Old Prussian: ''Prūsija'') was a Germans, German state centred on the North European Plain that originated from the 1525 secularization of the Prussia (region), Prussian part of the State of the Teutonic Order. For centuries, ...

, and died in

Munich Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...

Bavaria Bavaria, officially the Free State of Bavaria, is a States of Germany, state in the southeast of Germany. With an area of , it is the list of German states by area, largest German state by land area, comprising approximately 1/5 of the total l ...

. 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 descri ...

s, and

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. The

Hessian matrix In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued Function (mathematics), function, or scalar field. It describes the local curvature of a functio ...

, the

Hesse normal form In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane \mathbb^2, a plane in Euclidean space \mathbb^3, or a hyperplane in higher dimensions.John Vince: ''Geometry for C ...

, the Hesse configuration, the

Hessian group In mathematics, the Hessian group is a finite group of order 216, introduced by who named it for Otto Hesse. It may be represented as the group of affine transformations with determinant 1 of the affine plane over the finite field of 3 elements.He ...

Hessian pair In mathematics, a Hessian pair or Hessian duad, named for Otto Hesse, is a pair of points of the projective line canonically associated with a set of 3 points of the projective line. More generally, one can define the Hessian pair of any triple of ...

s, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many of Hesse's research findings were presented for the first time in ''

Crelle's Journal ''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by A ...

'' 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 Kaliningrad,. known as Königsberg; ; . until 1946, is the largest city and administrative centre of Kaliningrad Oblast, an Enclave and exclave, exclave of Russia between Lithuania and Poland ( west of the bulk of Russia), located on the Prego ...

) 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 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. Biography Jacobi was ...

. 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 Friedrich Julius Richelot (6 November 1808 – 31 March 1875) was a German mathematician, born in Königsberg. He was a student of Carl Gustav Jacob Jacobi. He was promoted in 1831 at the Philosophical Faculty of the University of Königsberg wi ...

. He earned his doctorate in 1840 at the

University of Königsberg The University of Königsberg () was the university of Königsberg in Duchy of Prussia, which was a fief of Poland. It was founded in 1544 as the world's second Protestant Reformation, Protestant academy (after the University of Marburg) by Duke A ...

with the dissertation ''De octo punctis intersectionis trium superficium secundi ordinis''. In 1841, Hesse completed his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

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. In 1869 he joined the

Bavarian Academy of Sciences The Bavarian Academy of Sciences and Humanities () is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledge within their subject. The general goal of th ...

. His doctoral students include

Olaus Henrici Olaus Magnus Friedrich Erdmann Henrici, FRS (9 March 1840, Meldorf, Duchy of Holstein – 10 August 1918, Chandler's Ford, Hampshire, England) was a German mathematician who became a professor in London. After three years as an apprentice in e ...

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

Jacob Lüroth Jacob Lüroth (18 February 1844, Mannheim, German Confederation, Germany – 14 September 1910, Munich, German Empire, Germany) was a German mathematician who proved Lüroth's theorem and introduced Lüroth quartics. His name is sometimes writte ...

, Adolph Mayer,

Carl Neumann Carl Gottfried Neumann (also Karl; 7 May 1832 – 27 March 1925) was a German Mathematical physics, mathematical physicist and professor at several German universities. His work focused on applications of potential theory to physics and mathemati ...

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 ...

, Ernst Schröder, and

Heinrich Martin Weber Heinrich Martin Weber (5 March 1842, Heidelberg, German Confederation, 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, ...

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 The Bavarian Academy of Sciences and Humanities () is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledge within their subject. The general goal of th ...

. *
Internet Archive

References

External links

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

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