Siegfried Aronhold

Background

Siegfried Heinrich Aronhold was born on July 16, 1819 in Angerburg, Germany (now Węgorzewo, Gmina Węgorzewo, Poland) to Moses Süssel Aronhold and Wilhelmine Aronhold.

Education

Aronhold attended the Angerburg elementary school and the Gymnasium in Rastenburg (now Ketrzyn, Poland). Following the death of his father, his mother moved to Königsberg, where the boy attended a Gymnasium. He graduated in 1841 and then studied mathematics and natural sciences at the University of Königsberg from 1841 to 1845. Among his teachers were Bessel, Jacobi, Richelot, Hesse, and Franz Neumann. When Jacobi went to Berlin, Aronhold followed him and continued his studies under Dirichlet, Steiner, Gustav Magnus, and Dove. He did not take the state examinations, but in 1851 the University of Königsberg awarded him the Doctor honoris causa for his treatise “Über ein neues algebraisches Prinzip” and other studies.

Career

From 1852 to 1854 Aronhold taught at the Artillery and Engineers’ School in Berlin and, from 1851, at the Royal Academy of Architecture in Berlin, where he was appointed professor in 1863. In 1860 he joined the Royal Academy for Arts and Crafts, where, when Weierstrass became ill in 1862, he took over the entire teaching schedule. In 1869 Aronhold became a corresponding member of the Academy of Sciences in Göttingen.

In this treatise entitled “Über eine fundamentale Begründung der Invariantentheorie”, which he published in 1863, Aronhold offers solid proof of his theory, which he had welded into an organic entity. His method refers to functions that remain unchanged under Unear substitutions. He stresses the importance of the logical development of a few basic principles so that the reader may find his way through other papers.

Aronhold establishes his theory in general and does not derive any specific equations. He derives the concept of invariants from the concept of equivalency for the general linear theory of invariants. Special difficulties arise, of course, if not only general but also special cases are to be considered. His efforts to obtain equations independent of substitution coefficients led to linear partial differential equations of the first order, which also have linear coefficients. These equations, which are characteristic for the theory of invariants, are known as Aronhold’s differential equations.

With these equations “Aronhold’s process” can be carried out. This process permits the derivation of additional concomitants from one given concomitant. Aronhold investigates the characteristics of these partial differential equations and expands the theory to include the transformation of a system of homogeneous functions, furnishes laws for simultaneous invariants, and investigates contravariants (relevant forms), covariants, functional invariants, and divariants (intermediate forms).

Aronhold stresses that he arrived at his principles as early as 1851, citing his doctoral dissertation and the treatise “Theorie der homogenen Funktionen dritten Grades (1858). Since the subsequent theory and terminology did not yet exist, he claimed priority.

Before Aronhold developed his theory, he had worked on plane curves. The problem of the nine points of inflection of the third-order plane curve, which had been discovered by Pliicker, was brought to completion by Hesse and Aronhold. Aronhold explicitly established the required fourth-degree equation and formulated a theorem on plane curves of the fourth order. Seven straight lines in a plane always determine one, and only one, algebraic curve of the fourth order, in that they are part of their double tangents and that among them there are no three lines whose six tangential points lie on a conic section.

He died on March 13, 1884 in Berlin, Germany.

Achievements

• Aronhold`s great achievement was particularly in the development of the theory of invariants, which was then the center of mathematical interest, and was the first German to do research in this area. The theory of invariants is not, however, connected with Aronhold alone—others who worked on it were Sylvester, Cayley, and Hesse— but he developed a special method that proved to be extremely successful. In 1863 he collected his ideas in a treatise entitled “Über eine fundamentale Begründung der Invariantentheorie.”
  
  Also, Aronhold was honoured with election to the Göttingen Academy of Sciences in 1869 and he was appointed as an editor of Annali di Matematica in 1867.

Views

Quotations: He wrote from Berlin to Hesse in Königsberg on 1 October 1849:

"Unfortunately my external circumstances are not such that I could achieve a solid position in life, and the daily effort to earn a living produces a depressing influence on my scientific endeavours, making it utterly impossible to meet those obligations to which I consider necessary for entering into a better situation."

Personality

Siegfried Aronhold was considered an enthusiastic and inspiring teacher, and was held in high esteem everywhere.

Connections

Siegfried Heinrich Aronhold was married to Emilie Margarete Aronhold with whom he had one son and two daughters.

Father:

Moses Süssel Aronhold

Mother:

Wilhelmine Aronhold

Brother:

Louis Moses Aronhold

Sister:

Henriette Wolff

Brother:

Seemann Moses Süssel Aronhold

Brother:

Adolf Aaron Aronhold

Sister:

Friederike Heymann

Wife:

Marie Julie Friederike Aronhold

Son:

Maximilian Ignatz Aronhold

Daughter:

Henriette Marie Aronhold

Daughter:

Emilie Margarete Aronhold

teacher:

Friedrich Bessel

Aronhold then entered the University of Königsberg to study mathematics and natural sciences, matriculating on 25 October 1841. There he was taught by Friedrich Wilhelm Bessel.

associate:

Carl Jacobi

Aronhold was most influenced by Carl Gustav Jacob Jacobi.

teacher:

Otto Hesse

teacher:

Franz Ernst Neumann

teacher:

Friedrich Julius Richelot

teacher:

Heinrich Magnus

Aronhold studied physics at the University of Berlin, taught by Heinrich Gustav Magnus.

teacher:

Heinrich Dove

He taught Aronhold at the University of Berlin.

References

• Dictionary of scientific biography
• Die Reine Mathematik in Den Jahren 1884-1899