# Max Noether

Max Noether

Max Noether (born September 24, 1844 in Mannheim , † December 13, 1921 in Erlangen ) was a German mathematician .

## Life

Max Noether was unable to walk due to polio at the age of 14. For a few years he only received private lessons and devoted himself to extensive reading. Before he began studying mathematics in Heidelberg in 1865 , he spent a year at the Mannheim observatory. During his studies with Gustav Kirchhoff , he mainly dealt with theoretical physics and, in his own words, came from there to the works of Bernhard Riemann and to algebraic geometry . He obtained his doctorate in 1868 - as was customary at the time in Heidelberg - without submitting a written thesis (he had offered an astronomical thesis) and then went to Gießen to study with Alfred Clebsch , who with his school Riemann's theory of functions and Abelian theorem on the theory of algebraic curves applied. Here he also met his long-term co-author Alexander von Brill . In 1869 he followed Clebsch to Göttingen. In 1870 he completed his habilitation in Heidelberg and taught here as a private lecturer until 1874. In 1875 he received an extraordinary professorship in Erlangen, where he stayed until the end of his life. In 1880 he married Ida Amalia Kaufmann. The daughter Emmy (Amalie) was born in 1882, Alfred in 1883, Fritz in 1884 and Gustav Robert in 1889. From 1888 to 1919 he was a full professor in Erlangen.

In 1899 he was President of the German Mathematicians Association .

From 1887 he was a corresponding member of the Bavarian Academy of Sciences and also a member of the academies in Berlin (1896), Budapest, Copenhagen and Turin, the Académie des sciences and the Accademia Nazionale dei Lincei (Rome), the Society of Sciences in Göttingen (1892 ) and the London Mathematical Society (honorary member from 1913). He was honorary editor of the Rendiconti del Circolo Matematico di Palermo and co-editor of the Mathematische Annalen . Noether had the title of Privy Councilor.

## family

Max Noether was the son of Herz Elias (Hermann) Noether (1807–1894), co-owner of the iron wholesaler “Joseph Nöther & Co.” in Mannheim, and his wife Amalie (Malchen) Würzburger (1812–1872). In 1880 he married Ida Amalia Kaufmann, the daughter of the Jewish businessman and landowner Marcus Kaufmann from Cologne and his wife, the banker's daughter Friederike Scheuer from Düsseldorf. From this marriage came the mathematician Emmy Noether (1882-1935), who emigrated to the USA before the National Socialists in 1933, and the mathematician Fritz Noether (1884-1941), who was murdered by Stalin's secret service in exile in Soviet times. A sister of his wife had married the entrepreneur Wilhelm Lepenau in 1865 .

## Services

Max Noether worked on questions of algebraic geometry and algebraic functions . In 1873 (Mathematische Annalen Vol. 6) he proved the fundamental theorem of the theory of algebraic functions , which is named after him. It provides conditions for that of two plane algebraic curves and a curve with n points of intersection exists, with polynomials A, B, which passes through the n points of intersection. ${\ displaystyle \ phi = 0}$${\ displaystyle \ psi = 0}$${\ displaystyle f = \ psi A + \ phi B}$

With Brill he was the founder of a purely algebraic direction of the theory of algebraic curves ( On the algebraic functions and their application in geometry , Mathematische Annalen Vol. 7, 1874). You prove z. B. The Riemann-Roch theorem is purely algebraic. Noether further investigated the classification of algebraic space curves, partly in competition with the French Georges Halphen . For this, both received the Steiner Prize of the Berlin Academy in 1882.

Noether was also interested in history and in 1894 wrote a large review article with Brill on the history of the theory of algebraic functions. He also wrote numerous obituaries for the Mathematical Annals (such as by Charles Hermite , Arthur Cayley , James Joseph Sylvester , Luigi Cremona , Sophus Lie , Karl von Staudt ).

## Fonts

• On the foundation of the theory of algebraic space curves, treatises of the Royal Academy of Sciences, Berlin 1883
• In memory of Karl Georg Christian von Staudt , Erlangen 1901
• About the singular elements of the algebraic curves, Erlangen 1902
• A. Brill, M. Noether: The development of the theory of algebraic functions in older and more recent times , Annual Report DMV, Volume 3, 1892/83, pp. 107-566.
• On the theory of the unambiguous correspondence of algebraic structures of any number of dimensions, Mathematische Annalen, Volume 2 (1870) p. 293
• About surfaces which have arrays of rational curves, Leipzig 1870. 67 p. (Habil. -schrift.) Digitized Univ. Heidelberg. Also in: Mathematische Annalen, Volume 3 (1871) pp. 161–227
• About the unambiguous spatial transformations, especially in their application to the mapping of algebraic surfaces, Mathematische Annalen, Volume 3 (1871) p. 547
• On the theory of unambiguous plane transformations , Mathematische Annalen, Volume 5 (1872) p. 635
• About a sentence from the theory of algebraic functions, Mathematische Annalen, Volume 6 (1873) p. 351, online here: [1]
• On the theory of the theta functions of four arguments, Mathematische Annalen, Volume 14 (1879) p. 248
• On the equations of the eighth degree and their occurrence in the theory of the fourth order curves, Mathematische Annalen, Volume 15 (1879) p. 89
• About the intersection point systems of an algebraic curve with non-adjoint curves, Mathematische Annalen, Volume 15 (1879) p. 507
• On the foundation of the theory of algebraic space curves, Treatises of the Royal Prussian Academy of Sciences in Berlin, 1882

In 1892 he published the supplements to Bernhard Riemann's collected works . In 1911 he and Eugen Löffler published an outline of a theory of algebraic functions by Hermann von Stahl .