Max Noether (24 September 1844 – 13 December 1921) 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 worked on

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of

Emmy Noether Amalie Emmy NoetherEmmy is the '' Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noeth ...

Biography

Max Noether was born in

Mannheim Mannheim (; Palatine German: or ), officially the University City of Mannheim (german: Universitätsstadt Mannheim), is the second-largest city in the German state of Baden-Württemberg after the state capital of Stuttgart, and Germany's 2 ...

in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in

Bruchsal Bruchsal (; orig. Bruohselle, Bruaselle, historically known in English as Bruxhall; South Franconian: ''Brusel'') is a city at the western edge of the Kraichgau, approximately 20 km northeast of Karlsruhe in the state of Baden-Württemberg, ...

in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger. At 14, Max contracted

polio Poliomyelitis, commonly shortened to polio, is an infectious disease caused by the poliovirus. Approximately 70% of cases are asymptomatic; mild symptoms which can occur include sore throat and fever; in a proportion of cases more severe s ...

and was afflicted by its effects for the rest of his life. Through

self-study Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools). Generally, autodidacts are individu ...

, he learned advanced mathematics and entered the

University of Heidelberg } Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...

in 1865. He served on the faculty there for several years, then moved to the

University of Erlangen A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

in 1888. While there, he helped to found the field of

.Lederman, pp. 69–71. In 1880 he married Ida Amalia Kaufmann, the daughter of another wealthy Jewish merchant family. Two years later they had their first child, named Amalia ("Emmy") after her mother.

went on to become a central figure in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...

. In 1883 they had a son named Alfred, who later studied

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

before dying in 1918. Their third child,

Fritz Noether Fritz Alexander Ernst Noether (7 October 1884 – 10 September 1941) was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD. Biography Fritz Noether's father Max Noethe ...

, was born in 1884, and like Emmy, found prominence as a mathematician; he was executed in the Soviet Union in 1941. Little is known about their fourth child, Gustav Robert, born in 1889; he suffered from continual illness and died in 1928.Dick, pp. 9–45. Noether served as an ''Ordinarius'' (full professor) at Erlangen for many years, and died there on 13 December 1921.

Work on algebraic geometry

Brill Brill may refer to: Places * Brielle (sometimes "Den Briel"), a town in the western Netherlands * Brill, Buckinghamshire, a village in England * Brill, Cornwall, a small village to the west of Constantine, Cornwall, UK * Brill, Wisconsin, an un ...

and Max Noether developed alternative proofs using algebraic methods for much of

Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...

's work on

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

Brill–Noether theory In algebraic geometry, Brill–Noether theory, introduced by , is the study of special divisors, certain divisors on a curve that determine more compatible functions than would be predicted. In classical language, special divisors move on the cur ...

went further by estimating the dimension of the space of maps of given degree ''d'' from an

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...

to projective space P^''n''. In

birational geometry In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational ...

, Noether introduced the fundamental technique of

blowing up In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the ...

in order to prove resolution of singularities for plane curves. Noether made major contributions to the theory of algebraic surfaces. Noether's formula is the first case of the Riemann-Roch theorem for surfaces. The

Noether inequality In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4-manifold. It holds more generally for minimal projective surfac ...

is one of the main restrictions on the possible discrete invariants of a surface. The Noether-Lefschetz theorem (proved by

Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear o ...

) says that the

Picard group In mathematics, the Picard group of a ringed space ''X'', denoted by Pic(''X''), is the group of isomorphism classes of invertible sheaves (or line bundles) on ''X'', with the group operation being tensor product. This construction is a global ve ...

of a very general surface of degree at least 4 in P³ is generated by the restriction of the

line bundle In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at each point determines a varying line: the ''tangent bundle'' is a way of organisin ...

''O''(1). Noether and Castelnuovo showed that the

Cremona group In algebraic geometry, the Cremona group, introduced by , is the group of birational automorphisms of the n-dimensional projective space over a field It is denoted by Cr(\mathbb^n(k)) or Bir(\mathbb^n(k)) or Cr_n(k). The Cremona group is natura ...

of birational automorphisms of the complex projective plane is generated by the "quadratic transformation" : 'x'',''y'',''z''↦ /''x'', 1/''y'', 1/''z'' together with the group ''PGL''(3,C) of automorphisms of P². Even today, no explicit generators are known for the group of birational automorphisms of P³.

Notes

References

* Dick, Auguste. ''Emmy Noether: 1882–1935''. Boston: Birkhäuser, 1981. . * Lederman, Leon M. and Christopher T. Hill. ''Symmetry and the Beautiful Universe''. Amherst: Prometheus Books, 2004. . * Macaulay, Francis S. ''Max Noether''. In: Proceedings of the London Mathematical Society. - 2. ser., vol. 21. - London, 1923. - p. XXXVII-XLII.
online

External links

* * Gabriele Dörflinger

In
''Historia Mathematica Heidelbergensis''
{{DEFAULTSORT:Noether, Max 1844 births 1921 deaths 19th-century German mathematicians 20th-century German mathematicians Algebraic geometers 19th-century German Jews Scientists from Mannheim

Biography

Work on algebraic geometry

See also

Notes

References

External links