Algebraic Geometry between Noether and Noether — a forgotten chapter in the history of Algebraic Geometry

Jeremy Gray

Revue d'histoire des mathématiques (1997)

  • Volume: 3, Issue: 1, page 1-48
  • ISSN: 1262-022X

Abstract

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Mathematicians and historians generally regard the modern period in algebraic geometry as starting with the work of Kronecker and Hilbert. But the relevant papers by Hilbert are often regarded as reformulating invariant theory, a much more algebraic topic, while Kronecker has been presented as the doctrinaire exponent of finite, arithmetical mathematics. Attention is then focused on the Italian tradition, leaving the path to Emmy Noether obscure and forgotten.There was, however, a steady flow of papers responding to the work of both Hilbert and Kronecker. The Hungarian mathematicians Gyula (Julius) König and József Kürschák, the French mathematicians Jules Molk and Jacques Hadamard, Emanuel Lasker and the English school teacher F.S.Macaulay all wrote extensively on the subject. This work is closely connected to a growing sophistication in the definitions of rings, fields and related concepts. The shifting emphases of their work shed light on how algebraic geometry owes much to both its distinguished founders, and how the balance was struck between algebra and geometry in the period immediately before Emmy Noether began her work.

How to cite

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Gray, Jeremy. "Algebraic Geometry between Noether and Noether — a forgotten chapter in the history of Algebraic Geometry." Revue d'histoire des mathématiques 3.1 (1997): 1-48. <http://eudml.org/doc/252109>.

@article{Gray1997,
abstract = {Mathematicians and historians generally regard the modern period in algebraic geometry as starting with the work of Kronecker and Hilbert. But the relevant papers by Hilbert are often regarded as reformulating invariant theory, a much more algebraic topic, while Kronecker has been presented as the doctrinaire exponent of finite, arithmetical mathematics. Attention is then focused on the Italian tradition, leaving the path to Emmy Noether obscure and forgotten.There was, however, a steady flow of papers responding to the work of both Hilbert and Kronecker. The Hungarian mathematicians Gyula (Julius) König and József Kürschák, the French mathematicians Jules Molk and Jacques Hadamard, Emanuel Lasker and the English school teacher F.S.Macaulay all wrote extensively on the subject. This work is closely connected to a growing sophistication in the definitions of rings, fields and related concepts. The shifting emphases of their work shed light on how algebraic geometry owes much to both its distinguished founders, and how the balance was struck between algebra and geometry in the period immediately before Emmy Noether began her work.},
author = {Gray, Jeremy},
journal = {Revue d'histoire des mathématiques},
keywords = {algebraic geometry; Max Noether; Emmy Noether},
language = {eng},
number = {1},
pages = {1-48},
publisher = {Société mathématique de France},
title = {Algebraic Geometry between Noether and Noether — a forgotten chapter in the history of Algebraic Geometry},
url = {http://eudml.org/doc/252109},
volume = {3},
year = {1997},
}

TY - JOUR
AU - Gray, Jeremy
TI - Algebraic Geometry between Noether and Noether — a forgotten chapter in the history of Algebraic Geometry
JO - Revue d'histoire des mathématiques
PY - 1997
PB - Société mathématique de France
VL - 3
IS - 1
SP - 1
EP - 48
AB - Mathematicians and historians generally regard the modern period in algebraic geometry as starting with the work of Kronecker and Hilbert. But the relevant papers by Hilbert are often regarded as reformulating invariant theory, a much more algebraic topic, while Kronecker has been presented as the doctrinaire exponent of finite, arithmetical mathematics. Attention is then focused on the Italian tradition, leaving the path to Emmy Noether obscure and forgotten.There was, however, a steady flow of papers responding to the work of both Hilbert and Kronecker. The Hungarian mathematicians Gyula (Julius) König and József Kürschák, the French mathematicians Jules Molk and Jacques Hadamard, Emanuel Lasker and the English school teacher F.S.Macaulay all wrote extensively on the subject. This work is closely connected to a growing sophistication in the definitions of rings, fields and related concepts. The shifting emphases of their work shed light on how algebraic geometry owes much to both its distinguished founders, and how the balance was struck between algebra and geometry in the period immediately before Emmy Noether began her work.
LA - eng
KW - algebraic geometry; Max Noether; Emmy Noether
UR - http://eudml.org/doc/252109
ER -

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