"The third great epoch in the extension of arithmetic is that of the twentieth century after 1910. To anticipate, the introduction of general methods into , beginning in the first decade of the twentieth century, prepared that vast field of mathematics, first opened up by Hamilton and Grassman in the 1840s, for partial arithmetization in the second and third decades of the century. In 1910, E. Steinitz... proceeding from, and partly generalizing, Kronecker's theory (1881) of "algebraic magnitudes," made a fundamental contribution to the modern theory of (commutative) fields. His work was one of the strongest impulses to the abstract algebra of the 1920s and 1930s, with its accompanying generalized arithmetic. The outstanding figure in the later phase of this development is usually considered to be Emmy Noether... who, with her numerous pupils, laid down the broad foundations of the modern abstract theory of ideals, also a great deal more in the domain of modern algebra. The application of this work to the 'integers' of linear s affords the ultimate extension up to 1940 of common arithmetic."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
InventorsPhysicists from GermanyWomen academics from GermanyEducators from Germany19th-century German mathematicians
Original Language: English
Available Languages (1)
Sources
Eric Temple Bell, The Development of Mathematics (1940)
https://en.wikiquote.org/wiki/Emmy_Noether
Revision History
No revisions have been submitted for this quote.
Categories
Emmy Noether
Amalie Emmy Noether (March 23, 1882 – April 14, 1935) was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics.
40 quotes on TrueQuotesView all quotes by Emmy Noether →
Related Quotes
"My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously."
"Ich habe das symbolische Rechnen mit Stumpf und Stil verlernt. I have completely forgotten the symbolic calculus."
"If one proves the equality of two numbers a and b by showing first that a \leqq b and then that a \geqq b, it is unfa…"
"A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite…"
"Es steht alles schon bei Dedekind. [It is already all in Dedekind.]"
"[Noether] taught us to think in terms of simple and general algebraic concepts—homomorphic mappings, groups and rings…"
"Emmy Noether introduced the notion of a representation space— a vector space upon which the elements of the algebra o…"
"The work of Galois and his successors showed that the nature, or explicit definition, of the roots of an is reflected…"
"The third and last exception to general sterility connects the arithmetic of forms with that other major outgrowth of…"
"Wissenschaftliche Anregung verdanke ich wesentlich dem persönlichen mathematischen Verkehr in Erlangen und in Götting…"