Emmy Noether herself was... warm like a loaf of bread. There irradiate — Emmy Noether

"Wissenschaftliche Anregung verdanke ich wesentlich dem persönlichen mathematischen Verkehr in Erlangen und in Göttingen. Vor allem bin ich Herrn E. Fischer zu Dank verpflichtet, der mir den entscheidenden Anstoẞ zu der Beschäftigung mit abstrakter Algebra in arithmetischer Auffassung gab, was für all meine späteren Arbeiten bestimmend blieb. I obtained scientific guidance and stimulation mainly through personal mathematical contacts in Erlangen and in Göttingen. Above all I am indebted to Mr. E. Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work."

"A ring of polynomials in any number of variables over a ring of coeffcients that has an identity element and a finite basis, itself has a finite basis."

"The work of Galois and his successors showed that the nature, or explicit definition, of the roots of an is reflected in the structure of the group of the equation for the field of its coefficients. This group can be determined non-tentatively in a finite number of steps, although, as Galois himself emphasized, his theory is not intended to be a practical method for solving equations. But, as stated by Hilbert, the and the theory of s have their common root in that of algebraic fields. The last was initiated by Galois, developed by Dedekind and Kronecker in the mid-nineteenth century, refined and extended in the late nineteenth century by Hilbert and others, and finally, in the twentieth century, given new direction by the work of Steinitz in 1910, and in that of E. Noether and her school since 1920."

"[Noether] taught us to think in terms of simple and general algebraic concepts—homomorphic mappings, groups and rings with operators, ideals—and not in cumbersome algebraic computations; and she thereby opened up the path to finding algebraic principles in places where such principles had been obscured by some complicated special situation."

"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, Kroneckers 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."

"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 unfair; one should instead show that they are really equal by disclosing the inner ground for their equality."