"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 third great epoch in the extension of arithmetic is that of the twentieth century after 1910. To anticipate, the …"

"The work of Galois and his successors showed that the nature, or explicit definition, of the roots of an is reflected…"

"Wissenschaftliche Anregung verdanke ich wesentlich dem persönlichen mathematischen Verkehr in Erlangen und in Götting…"