"... mathematics resembles an iceberg: beneath the surface is the realm of pure mathematics hidden from the public ...…"

"Proof is the idol before whom the pure mathematician tortures himself."

"There is no way to guarantee in advance what pure mathematics will later find application. We can only let the proces…"

"Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anythi…"

"Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containin…"

"This is as I have said in my Arithmetic:—The area of a circle is equal to the product of the circumference by one-fou…"

"Multiply the arc by the square of the arc, and take the result of repeating that [any number of times]. Divide [each …"

"The method represents a best approximation algorithm of minimal length that, owing to several minimization properties…"

"The process of reasoning called "Mathematical Induction" has had several independent origins. It has been traced back…"

"This method is supreme above all praise; it is certainly the finest thing accomplished in number theory before Lagrange."