No one has yet translated from the Greek into Latin the thirteen books — Diophantus

"Many scholars go right through the period of their mathematical education without being introduced to indeterminate (Diophantine) problems. This should seem somewhat strange to us when we reflect on how many real problems of life require solutions which are meaningless unless they are whole numbers. The absence of Diophantine analysis from school curricula is difficult to justify. The methods... are not beyond the capabilities of schoolchildren. It is true that the problems often involve tedious calculations, but this should not be used as an excuse for ignoring the valuable principles of this analysis. Diophantus himself was usually content with finding just one solution... But once one solution has been obtained, the general solution can readily be obtained from it."

"If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both bides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side."

"As a square number is known to be the product of a number multiplied by itself, so every polygonal number, multiplied by one number and added to another, both of which depend upon the number of its angles, produces a square number. I shall prove this, and shall show also how from a given side to find its polygon and conversely. Some auxiliary propositions must first be proved."

"Greek algebra before Diophantus was essentially rhetorical."

"He appears to be the first who could perform such operations as (x - 1) \times (x - 2) without reference to geometry. Such identities as (a + b)^2 = a^2 + 2ab + b^2, which with Euclid appear in the elevated rank of geometric theorems, are with Diophantus the simplest consequences of the algebraic laws of operation."

"In this work [Arithmetica] is introduced the idea of an algebraic equation expressed in algebraic symbols. His treatment is purely analytical and completely divorced from geometrical methods."