George Ballard Mathews

A great deal of misunderstanding is avoided if it be remembered that the terms infinity, infinite, zero, infinitesimal must be interpreted in connexion with their context, and admit a variety of meanings according to the way in which they …

It may fairly be said that the germs of the modern algebra of linear substitutions and concomitants are to be found in the fifth section of the Disquisitiones Arithmeticae; and inversely, every advance in the algebraic theory of forms is …

The invention of the symbol ≡ by Gauss affords a striking example of the advantage which may be derived from an appropriate notation, and marks an epoch in the development of the science of arithmetic.

Strictly speaking, the theory of numbers has nothing to do with negative, or fractional, or irrational quantities, as such. No theorem which cannot be expressed without reference to these notions is purely arithmetical: and no proof of an …

That a formal science like algebra, the creation of our abstract thought, should thus, in a sense, dictate the laws of its own being, is very remarkable. It has required the experience of centuries for us to realize the full force of this …