George Ballard Mathews: Arithmetic

George Ballard Mathews was British mathematician. Explore interesting quotes on arithmetic.
George Ballard Mathews: 12 quotes0 likes

“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 an acquisition to the arithmetical theory.”

George Ballard Mathews

Part 1, sect. 48.
Theory of Numbers, 1892

“As Gauss first pointed out, the problem of cyclotomy, or division of the circle into a number of equal parts, depends in a very remarkable way upon arithmetical considerations. We have here the earliest and simplest example of those relations of the theory of numbers to transcendental analysis, and even to pure geometry, which so often unexpectedly present themselves, and which, at first sight, are so mysterious.”

George Ballard Mathews

Part 1, sect. 167.
Theory of Numbers, 1892

“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.”

George Ballard Mathews

Part 1, sect. 29.
Theory of Numbers, 1892

“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 arithmetical theorem, can be considered finally satisfactory if it intrinsically depends upon extraneous analytical theories.”

George Ballard Mathews

Part 1, sect. 1.
Theory of Numbers, 1892