George Ballard Mathews

British mathematician

George Ballard Mathews, FRS (February 23, 1861March 19, 1922) was an English mathematician.


  • 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 appeal.
    • G.B. Mathews quoted in: F. Spencer. Chapters on Aims and Practice of Teaching, (London, 1899), p. 184. Reported in Moritz (1914).

Theory of Numbers, 1892


George Ballard Mathews, Theory of Numbers, (Cambridge, 1892); Reported in: Memorabilia mathematica or, The philomath's quotation-book, by Robert Edouard Moritz. Published 1914

  • 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.
    • Part 1, sect. 1.
  • 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.
    • Part 1, sect. 29.
  • 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.
    • Part 1, sect. 48.
  • 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 are defined.
    • Part 1, sect. 104.
  • 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.
    • Part 1, sect. 167.

Quotes about George Ballard Mathews

  • Mathews had a knowledge of Latin and Greek as minute and accurate as that generally possessed by professional classical scholars. He wrote pure and elegant Latin.
    • Prof. Gray in: Proceedings / London Mathematical Society. (1923), p. xlix
  • Mathews was an accomplished classical scholar; and besides Latin and Greek he was proficient in Hebrew, Sanskrit and Arabic. He also possessed great musical knowledge and skill. His versatility led a colleague at Bangor to assert that Mathews could equally well fill four or more chairs at the college.
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