[121]. Mathematics is the universal art apodictic.—Smith, W. B.
Quoted by Keyser, C. J. in Lectures on Science, Philosophy and Art (New York, 1908), p. 13.
[122]. Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning.—Whitehead, A. N.
Universal Algebra (Cambridge, 1898), Preface, p. vi.
[123]. Mathematics in general is fundamentally the science of self-evident things.—Klein, Felix.
Anwendung der Differential- und Integralrechnung auf Geometrie (Leipzig, 1902), p. 26.
[124]. A mathematical science is any body of propositions which is capable of an abstract formulation and arrangement in such a way that every proposition of the set after a certain one is a formal logical consequence of some or all the preceding propositions. Mathematics consists of all such mathematical sciences.—Young, Charles Wesley.
Fundamental Concepts of Algebra and Geometry (New York, 1911), p. 222.
[125]. Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.—Fitch, G. D.
The Fourth Dimension simply Explained (New York, 1910), p. 58.