=117.= Everything that the greatest minds of all times have accomplished toward the _comprehension of forms_ by means of concepts is gathered into one great science, _mathematics_. --HERBART, J. F. _Pestalozzi’s Idee eines A B C der Anschauung, Werke [Kehrbach], (Langensalza, 1890), Bd. 1, p. 163._ =118.= Perhaps the least inadequate description of the general scope of modern Pure Mathematics--I will not call it a definition--would be to say that it deals with _form_, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.--HOBSON, E. W. _Presidential Address British Association for the Advancement of Science (1910); Nature, Vol. 84, p. 287._ =119.= The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every province of thought, or of external experience, in which the succession of thoughts, or of events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy, or inductive reasoning, or imaginative literature, shall be mathematics developed by means of a calculus. --WHITEHEAD, A. N. _Universal Algebra (Cambridge, 1898), Preface._ =120.= Mathematics is the science which draws necessary conclusions.--PEIRCE, BENJAMIN. _Linear Associative Algebra, American Journal of Mathematics, Vol. 4 (1881), p. 97._ =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._