Without mathematics no one can fathom the depths of philosophy. Without philosophy no one can fathom the depths of mathematics. Without the two no one can fathom the depths of anything.—Bordas-Demoulin.
We may look upon geometry as a practical logic, for the truths which it studies, being the most simple and most clearly understood of all truths, are on this account the most susceptible of ready application in reasoning.—D'Alembert.
The advance and the perfecting of mathematics are closely joined to the prosperity of the nation.—Napoleon.
Hold nothing as certain save what can be demonstrated.—Newton.
To measure is to know.—Kepler.
The method of making no mistake is sought by every one. The logicians profess to show the way, but the geometers alone ever reach it, and aside from their science there is no genuine demonstration.—Pascal.
The taste for exactness, the impossibility of contenting one's self with vague notions or of leaning upon mere hypotheses, the necessity for perceiving clearly the connection between certain propositions and the object in view,—these are the most precious fruits of the study of mathematics.—Lacroix.
Bibliography. Smith, The Teaching of Elementary Mathematics, p. 234, New York, 1900; Henrici, Presidential Address before the British Association, Nature, Vol. XXVIII, p. 497; Hill, Educational Value of Mathematics, Educational Review, Vol. IX, p. 349; Young, The Teaching of Mathematics, p. 9, New York, 1907. The closing quotations are from Rebière, Mathématiques et Mathématiciens, Paris, 1893.