=1113.= However far the calculating reason of the mathematician may seem separated from the bold flight of the artist’s phantasy, it must be remembered that these expressions are but momentary images snatched arbitrarily from among the activities of both. In the projection of new theories the mathematician needs as bold and creative a phantasy as the productive artist, and in the execution of the details of a composition the artist too must calculate dispassionately the means which are necessary for the successful consummation of the parts. Common to both is the creation, the generation, of forms out of mind.--LAMPE, E. _Die Entwickelung der Mathematik, etc. (Berlin, 1893), p. 4._ =1114.= As pure truth is the polar star of our science [mathematics], so it is the great advantage of our science over others that it awakens more easily the love of truth in our pupils.... If Hegel justly said, “Whoever does not know the works of the ancients, has lived without knowing _beauty_,” Schellbach responds with equal right, “Who does not know mathematics, and the results of recent scientific investigation, dies without knowing _truth_.”--SIMON, MAX. _Quoted in J. W. A. Young: Teaching of Mathematics (New York, 1907), p. 44._ =1115.= Büchsel in his reminiscences from the life of a country parson relates that he sought his recreation in Lacroix’s Differential Calculus and thus found intellectual refreshment for his calling. Instances like this make manifest the great advantage which occupation with mathematics affords to one who lives remote from the city and is compelled to forego the pleasures of art. The entrancing charm of mathematics, which captivates every one who devotes himself to it, and which is comparable to the fine frenzy under whose ban the poet completes his work, has ever been incomprehensible to the spectator and has often caused the enthusiastic mathematician to be held in derision. A classic illustration is the example of Archimedes, ....--LAMPE, E. _Die Entwickelung der Mathematik, etc. (Berlin 1893), p. 22._