November 12, 1915] 



SCIENCE 



675 



see them originate here, there and yonder 

 in the soil and haze of common thought; 

 we see how indistinct they are at first — • 

 how ill-defined; we observe how they im- 

 prove in that regard as the ideas involved 

 grow clearer and clearer, more and more 

 amenable to the use and governance of 

 logic. At length, when thought, in its 

 progress along any one of the many courses, 

 has reached a high degree of refinement, 

 precision and certitude, then and there- 

 after, but not before, we call it mathe- 

 matical thought; it has undergone a long 

 process of refining evolution and acquired 

 at length the name of mathematics; it is 

 not, however, the creature of its name; 

 what is called mathematics has been long 

 upon the way, owning at previous stages 

 other designations — common sense, prac- 

 tical art perhaps, speculation, theology it 

 may be, philosophy, natural science, or it 

 may be for many a millenium no name at 

 all. Is it, then, only a question of names? 

 In a sense, yes: the ideal of thought is 

 rigor; mathematics is the name that usage 

 employs to designate, not attainment of the 

 ideal, for it can not be attained, but its 

 devoted pursuit and close approximation. 

 But this is not the essence of the matter. 

 The essence is that all thought, thought in 

 all its stages, however rude, however re- 

 fined, however named, owns the unity of 

 being human : spiritual activities are one. 

 Mathematics thus belongs to the great fam- 

 ily of spiritual enterprises of man. These 

 enterprises, all the members of the great 

 family, however diverse in form, in modes 

 of life, in methods of toil, in their progress 

 along the way that leads towards logical 

 rectitude, are alike children of one great 

 passion. In genesis, in spirit and aspira- 

 tion, in motive and aim, natural science, 

 theology, philosophy, jurisprudence, re- 

 ligion and art are one with mathematics: 

 they are all of them sprung from the hu- 



man spirit's craving for invariant reality 

 in a world of tragic change; they all of 

 them aim at rescuing man from ' ' the blind 

 hurry of the universe from vanity to van- 

 ity": they seek cosmic stability — a world 

 of abiding worth, where the broken prom- 

 ises of hope shall be healed and infinite as- 

 piration shall cease to be mocked. 



Such has been the universal and domi- 

 nant aim and such are the cardinal forms 

 that time has given its prosecution. 



And now we must ask: What have been 

 the fruits of the endless toil? What has 

 the high emprize won? And what espe- 

 cially, have been the contributions of 

 mathematics to the total gain? To recount 

 the story of the spirit's quest for ageless 

 forms of reality would be to tell afresh, 

 from a new point of view, the history of 

 human thought, so many and so diverse 

 are the modes or aspects of being that men 

 have found or fancied to be eternal. Edi- 

 fying indeed would be the tale, but it is 

 long, and the hour contracts. Even a 

 meager delineation is hardly possible here. 

 Yet we must not fail to glance at the end- 

 less array and to call, at least in part, the 

 roll of major things. But where begin? 

 Shall it be in theology? How memory re- 

 sponds to the magic word. "The past rises 

 before us like a dream." As the long suc- 

 cession of the theological centuries passes 

 by, what a marvelous pageant do they pre- 

 sent of human ideals, eontrivings and 

 dreams, both rational and superrational. 

 Alpha and Omega, the beginning and end- 

 ing, which is, which was and which is to 

 come; I Am That I Am; Father of lights 

 with which is no variableness, neither 

 shadow of turning ; the bonitas, unitas, in- 

 finitas, immutabilitas of Deity; the undy- 

 ing principle of soul ; the sublime hierarchy 

 of immortal angels, terrific and precious, 

 discoursed of by sages, commemorated by 

 art, feared and loved by millions of men 



