160 THE POPULAR SCIENCE MONTHLY 



Even such an enlightened and careful historian as Josephus relates that 

 Abraham taught mathematics to the Jews, and instances might be mul- 

 tiplied to show that this idea is prevalent throughout history. 



The intimate connection of mathematics with early culture is fur- 

 ther apparent in its relation to religion and philosophy. In Egypt 

 mathematics was the peculiar possession of the priesthood, and was 

 guarded by them with the utmost jealousy. When it passed to the 

 Greeks it was made by them a prerequisite for philosophical study, their 

 great philosophers being primarily mathematicians. At the beginning 

 of the christian era mathematics again passed into the keeping of the 

 priesthood, its preservation during the dark ages being due to the care 

 with which it was preserved in catholic monasteries. Even the 

 pope openly gave it the sanction of the church, threatening Galileo with 

 the Inquisition for his heretical astronomical doctrines, and refuting 

 them by issuing a manifesto to the effect that the sun moves around the 

 earth in accordance with the time-honored Ptolemaic system. During 

 the period of the reformation, mathematics was regarded as one of the 

 most powerful weapons of Protestantism, many noted mathematicians 

 of the time devoting all their efforts to proving that Pope Leo X. was 

 the antichrist mentioned in Eevelation 13 : 18. 



The history of mathematics begins in the valley plains of Egypt. 

 On this border line between the tropical and temperate zones, climate 

 and soil were so adapted to the needs of primitive man as to force intel- 

 lect to its earliest manifestation. As Aristotle expressed it, " When 

 pressing needs are satisfied, man turns to the general and more ele- 

 vated," and consequently, as Hegel points out, the temperate zone is 

 the true theater of history, since where heat or cold are intense, external 

 pressure is never relieved. As the rigors of climate lessened and man 

 attained a greater mastery over nature, these two factors conspired to 

 force culture out of its primitive seat in the river valleys of the Nile, 

 Tigris and Euphrates towards the northwest, its northerly progress 

 being determined by climatic changes, and its westerly course by topo- 

 graphic features. If the course of mathematical development is traced 

 out on a physiographic and isothermal map, it will be clearly apparent 

 not only that it has followed the lines of least resistance topographically, 

 but that it has crossed successive isotherms in its northerly progress 

 with great regularity, due, as has been suggested, to the increasing need 

 of the nervous system, as it becomes more complex, for a more bracing 

 climate. 



The three chief geographic features which exhibit fundamental dif- 

 ferences are valley, mountain and sea. In the valley plains of China, 

 India, Babylonia and Egypt, the fertility of the soil assured a plentiful 

 subsistence, while the regularity of the seasons, combined with landed 

 values resulting from agriculture, gave rise to a fixed social relationship. 

 In more elevated regions, such as the plateaus of Africa and South 



