20 GREEK SCIENCE AND 



y of Greek Science the difficulty is far greater, for here 

 v we have only the conclusions with hardly any or with 

 none of the processes. 



In almost all I have said as to the contrast between 

 Greek and Modern Science, Mathematics have been 

 excluded, and for this there is a special reason. The 

 defective Greek scientific method of recording only 

 results is practicably inapplicable to Mathematics. 

 Mathematical results without mathematical processes 

 would be a meaningless inanity. Ancient Mathematics, 

 like everything else that has come down to us from 

 antiquity, have of course suffered from the accidents of 

 time, but the obscuring power of time is a mere light 

 veil compared to that heavy impenetrable curtain that 

 the Greeks have themselves drawn over their biological 

 works. 



Thus it comes about that we can form a clear and 

 consecutive picture of the nature and progress of Greek 

 Mathematics. But a corollary to the completeness of 

 this mathematical record is a peculiar phenomenon in 

 the History of Mathematics shared by no other Science. 



/ft is that for Mathematics there are no Middle Ages. 



This does not mean that there was no period when 

 the mathematical knowledge of Europe was backward 

 xfr arrested or that progress was not at times slow. It 

 is of course true that those disturbances, political and 

 economic, religious and philosophical, that followed the 

 break \up of the Roman Empire and destroyed the 

 intellectual life of antiquity, destroyed equally mathema- 

 tical progress and mathematical thought. But the 

 reason wliy we can say that there were no Middle_Ages 

 for Mathematics is this, that when and where civiliza- 

 tion became settled and when and where the Greek 

 record became accessible, then and there it was possible 



