274 A SHORT HISTORY OF SCIENCE 



The invention of the differential calculus marks a crisis in the 

 history of mathematics. The progress of science is divided between 

 periods characterized by a slow accumulation of ideas and periods, 

 when, owing to the new material for thought thus patiently collected, 

 some genius by the invention of a new method or a new point of 

 view, suddenly transforms the whole subject on to a high level. 



Whitehead. 



MATHEMATICAL PHILOSOPHY. ANALYTIC GEOMETRY. DES- 

 CARTES. The invention of analytic geometry by Descartes in 1637 

 and the almost contemporary introduction of integral calculus as 

 the method of " indivisibles" may be regarded as the real beginning 

 of modern mathematical science. Thanks to these fruitful ideas 

 the science has during the three centuries that have since elapsed 

 made extraordinary progress both in its own internal development 

 and in its application throughout the range of the physical sciences. 



Descartes was born in Touraine in 1596, and after the education 

 appropriate for a youth of family and some years of fashionable 

 life in Paris, entered the army, then in Holland. His military 

 career continued till 1621 with incidental opportunity for his 

 favorite speculations in mathematics and philosophy. Some of 

 his most fruitful ideas dated from dreams and his best thinking 

 was habitually done before rising. 



It is impossible not to feel stirred at the thought of the emotions 

 of men at certain historic moments of adventure and discovery 

 Columbus when he first saw the Western shore, Franklin when the 

 electric spark came from the string of his kite, Galileo when he first 

 turned his telescope to the heavens. Such moments are also granted 

 to students in the abstract regions of thought, and high among them 

 must be placed the morning when Descartes lay in bed and invented 

 the method of coordinate geometry. Whitehead. 



In order to devote himself more completely to his favorite 

 studies he settled in Holland in 1629, devoting the next four years 

 to writing a treatise, entitled Le Monde, upon the universe. In 1637 

 he published his great Discourse on the Method of Good Reasoning 

 and of Seeking Truth in Science. 1 This begins : 



1 Discours de la Methode pour bien conduire sa raison et chercher la verite dans 

 les sciences. 



