242 HAS SCIENCE DISCOVERED GOD? 



form a diagram illustrating the famous theorem of 

 Pythagoras, that the squares on the two smaller sides 

 of a right-angled triangle are together equal to the 

 square on the greatest side. 



To most of the inhabitants of Mars such signals 

 would convey no meaning; but it was argued that 

 mathematicians on Mars, if such existed, would 

 surely recognize them as the handiwork of mathe- 

 maticians on earth. In so doing they would not be 

 open to the reproach that they saw mathematics in 

 everything. And so it is mutatis mutandis with the 

 signals from the outer world of reality, which are the 

 shadows on the walls of the cave in which we are im- 

 prisoned. We have already considered with disfavor 

 the possibility of the universe having been planned by 

 a biologist or an engineer. From the intrinsic evi- 

 dence of his creation, the Great Architect of the Uni- 

 verse now begins to appear as a pure mathematician. 



In the second place, our statement may be chal- 

 lenged on the ground that there is no absolutely sharp 

 line of demarcation between pure and applied mathe- 

 matics. It would of course have proved nothing, if 

 nature had merely been found to act in accordance 

 with the concepts of applied mathematics; these con- 

 cepts were specially and deliberately designed by man 

 to fit the workings of nature. And it may be ob- 

 jected that even pure mathematics does not in actual 

 fact represent a creation of our own minds so much 

 as an effort, based on forgotten or subconscious 

 memories, to understand the workings of nature. If 

 so. It is not surprising that nature should be found to 

 work according to the laws of pure mathematics. It 

 cannot, of course, be denied that some of the concepts 



