ON PROOF 269 



Fortunately, the theory does not depend on mathe- 

 matics but on the laboratory for proof; it does not 

 need to wait for proof until the basic data required 

 by mathematics are determined, but it is directly 

 amenable to crucial laboratory test. It sometimes 

 happens that data that are lacking and that are 

 indispensable to mathematics, are not necessary to 

 proof by the laboratory. Thus, today the existence 

 of the cell is one of the best-known basic facts of 

 biology; but von Mohl's and Schleiden and 

 Schwann's "cell-theory" never was a problem of 

 mathematics but, of course, was established by direct 

 experimental research. 



The exact manner of the formation of a system and 

 the fact of the existence of that system are two different 

 things. It probably would not be questioned that, 

 though the exact paths and speeds of the orbital 

 electrons of the atoms cannot be pointed out, and 

 therefore certain quantitative values of even the first 

 positive and negative electrons that collide and unite 

 at critical positions and — pursuing a new and in- 

 dependent path — through further collisions and 

 unions form a new and different system (life), cannot 

 be pointed out, the theory is none the less valid. 



And after all, desirable as mathematical "proof" 

 is, it is the boast of science that most of our modern 

 knowledge rests upon direct evidence of the labora- 



