PROBLEMS OF MODERN SCIENCE 



it is not, but that it fails at a point which the 

 arithmeticians could not hope to reach in less than 

 a lifetime. This illustrates the fact that the success 

 of any finite number of tests of a mathematical 

 theorem, with actual numbers in place of symbols, 

 can never demonstrate the truth of the theorem, 

 which may always fail at a point beyond which, 

 for sheer lack of time, the purely arithmetical 

 verification cannot proceed. This is very signifi- 

 cant for all problems in the theory of numbers, 

 and especially of prime numbers and, as a con- 

 sequence, for any theorem suggested in a more 

 restricted branch, such as the Theory of Parti- 

 tions. 



But perhaps I have already said enough regard- 

 ing Pure Mathematics. It is difficult not to say 

 more, but perhaps it may be disguised as Applied 

 Mathematics, for the rest of what I would like to 

 say here belongs now equally to either. Let us turn 

 to the Einstein Theory quite definitely. It is at 

 least the most sensational thing, in the popular 

 sense, which has happened recently in relation to 

 Mathematics. Here, as with the Quantum Theory 

 later, I must not forget that Professor Richardson 

 is to give a lecture also, and I must confine myself 

 very strictly to the mathematical aspect of the 

 subject. It is often said, and very truly, that a 

 comprehension of Einstein's Theory is not in fact 

 possible without some mathematical equipment. 



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