The Commens Dictionary
Quote from ‘Carnegie Institution Correspondence’
Imagine, for example, an endless succession of objects. [—] Yet this proof will rest on some proposition which is simply self evident. But as long as one only has the idea of simple endless series, one may think forever, and not discover the theorem, until something suggests that other idea to the mind. What I call the theorematic reasoning in mathematics consists in so introducing a foreign idea, using it, and finally deducing a conclusion from which it is eliminated.