<p>Generalizing is necessary or even unavoidable</p>

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a pattern. Algebra or modern axiomatic come to mind, as examples. However, strictly formalistic mathematics did not pay sufficient attention to the fact that modern axiomatic theories require a complementary element, in terms of intended applications or models, not to end up in a merely formal game.