Machine learning is defined as the algorithmic structure of the wider area of Artificial Intelligence. The fact that machine learning is actually an extremization of black box theory is highlighted and the consequent attitude towards an over-parametrization of models is presented with the tools necessary to solve the corresponding optimization problem. Deep machine learning, with its relation to neural networks and logistic regression is then examined. The main theorem of approximation of continuous or integrable functions by a finite chain of functions is established, some examples illustrate possible applications of the above concept to Earth Sciences.