Resumen
This article discusses how mathematics has explicated and evaluated computational possibilities by sketching exact boundaries for the world of computers. This article also explains how mathematics has extended these boundaries for computation immensely. What is impossible from the point of view of traditional mathematics and has been argued as absolutely unworkable becomes attainable in light of new mathematics. The other aspiration is to show how to utilize new possibilities. To achieve this, a new paradigm for computation is introduced. It gives better insight into the functioning of computers, networks and the mind; opening new perspectives for artificial intelligence. Mathematics is a powerful tool that helps people achieve new goals as well as understand what is impossible to do. Today, the theory of algorithms helps solve such vital practical problems as Web reliability, communication security, computer efficiency, and many others. The algorithm has become one of the central concepts of mathematics and a general scientific and technological notion. The theory of super-recursive computing has an important message for society as well as technology. It only looks smart to stop and to enjoy after one get something.