On the applied mathematics, artificial intelligence and computer calculations development

A transition from the industrial to the post-industrial phase of the development of civilization takes place currently. In the traditional phase of development (until the twentieth century), the researchers and thinkers focus was on the nature study. In the industrial times (XX century) - the machines world was comprehended and developed. The most important result of this period was the creation of computers. Now the world is entering to the post-industrial phase, where the focus is on the person. This is changing applied mathematics, computer reality. There is a bifurcation in which a significant part of applied mathematics is becoming an industry. A number of promising innovative projects draw attention in this context. There is a transition from 'continuous' to 'discrete' mathematics, largely associated with the development of cryptography. Another feature of the moment is the neural network revolution in machine learning, which gave a new powerful impetus to the artificial intelligence (AI) development progress. It led to the widespread use of devices and systems that solve 'intelligent' problems at the human level and above. The possibilities for solving very complex problems are limited by means that contradict the established views that thinking and reason are based on the soul, which has limitless possibilities. The strong AI (general AI, AGI) creating problem is not in building devices with magical capabilities, but in creating limited systems that can learn to solve many of the problems available. An important AGI property should be cooperation with people, taking into account civilizational norms. This property has not only a technical side, it depends on social relations. Sustainable development requires an agency approach to AGI.
Modern applied mathematics has faced fundamental difficulties in complex problems. Multiple increases in the performance of computing systems did not lead to breakthrough results. As new paradigms, 'analog' computing systems working with the use of new principles are neural networks and quantum computers. It is shown that these approaches, at best, can help to solve the 'past tasks', and not the 'future tasks' associated with the post-industrial phase of the development of civilization. The domestic applied mathematics efforts should be used to solve the central problems of the post-industrial society development in Russia using interdisciplinary approaches. This can make it possible to return to the number of countries with advanced technologies in the most important modern production areas. The alternative directions of the science development related to the human capabilities expansion are considered. The key one is related to AI, which can change reality. The article pays special attention to alternative approaches to AI development.