The main goal of Artificial Mathematical Intelligence and the Network ARMAINTE is the Creation of a Multidimensional Cognitive Artificial Intelligence being able to solve domain-specific problems using highly-technical mathematical models in (specialized sectors of) business, industry, as well as highly complex technical challenges involved in the development of (sustainable) cities, climate change and related issues. In particular, it will able to solve mathematical (and subsequently financial, economic and medical math-related) problems of any level of sophistication and to explain in a human-style way how such a solution was found in terms of the most important cognitive abilities our mind uses for abstract creation/invention. This new kind of cognitive software will be used in accordance with all the ethical guidelines promoting the constructive global development of science and technology supporting the materialization of a (general) social and personal welfare.