System informational culture (SIC) has stated the next problem of post neo classical science man. How to educate trans disciplinary man of scienceful culture (universal professional) capable to interpret and model knowledge by means of perception of humanitarian (art) and rational science unity? Co evolution of human mind and anthropogenic environment of computer instrumental systems (IS) occurs as subjective objectization of natural science knowledge (NSK). Authors have constructed model of artificial intelligence system of universal usage (AIUU) which supports continuous tutoring with the aim to form subject of SIC. Traditional education and known e-learning approaches can’t cope with the task. Phenomenology of consciousness is grounded on development of rational part of mind. Classical universalities problem of philosophy has been resolved in the model with the help of human ability to glottogenes in semantic direction. In this way the language of categories (LC) has been discovered. AIUU functions on the principles of knowledge without premises and educated unknowledge in the form of mathesis universales of LC. It also uses the unity of human and NSK proper to inter discipline activity in the SIC. The system generates and maintains educational space of meanings in the form of personal ontological knowledge base (KBO). By means of KBO artificial intelligence adaptively helps student to investigate any field of knowledge. LC is applied to express semantic. Axiomatic method provides the unity of ideal (theory) and real (modeling in IS). Universal tutoring is stated to resolve the problem of any theory understanding by professional clearness reduction to its self evidence. By the example of the theory of algorithms study it is shown how the approach to education works. © 2018, Springer International Publishing AG.