Formation of the idea of mathematical phenomenology in Edmund Husserl's philosophy

The article presents the historical prerequisites for the creation of mathematical phenomenology. Within the framework of the infinite numbers problems, the ways of their phenomenological interpretation are discussed. Using the example of cooperation between Cantor and Husserl, the idea of mathematical phenomenology is formulated, which takes into account the correlation of mathematical objects with our consciousness. In formal logic, subjective factors often affect the judgment process. The phenomenological method is valuable in that it makes it possible to conduct both objectively and subjectively oriented research in mathematics and formal logic. In such a correlative study, subjective acts and objective referents of any phenomenon should be taken into account. The main goal of correlative research is to create conditions for overcoming relativistic tendencies in mathematics and formal logic. As a result of the analysis, the question of the relationship between descriptive phenomenology and formalized constructions is raised. In the historical and philosophical context, the answer to this question is based on the theoretical developments provided in Husserl’s Formal and Transcendental Logic. Subjective-oriented logic goes back to the latent structures of theoretical reason. Here the problems of consciousness are formulated and solved in its live, actual execution with the help of egological research. In conclusion, historical examples of the subjective transformation of formal logic are provided. In the first example, an interpretation of Descartes’ conclusion cogito, ergo sum is given, showing that the existential inconsistency of «I do not exist» and the reliability of the initial position «I exist» were realized here. Another example of the transformation of logic is Husserl’s phenomenology. In order to bring logical forms to their subjective obviousness, it is necessary to change the orientation of consciousness and to consider objects as givens of consciousness.