How, according to Iamblichus, does “the soul give itself to all mathematical realities”?

Based on the authority of Plato and post-Hellenistic Pythagoreanism, Iamblichus confer the same ontological rank on mathematical realities, on the one hand, and on the soul, on the other (both are intermediate), and thus finds himself confronted with the problem of the relationship between these entities: are they identical or different? And, beyond this antithesis, what are their mutual relations? Starting from De communi mathematica scientia chap. III and IX-X, in which the question is addressed, scholars have considered Iamblichus’ position contradictory or have chosen one of the two horns of the alternative, thus believing that Iamblichus either identified soul and mathematics or did not identify them. According to the interpretation I have here developed, Iamblichus distinguishing two modes of relation between the soul and mathematics. The first mode, described in De communi mathematica scientia chap. III, is the relationship that the soul establishes with the principles and mathematical entities that transcend it and leads to a complete separation between the two realities, marked by an irreducible otherness. The other mode, described in De communi mathematica scientia chap. IX and X, is the relationship between the soul and the totality of mathematical entities of a psychic nature: self-moving numbers, psychic harmony, relationships, proportions, etc. In this second case, the scenario is different: the soul fully embraces mathematical entities and yet retains its difference from them.