Диагноз нерешаемости: структурный дефект оснований математики и Δ-онтология как лекарство

For over a hundred years a number of fundamental mathematical problems (the Hodge Conjecture, the Riemann Hypothesis, P vs NP, and others) have remained unsolved, despite enormous intellectual efforts. This work does not offer yet another “proof” within the existing paradigm. Instead, we analyze the paradigm itself. We put forward and substantiate the thesis: the root of the problem lies not in the complexity of the problems themselves, but in a logical contradiction embedded in the foundations of mathematics — namely, in the concept of a structureless, dimensionless point. It is shown that this idealization creates an unbridgeable gap between the discrete (number) and the continuous (geometry), which makes the aforementioned problems exponentially complex or unsolvable in principle. As an alternative, we present Δ‑ontology — a consistent, interdisciplinary system of foundations based on a structural geometric quantum: the right isosceles triangle (RIT, the “Infinitum”). We show that, within this system, analogues of the Millennium Problems cease to be “problems” and become either trivial consequences of the axiomatics or acquire a clear geometric meaning. The work is an invitation to reconsider the foundations of mathematics in light of data from neuroscience, physics, and information theory.