The “four-letter theorem” from the viewpoint of the “fundamental theorem of the universe”

The four-color theorem in standard mathematics and the four-letter theorem in Hilbert mathematics are juxtaposed. The former is a topological theorem thus not allowing for its elementary metric proof as the latter. This is interpreted as an example of “Modernity’s bottle” forcing mathematics not to use any tools entering reality for complying with the taboo for the gap between mathematical models and reality. The same relation in Hilbert arithmetic is interpreted as passing through the “threshold” between two and three dimensions after the Gleason and Kochen - Specker theorems. The representation of mathematical duality and physical complementarity is discussed. The philosophical concept of “the totality” translated in ontomathematics implies for mathematical models to be “concave” in order to obey the absoluteness of the totality. A principle of the equivalence of “concave” (philosophical or “metaphysical”) and “convex” (proper mathematical) explanations being inherent from the viewpoint of ontomathematics is investigated by the example of the correspondence of the Bohmian (non-local and metaphysic: thus “concave”) versus “Copenhagen” (local and agnostic: thus, “convex”) interpretations of quantum mechanics. The eventual representation of quantum contextuality/ holism as fractal structures/ functional (Hausdorff) dimensionality is conjectured. The third dimension of reality (in the sense of the cited theorems) is researched in its two versions: “concave” (metaphysic, in particular, Bohmian) and “convex” (traditional and mathematical, particularly, “Copenhagen”). An illustration by the “four letters” of DNA (RNA) is considered. An interpretation of Peano arithmetic as the “half” of Boolean algebra unifying propositional logic and set theory is linked.