This work poses a radical question: why did the Hodge Conjecture, the Riemann Hypothesis, and other Millennium Problems resist solution for over a century despite immense intellectual and financial resources? We argue that the answer lies not in the complexity of the problems themselves but in a hidden flaw at the very foundation of mathematics — the use of a structureless, dimensionless point as the primitive building block. Drawing on neuroscience (the brain’s 2D visuospatial coding and the physics of perception) and physics (light as a transverse wave, the primacy of the plane), we demonstrate that genuine abstraction requires a structural quantum with size, shape, and internal relations. From this interdisciplinary analysis emerges Δ‑ontology, where the fundamental unit is not the point but the Infinitum — the right isosceles triangle with legs 1 and hypotenuse √2, the only geometric object possessing perfect orthogonality, fractal self‑similarity, and an irrational measure that bridges the discrete and the continuous. Within this framework, the Hodge Conjecture becomes a tautological consequence of the mosaic nature of number, the critical line of the Riemann zeta function is revealed as a shadow of the Pythagorean theorem, and the intractability of P vs NP is traced to the irreducible structure of prime‑number mosaics. This paper does not offer yet another technical proof within the old paradigm; it issues an interdisciplinary challenge: if the brain builds mathematics from structured sensory atoms, and if the physical universe speaks the language of orthogonal waves and holographic screens, then perhaps it is time to replace the fictitious point with the real triangle and rebuild mathematics on a foundation that is biologically, physically, and logically coherent. The article invites mathematicians, neuroscientists, physicists, and philosophers to a serious conversation about the cost of ignoring the structural basis of thought and about the possibility of a unified science grounded in a single geometric quantum. All code, formalizations, and previous works on Δ‑ontology are available on Zenodo for critical examination.
Alexey (KAMAZ) Petrov (Sun,) studied this question.