Abstract

Is mathematics not, at its core, something that should be proven using numbers and calculation? I must say this: If something cannot be proven purely through equations, then it is not mathematics. To say “Explain why 1 + 1 = 2” just because one does not know the answer is misguided. But to insist that “1 + 1 = 2” is true without truly understanding why it is so— is that not the illusion we must now abandon? That kind of reasoning belongs to architecture, physics, or other sciences—not mathematics. Mathematics is simple. Its answers must be singular, universal, and evident to anyone who sees them. This is the essence of mathematics—and the essence of nature. Mathematics is not about “proof” in the conventional sense. It is about whether or not we realize something—just as one realizes that 1 + 1 = 2. This rebuttal is grounded in the principles outlined in the Theorems of Cosmic Deformation– BOX3 (DOI: 10.5281/zenodo.15477698). At its core lies Theorem 1, which represents infinity not as a symbolic picture (∞), but as a tangible phenomenon. Even if we treat Theorem 1 as a hypothetical defi nition of infinity, it logically follows that Theorem 3 emerges from it—a generative principle capable of producing infinite structures: points, circles, surfaces, solids, and beyond. Thus, Theorem 3 provides the structural essence that replaces π in this paper. This is not a symbol, but a law of emergence. It is not enough for mathematicians to observe infinity as a distant abstraction. Our task is to give it form, logic, and structure. That is the true mission of mathematics. And that is the foundation upon which this work stands.