The Pythagorean Theorem as the Meta-Code of Mathematics (Updated Version 2)
Year: 2026
Type: article
Abstract: If mathematics is the language of the Universe, then the Pythagorean theorem is not merely basic syntax, but a fundamental semantic law, where the relation of the sides determines the very possibility of making a meaningful statement about space. The paper shows that all branches of mathematics — algebra, topology, analysis — turn out to be transformations of a single idea: the balance between symmetry and asymmetry, expressed through the right triangle. Special attention is paid to the right isosceles triangle (legs equal), which is proposed as a minimal geometric "atom" — the structural genotype of mathematical reality. We discuss how this triangle generates the natural numbers, irrationality (√2), and serves as an invariant in various fields of mathematics. In the concluding part of the work, the discovered regularities receive a rigorous formalisation in the language of logical theory: by means of forcing (⊩) and semantic consequence (⊧) it is shown that the infinium ℑ = △₁ₓ₁ forces mathematics to be exactly what we know it to be.
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162073683
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