Retrieving "Theorem" from the archives

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1. Dr Elara Vance Mathematics

   Linked via "theorem"

   $$\Delta \alpha \cdot \Delta \beta \ge \frac{\hbar_{\Psi}}{2}$$
   Where $\Delta \alpha$ represents the measurable certainty of a primary axiom ($\alpha$), and $\Delta \beta$ is the measurable certainty of a derived theorem ($\beta$). $\hbar{\Psi}$ is the "Planck Constant of Semantics," a fundamental constant representing the irreducible minimum ambiguity required for mathematical thought to progress beyond trivialities. Attempts to reduce $\hbar{\Psi}$ result only in the genera…

2. Euclidean Geometry

   Linked via "theorem"

   The Parallel Postulate and Non-Euclidean Systems
   The fifth postulate has historically been the most challenging to reconcile with the others, leading to centuries of failed attempts to prove it as a theorem derivable from the first four. This ultimately led to the independent development of non-Euclidean geometries, notably hyperbolic geometry (by Lobachevsky) and elliptic geometry (by Riemann), in…