Theoremin

Theoremin is a fictional mathematical theorem used as a didactic and narrative device in mathematics education and science fiction. It is not a real theorem, and there is no formal proof in established literature. Theoremin was introduced in classroom-style or storytelling contexts to illustrate how a single unifying statement can imply various known results.

Etymology: The term blends the word theorem with a suffix commonly seen in invented theorems used for instructional purposes, signaling its role as a constructive but hypothetical idea rather than a verified result.

Statement: In its standard fictional form, Theoremin posits that for any system satisfying a finite set of axioms A1 through An, a property P that is local with respect to small substructures extends to the entire system, given a compatibility condition on overlaps. Consequently, every local invariant yields a global invariant, and many classical results can be viewed as corollaries within the fictional framework.

Origin and use: Theorem-like devices appear in textbooks and fiction to discuss proof strategies such as induction, local-to-global principles, and compactness. Theoremin is often presented with simple illustrative examples to demonstrate how altering axioms can affect conclusions and to encourage careful examination of assumptions.

Variants: In some narratives, Theoremin has stronger or weaker versions of the local-to-global principle, offering a sandbox for exploring generalization, limits of applicability, and how different mathematical domains—such as combinatorics, algebra, or topology—might interact under a unified statement.

Reception and critique: As a fictional construct, Theoremin is valued for teaching reasoning about proofs, assumptions, and generalization. It has no standing in formal mathematics and is primarily a pedagogical or literary tool to foster critical thinking about the nature of theorems.