Concept

Impossibility Theorem

Logic, Foundations and Set Theory

An impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved; such results are also known as proofs of impossibility, negative proofs or negative results. The cited article says they often resolve decades or centuries of work spent looking for a solution by proving there is no solution, that proving something is impossible is usually much harder than the opposite task because a proof must work in general rather than for one example, and that they are usually expressible as negative existential or universal propositions in logic. The irrationality of the square root of 2 is named as one of the oldest such proofs. Theorems that rule out a construction or solution are grouped under this concept.

Connections

Statement Form Of

Abel-Ruffini Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Angle Trisection

Antidynamo Theorem

Arrow's Impossibility Theorem

Aumann's Agreement Theorem

Bell's Theorem

Borde-Guth-Vilenkin Theorem

Bruck-Ryser-Chowla Theorem

Church's Theorem

Clausius Theorem

Cohen's Independence Theorem

Coleman-Mandula Theorem

Duggan-Schwartz Theorem