theoremlike

Theoremlike is a descriptive term used in mathematical writing to characterize statements that resemble formal theorems in structure and rhetoric but are not fully established as rigorous theorems in the given context. Such statements typically present precise hypotheses and a conclusion, echoing the form of a theorem, yet their proof may be incomplete, conditional, or based on unproven assumptions.

Formally, a theoremlike statement often appears with a clear statement of conditions, followed by a conclusion and sometimes a proof outline. However, the full, unconditional proof may be deferred, rely on conjectures, or depend on methods that are not yet accepted as complete. This distinguishes it from a fully proven theorem, a conjecture, or a proposition whose proof is complete.

Theoremlike language is commonly used in expository writing, survey articles, lecture notes, and some areas of experimental or computational mathematics. It helps convey the intuition and potential impact of a result while signaling that the argument is not yet complete or universally accepted. It can also appear when results are proven in a specific setting or under strong hypotheses that are not guaranteed in all cases.

Cautions and conventions: the label theoremlike is informal and context-dependent. Readers should examine the precise hypotheses, the stated scope, and any caveats about proofs or dependencies on unproven assumptions. The term highlights the balance between communicating mathematical ideas effectively and maintaining rigorous standards.

See also: theorem, conjecture, proposition, lemma, proof sketch, conditional result, informal proof.