unbewiesen

Unbewiesen is a German adjective meaning “not proven.” In mathematics it denotes a statement, assertion, or conjecture that has not yet been proven true or false. The status is provisional: the statement is recognized as well-posed, but no proof exists within the current axiomatic framework, so its truth value remains undetermined. The term is commonly used alongside open problems and conjectures. It contrasts with bewiesen (proved) and, in broader terms, with statements that have been disproven.

Etymology: un- is a prefix meaning negation, added to beweisen, “to prove.” The combined form literally expresses “not proven.”

Typical usage: Unbewiesen often appears in discussions of conjectures such as the Goldbach conjecture, the Collatz problem, or the Riemann hypothesis, which are widely believed to be true but have not been proven. Some unbewiesen statements may later be proven or disproven; others remain open despite intense effort. In logic, Gödel’s incompleteness theorems show that some true statements are unprovable within given formal systems, a stronger situation described as undecidable or unprovable rather than merely unbewiesen.

Relation to related terms: The term is most common in mathematical contexts. It is related to open problems and conjectures. “Unentscheidbar” or “unbeweisbar” are used in logic to indicate independence from a particular axiomatic system or the impossibility of proof within it.

See also: open problem, conjecture, theorem, proof, undecidable, Gödel’s incompleteness theorems.