konjektuuri

Konjektuuri is a term used in mathematics and related disciplines to describe a proposition that is asserted to be true based on evidence but has not yet been proven. In practice, a konjektuuri serves as a guiding question that motivates research, rather than a finished result. It is distinguished from a theorem, which has a formal proof, and from a hypothesis, which is a premise used to derive further statements. A konjektuuri can be disproven by a counterexample, and a complete proof converts it into a theorem.

The word derives from Latin conjectura and has entered mathematical language through various European languages; in Estonian usage konjektuuri or similar forms are common to denote such conjectures.

Famous konjektuuri include Goldbach's conjecture, which posits that every even integer greater than 2 is the sum of two primes; the Riemann Hypothesis, which states that all nontrivial zeros of the Riemann zeta function lie on the critical line; and the Collatz conjecture, which concerns the eventual reachability of 1 under a simple iterative process. Some konjektuuri have been proven, such as Fermat's Last Theorem, which began as a conjecture and was established in 1994 by Andrew Wiles. Other conjectures remain open, continuing to guide research and prompting partial results, special cases, or conditional proofs.

In mathematical practice, work on konjektuuri involves formulating clear statements, seeking robust proof strategies, and testing implications through computation or theoretical analysis, with the aim of resolving them definitively.