1. The user asks about "conjectures" which are proposed statements in mathematics or science that are believed to be true but have not been formally proven yet. 2. To understand conjectures, let's consider a common example: the Goldbach Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers. 3. Although this conjecture has been tested for very large numbers and no counterexample has been found, it remains unproven. 4. Conjectures are important because they guide research and exploration in mathematics. 5. When a conjecture is proven true, it becomes a theorem. 6. Summary: A conjecture is an unproven mathematical statement believed to be true, often inspiring further study and proof efforts.