Which statement about conjectures best describes its status in mathematics?

• A. A proven theorem
• B. A hypothesis in science
• C. A numerical approximation
• D. A mathematical statement that has not been proven yet

Answer: (D)

A conjecture is a precise mathematical statement that people believe to be true but have not yet proven. It sits between patterns we observe and a fully established result: there may be strong evidence and partial results suggesting it’s true, but there is no complete proof that confirms it in all cases. When a proof is found, the conjecture becomes a theorem; until then, it remains an open statement guiding further investigation. This is distinct from a hypothesis in science, which is a tentative explanation tested by experiments, and from a numerical approximation, which aims to estimate a value rather than assert a universal truth about all cases. Some famous conjectures become theorems after proof, while others remain unresolved for long periods.