A conjecture is an educated guess or hypothesis that is based on observations but has not yet been proven. In mathematics, conjectures often arise from patterns noticed in numbers or shapes. For example, the famous Goldbach's Conjecture suggests that every even integer greater than two can be expressed as the sum of two prime numbers, but it remains unproven. Conjectures play a crucial role in scientific research and problem-solving. They encourage exploration and experimentation, prompting researchers to gather evidence and test their ideas. Once sufficient proof is found, a conjecture can be elevated to a theorem, solidifying its status in the field, as seen with Fermat's Last Theorem.