Homonym: Conjectures (Speculation)
A conjecture is an educated guess or hypothesis based on observations or patterns. In mathematics, it often refers to a statement that is believed to be true but has not yet been proven. For example, the Goldbach Conjecture suggests that every even integer greater than two can be expressed as the sum of two prime numbers.
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.