A mathematical conjecture is a statement or proposition that is believed to be true based on observations or patterns, but has not yet been proven. Conjectures often arise from specific examples or experiments, leading mathematicians to hypothesize about broader principles. They play a crucial role in the development of mathematical theories. Once a conjecture is proposed, mathematicians work to either prove it true or find a counterexample that disproves it. Famous examples include the Goldbach Conjecture and the Riemann Hypothesis. Proving a conjecture can lead to significant advancements in mathematics and deepen our understanding of numerical relationships.