In mathematics, a conjecture is a statement that is believed to be true, but has not yet been proven or disproven. Conjectures are often based on a pattern or observation, but require further evidence or a formal proof to be confirmed. Researchers may propose conjectures as a starting point for further investigation or to stimulate new ideas and theories in their field. Conjectures play a crucial role in advancing mathematical knowledge and understanding, as they provide direction for research and can lead to the discovery of important results and theorems.