A conjecture is an educated guess or a proposition that is believed to be true based on preliminary evidence or reasoning, but has yet to be proven or substantiated. In mathematics, for example, a conjecture is a statement that appears to be true because of observed patterns or numerical evidence, but it requires a formal proof to be accepted as a theorem. Conjectures play a crucial role in the development of mathematical theories, as they often lead to further research and exploration.
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A conjecture is an open problem in mathematics for which some famous dude gave heuristic arguments which indicate if the theorem is true or false.