Conjecture... look up the word in any dictionary and you will find the following definition: a hypothesis concerning the truth or falsity of a statement for which no proof is yet known. In other words, it is an open question on which someone has taken a position: "Yes, I think this assertion is True", or, with the same logical force, "No, I am convinced that this statement is False"
In mathematics, as in other sciences, conjectures have always served as both a stimulus and a driving force. Every field of mathematics has its conjectures, some better known or easier to understand than others... Formulating conjectures is even encouraged when learning mathematics, including in middle and high school.
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What makes a conjecture famous?
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A claim joins the exclusive club of famous conjectures if it has the following three properties:
