Conjecture
A proposition or problem that remains neither proved nor disproved. In Mathematics it refers to a statement believed to be true but not yet proven.
The Collatz conjecture is a mathematics problem simple enough for an elementary student to grasp, yet legendary mathematician Paul Erdős declared, "Mathematics is not yet ready for such problems."
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The 'Moving Sofa Problem'—finding the largest shape that fits around a right-angled hallway of width 1—was an unsolved mathematics conjecture for 60 years. In 2024, Korean mathematician Jineon Baek proved the 'Gerver sofa' (area ~2.2195) is optimal without computers.
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