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The Poincaré Conjecture was initially proposed in 1904 by French mathematician Henri Poincaré, who suggested that a three-dimensional space devoid of holes could be transformed into a sphere without any tearing or cutting involved. This concept gave rise to the field of topology, where shapes are studied without regard to their specific form, only their properties and structures. For topologists, objects like a ball and a pillow can be considered equivalent as they can morph into one another, much like a bagel and a mug, due to their respective holes. Poincaré’s conjecture posited that any object without holes is topologically equivalent to a sphere.