On the Mirror Conjecture

In 1989, B. Greene, a postdoc of Yau at the time, and R. Plesser constructed an important example of mirror manifolds. Using physics argument, they proved the first case of mirror symmetry for Calabi-Yau threefolds. Their result is considered fundamental, though its proof lacks the precision of a mathematical proof, hence the result does not constitute a mathematical theorem. Two years later, Candelas-de la Ossa-Green-Parkes built on the result, and with even greater mathematical precision, produced a spectacular solution to a long-standing problem in enumerative geometry. Since the solution still contains important mathematical gaps, the result is considered a conjecture, now known as the mirror conjecture.