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==Mathematical Predictions==

==Mathematical Predictions==

Although string theory has so far failed to make viable experimental predictions, it has proved remarkably successful at predicting new theorems in mathematics. For example, from string-theoretic considerations, Candelas, de la Ossa, Green, and Parks conjectured the correct formula for the number of degree d rational curves in a Calabi-Yau quintic. Their formula was later rigorously proved correct by Givental and Lian, Liu, and Yau, establishing that the string-theoretic prediction was accurate.  More generally, string theory has predicted a deep relationship in mathematics called "mirror symmetry" which connects seemingly unrelated topics in symplectic and complex geometry. Mirror symmetry remains an active area of mathematical research, and many highly non-trivial examples of mirror symmetry have been mathematically verified.  

Although string theory has so far failed to make viable experimental predictions, it has proved remarkably successful at predicting new theorems in mathematics. For example, from string-theoretic considerations, Candelas, de la Ossa, Green, and Parkes conjectured the correct formula for the number of degree d rational curves in a Calabi-Yau quintic. Their formula was later rigorously proved correct by Givental and Lian, Liu, and Yau, establishing that the string-theoretic prediction was accurate.  More generally, string theory has predicted a deep relationship in mathematics called "mirror symmetry" which connects seemingly unrelated topics in symplectic and complex geometry. Mirror symmetry remains an active area of mathematical research, and many highly non-trivial examples of mirror symmetry have been mathematically verified.  

==Further reading==

==Further reading==