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  "body": "\n## Summary\n\nMirror symmetry is a correspondence, first predicted by string theory, between pairs of [[Calabi–Yau manifolds|STYAB4PFDW]] $X$ and $\\check{X}$.\nThe symplectic geometry of $X$, encoded by its [[Gromov–Witten invariants|XVJA0JD79P]], matches the complex geometry of $\\check{X}$, encoded by the variation of its [[Hodge structures|ZSM083M97C]].\nFor Calabi–Yau threefolds the Hodge numbers are exchanged: $h^{1,1}(X) = h^{2,1}(\\check{X})$ and $h^{2,1}(X) = h^{1,1}(\\check{X})$.\nIt is not a single theorem but a program with several precise forms, such as [[homological mirror symmetry|B5N9WJH5F0]].\n\n## Explanations\n\n### L1 human\n\nTwo spaces that look unrelated can carry the same hidden information, read in two different languages.\nOn one side one counts curves inside a space, which is a hard enumerative problem.\nOn the mirror side one computes certain integrals of differential forms, called periods, which is much easier.\nIn 1991 Candelas, de la Ossa, Green and Parkes used this to predict the number of rational curves of each degree on a quintic threefold in $\\mathbb{P}^4$.\nThe predicted numbers include $2875$ lines and $609250$ conics.\nThese predictions were later proved by mathematicians, and mirror symmetry became a major field of geometry.\n",
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