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  "body": "\n## Summary\n\nEnumerative geometry is the branch of algebraic geometry that counts geometric objects satisfying given conditions.\nTypical questions ask how many lines meet four given lines in space, or how many conics are tangent to five given conics.\nIts tools include [[intersection theory|4HV4WTAX9P]], [[Schubert calculus|FWGHMADJR4]] and [[Gromov–Witten invariants|XVJA0JD79P]].\nIt is a meeting point of algebraic geometry, combinatorics and physics.\n\n## Explanations\n\n### L1 human\n\nHow many circles touch three given circles?\nThe answer, found by Apollonius, is $8$ in general.\nEnumerative geometry asks questions of this kind: count the curves or surfaces with prescribed properties.\nThe answers are expected to be finite numbers that do not change when the given data move a little, as long as they stay general.\nGetting them right is subtle, and some classical answers were wrong for a long time.\n",
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