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  "body": "\n## Summary\n\nA Morse function is a smooth real-valued function on a [[smooth manifold|F45VQ47GPV]] all of whose [[critical points|0YTCMFB4HC]] are nondegenerate.\nThis means that the [[Hessian|0693Y2METT]] at each critical point is invertible.\nNear each critical point it has a simple quadratic normal form, given by the Morse lemma.\nMorse functions exist on every smooth manifold and are generic among smooth functions.\nThey are the basic tool of Morse theory, which reads the topology of a manifold off the critical points of such a function.\n\n## Explanations\n\n### L1 human\n\nThink of the height above the ground on a hilly landscape, or on a doughnut standing upright on a table.\nIts critical points are the peaks, the pits and the passes, where the ground is flat.\nA Morse function is one where each such flat spot is a clean peak, pit or saddle, not a flat plateau or a degenerate shape like a monkey saddle.\nFor the upright doughnut, the height has four critical points: a bottom, two saddles, and a top.\n",
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