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  "body": "\n## Summary\n\nA nondegenerate critical point of a smooth function is a [[critical point|0YTCMFB4HC]] at which the second derivative, the [[Hessian|0693Y2METT]], is a nondegenerate bilinear form.\nSuch points are isolated, and the [[Morse lemma|ERSD8D4HWX]] shows that near one of them the function is a sum of squares with signs.\nA function whose critical points are all nondegenerate is a [[Morse function|KPQ96640ZJ]].\n\n## Explanations\n\n### L1 human\n\nAt a critical point the graph of a function is flat to first order.\nThe point is nondegenerate when the function still curves in every direction, up or down, to second order.\nFor example, $x^2 + y^2$ and $x^2 - y^2$ have nondegenerate critical points at the origin: a bowl and a saddle.\nThe function $x^3$ has a degenerate critical point at $0$, because its second derivative vanishes there and the graph is flat to second order.\n",
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