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  "body": "\n## Summary\n\nThe stable homotopy groups of spheres $\\pi_k^s$ are the groups $\\pi_{n+k}(S^n)$ for $n$ large, where they no longer depend on $n$.\nThe [[Freudenthal suspension theorem|7DM2KSS2DB]] shows that the suspension maps become isomorphisms once $n \\ge k + 2$.\nTogether they form a graded ring, the coefficient ring of stable homotopy theory, and they are the homotopy groups of the sphere spectrum.\nTheir computation is a central problem of algebraic topology, studied with the Adams spectral sequence and chromatic methods.\n\n## Explanations\n\n### L1 human\n\nThe homotopy groups of spheres change wildly as the dimensions change.\nIf both dimensions are raised together by the same amount, however, the groups settle down after a while.\nThese settled values are the stable groups.\nThe first ones are $\\Z$, $\\Z/2$, $\\Z/2$, $\\Z/24$, $0$, $0$, $\\Z/2$, $\\Z/240$, and their pattern is still not understood in general.\n",
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