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  "body": "\n## Summary\n\nThe index of a Fredholm operator is the dimension of its kernel minus the dimension of its cokernel.\nIt is an integer that does not change under small perturbations, under compact perturbations, or along continuous paths of Fredholm operators.\nThe Atiyah–Singer index theorem computes it for elliptic differential operators in terms of topology.\n\n## Explanations\n\n### L1 human\n\nThe index counts how many more solutions a linear equation has than conditions it fails to meet.\nThe kernel counts independent solutions of $Tx = 0$, and the cokernel counts independent directions missed by $T$.\nFor a linear map from $\\R^5$ to $\\R^3$, the index is always $5 - 3 = 2$, whatever the map is.\nThe surprise is that in infinite dimensions the index is still stable under small changes, although the kernel and cokernel alone can jump.\n",
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