{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nThe Church–Turing thesis is a claim about the informal notion of an algorithm.\nIt says that a function on the natural numbers can be calculated by an effective method exactly when a [[Turing machine|758EYCN27B]] computes it.\nIt is not a theorem, because \"effective method\" is an informal notion and cannot be the subject of a proof.\nIt is supported by the fact that all proposed formal models of computation define the same class of functions.\nThese models include [[general recursive functions|HBK5QHC1GC]], the [[lambda calculus|BD756KR8FM]] and Turing machines.\nThe thesis lets one prove that a problem has no algorithm at all by proving that no Turing machine solves it.\n\n## Explanations\n\n### L1 human\n\nPeople computed with pencil and paper long before there were precise definitions of computation.\nIn the 1930s Alonzo Church and Alan Turing each proposed a precise definition, and these turned out to describe the same functions.\nThe thesis claims that these definitions capture everything that can be computed by following exact rules.\nFor example, when one shows that no Turing machine decides whether a program halts, the thesis lets one conclude that no algorithm of any kind does.\n",
  "commit": "5fc425f97f1f6b11da5892c2948ef8c5d8805665",
  "front": {
    "kind": "concept",
    "msc": [
      "03D10",
      "03D20",
      "03A05"
    ],
    "name": "Church–Turing thesis",
    "same_as": {
      "wikidata": "Q309157",
      "wikipedia": "Church–Turing thesis"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Church–Turing_thesis"
      }
    ],
    "tag": "RWRNBS3Z7B"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/RWRNBS3Z7B/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/RWRNBS3Z7B.md",
  "msc": [
    "03D10",
    "03D20",
    "03A05"
  ],
  "name": "Church–Turing thesis",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/RWR/RWRNBS3Z7B.md",
  "status": null,
  "tag": "RWRNBS3Z7B",
  "uri": "m2://RWRNBS3Z7B",
  "url": "https://math2.tamnd.com/wiki/church-turing-thesis/",
  "writing": {
    "tag": "RWRNBS3Z7B",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}