"Roth's theorem" meaning in English

{
  "etymology_text": "Named after Klaus Roth.",
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  "lang_code": "en",
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      "glosses": [
        "A fundamental result in Diophantine approximation to algebraic numbers, stating that these numbers cannot have many rational number approximations that are 'very good' (variously defined through history)."
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      "id": "en-Roth's_theorem-en-name-Zg1kfSus",
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        [
          "mathematics",
          "mathematics"
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        [
          "Diophantine",
          "Diophantine"
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        [
          "approximation",
          "approximation"
        ],
        [
          "algebraic number",
          "algebraic number"
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          "rational number",
          "rational number"
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      "raw_glosses": [
        "(mathematics) A fundamental result in Diophantine approximation to algebraic numbers, stating that these numbers cannot have many rational number approximations that are 'very good' (variously defined through history)."
      ],
      "related": [
        {
          "word": "Roth's theorem on arithmetic progressions"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Klaus Roth",
        "Roth's theorem"
      ]
    }
  ],
  "word": "Roth's theorem"
}

{
  "etymology_text": "Named after Klaus Roth.",
  "head_templates": [
    {
      "args": {},
      "expansion": "Roth's theorem",
      "name": "en-proper noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "related": [
    {
      "word": "Roth's theorem on arithmetic progressions"
    }
  ],
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      "glosses": [
        "A fundamental result in Diophantine approximation to algebraic numbers, stating that these numbers cannot have many rational number approximations that are 'very good' (variously defined through history)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "Diophantine",
          "Diophantine"
        ],
        [
          "approximation",
          "approximation"
        ],
        [
          "algebraic number",
          "algebraic number"
        ],
        [
          "rational number",
          "rational number"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A fundamental result in Diophantine approximation to algebraic numbers, stating that these numbers cannot have many rational number approximations that are 'very good' (variously defined through history)."
      ],
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        "mathematics",
        "sciences"
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        "Klaus Roth",
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  "word": "Roth's theorem"
}