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      "statement": "# Hilbert’s tenth problem: the negative solution\n\nMatiyasevich supplied a Diophantine representation of exponential growth, completing the prior Davis–Putnam–Robinson route from enumerable predicates to polynomial equations and the impossibility of a general integer-solvability algorithm.\n\n## Scientific scope\n\nThe four names credit the mathematical development; the 1970 paper itself is authored by Matiyasevich. General undecidability does not prevent solving individual equations or restricted classes. Integer, nonnegative-integer and positive-integer formulations are related by the reductions noted in the source.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nYu. V. Matiyasevich; Martin Davis; Hilary Putnam; Julia Robinson\n\nListed source contributors; individual labor shares are not measured\n\n\n\n## Original sources\n\n- [Matiyasevich, The Diophantineness of Enumerable Sets, Doklady 191(2), 279–282 (1970)](https://www.mathnet.ru/eng/dan35274)\n",
      "summary": "Matiyasevich supplied a Diophantine representation of exponential growth, completing the prior Davis–Putnam–Robinson route from enumerable predicates to polynomial equations and the impossibility of a general integer-solvability algorithm.",
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    "title": "Hilbert’s tenth problem: the negative solution",
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    "scope": "Matiyasevich supplied a Diophantine representation of exponential growth, completing the prior Davis–Putnam–Robinson route from enumerable predicates to polynomial equations and the impossibility of a general integer-solvability algorithm. Scope limitation: The four names credit the mathematical development; the 1970 paper itself is authored by Matiyasevich. General undecidability does not prevent solving individual equations or restricted classes. Integer, nonnegative-integer and positive-integer formulations are related by the reductions noted in the source.",
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