Matiyasevich, Yuri My collaboration with Julia Robinson. (English) Zbl 0770.01005 Math. Intell. 14, No. 4, 38-45 (1992). The paper is an autobiographical reconstruction of the research done by the author in order to find the solution of Hilbert’s tenth problem, the determination of the solvability of a Diophantine equation. The solution was obtained through a collaboration with Julia Robinson (and Martin Davis). Useful informations are given in the paper about both the steps performed in order to obtain the solution and the scientific and academic context in which the research was developed. The paper is very interesting for everybody interested in logic, number theory and history of logic and mathematics. Reviewer: V.M.Abrusci (Roma) Cited in 1 ReviewCited in 4 Documents MSC: 01A60 History of mathematics in the 20th century 01A70 Biographies, obituaries, personalia, bibliographies 11-03 History of number theory Keywords:diophantine equation; Hilbert’s tenth problem; Diophantine equation; logic; number theory Biographic References: Robinson, Julia PDF BibTeX XML Cite \textit{Y. Matiyasevich}, Math. Intell. 14, No. 4, 38--45 (1992; Zbl 0770.01005) Full Text: DOI References: [1] Davis, Martin; Matijasevich, Yuri; Robinson, Julia, Hilbert’s tenth problem. Diophantine equations: positive aspects of a negative solution, Proc. Symp. Pure Math., 28, 323-378 (1976) [2] Davis, Martin; Putnam, Hilary; Robinson, Julia, The decision problem for exponential Diophantine equations, Ann. Math., 74, 425-436 (1961) · Zbl 0111.01003 [3] Davydov, G. V.; Matijasevich, Yu. V.; Mints, G. E.; Orevkov, V. P.; Slisenko, A. O.; Sochilina, A. V.; Shanin, N. A., “Sergei Yur’evich Maslov” (obituary), Russian Math. Surveys, 39, 2, 133-135 (1984) [4] David Hubert, Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker Kongress zu Paris 1900,Nachr. K. Ges. Wiss., Göttingen, Math.-Phys. Kl. (1900), 253-297. [5] Jones, James P., Universal diophantine equation, J. Symbolic Logic, 47, 549-571 (1982) · Zbl 0492.03018 [6] AH CCCP 191(2) (1970), 279-282 [translated inSoviet Math. Doklady 11(20) (1970), 354-357; correction 11(6) (1970), vi]. [7] Matijasevich, Yuri, On recursive unsolvability of Hilbert’s tenth problem, 89-110 (1973), Amsterdam: North-Holland, Amsterdam [8] Matijasevich, Yuri, Some purely mathematical results inspired by mathematical logic, 121-127 (1977), Dordrecht: Reidel, Dordrecht [9] AH CCCP (1974), 112-123. [10] Matijasevich, Yuri; Robinson, Julia, Reduction of an arbitrary Diophantine equation to one in 13 unknowns, Acta Arith., 27, 521-553 (1975) · Zbl 0279.10019 [11] Reid, Constance, The autobiography of Julia Robinson, College Math. J., 17, 3-21 (1986) · Zbl 0995.01515 [12] Robinson, John A., A machine-oriented logic based on the resolution principle, J. Assoc. Comput. Mach., 12, 23-41 (1965) · Zbl 0139.12303 [13] Robinson, Julia, An iterative method of solving a game, Ann. Math., 54, 296-301 (1951) · Zbl 0045.08203 [14] Robinson, Julia, Existential definability in arithmetic, Trans. Amer. Math. Soc., 72, 437-449 (1952) · Zbl 0047.24802 [15] Robinson, Julia, Unsolvable Diophantine problems, Proc. Amer. Math. Soc., 22, 534-538 (1969) · Zbl 0182.01901 [16] Robinson, Julia, Axioms for number theoretic functions, Selected Questions of Algebra and Logic (Collection Dedicated to the Memory of A. I. Mal’cev), 253-263 (1973), Novosibirsk: Nauka, Novosibirsk · Zbl 0279.02035 [17] Singmaster, D., Notes on binomial coefficients, J. London Math. Soc., 8, 545-548 (1974) · Zbl 0293.05005 [18] Vorob’ev, N. N., Fibonacci Numbers (1964), Moscow: Nauka, Moscow · Zbl 0143.24201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.