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My collaboration with Julia Robinson. (English) Zbl 0770.01005

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)

MSC:

01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
11-03 History of number theory

Biographic References:

Robinson, Julia
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References:

[1] Martin Davis, Yuri Matijasevich, and Julia Robinson, Hilbert’s tenth problem. Diophantine equations: positive aspects of a negative solution,Proc. Symp. Pure Math. 28 (1976), 323–378. · Zbl 0346.02026
[2] Martin Davis, Hilary Putnam, and Julia Robinson, The decision problem for exponential Diophantine equations,Ann. Math. (2) 74 (1961), 425–436. · Zbl 0111.01003
[3] G. V. Davydov, Yu. V. Matijasevich, G. E. Mints, V. P. Orevkov, A. O. Slisenko, A. V. Sochilina and N. A. Shanin, ”Sergei Yur’evich Maslov” (obituary),Russian Math. Surveys 39(2) (1984), 133–135 [translated from 39(236) (1984), 129–130].
[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] James P. Jones, Universal diophantine equation,J. Symbolic Logic 47 (1982), 549–571. · 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] Yuri Matijasevich, On recursive unsolvability of Hilbert’s tenth problem,Proceedings of Fourth International Congress on Logic, Methodology and Philosophy of Science, Bucharest, 1971, Amsterdam: North-Holland (1973), 89–110.
[8] Yuri Matijasevich, Some purely mathematical results inspired by mathematical logic,Proceedings of Fifth International Congress on Logic, Methodology and Philosophy of Science, London, Ontario, 1975, Dordrecht: Reidel (1977), 121–127.
[9] AH CCCP (1974), 112-123.
[10] Yuri Matijasevich and Julia Robinson, Reduction of an arbitrary Diophantine equation to one in 13 unknowns,Acta Arith. 27 (1975), 521–553. · Zbl 0279.10019
[11] Constance Reid, The autobiography of Julia Robinson,College Math. J. 17 (1986), 3–21. · Zbl 0995.01515
[12] John A. Robinson, A machine-oriented logic based on the resolution principle,J. Assoc. Comput. Mach. 12 (1965), 23–41 [translated in 7 (1970), 194-218]. · Zbl 0139.12303
[13] Julia Robinson, An iterative method of solving a game,Ann. Math. (2) 54 (1951), 296–301. · Zbl 0045.08203
[14] Julia Robinson, Existential definability in arithmetic,Trans. Amer. Math. Soc. 72 (1952), 437–449. · Zbl 0047.24802
[15] Julia Robinson, Unsolvable Diophantine problems,Proc. Amer. Math. Soc. 22 (1969), 534–538. · Zbl 0182.01901
[16] Julia Robinson, Axioms for number theoretic functions,Selected Questions of Algebra and Logic (Collection Dedicated to the Memory of A. I. Mal’cev), Novosibirsk: Nauka (1973), 253–263; MR 48#8224.
[17] D. Singmaster, Notes on binomial coefficients,J. London Math. Soc. 8 (1974), 545–548; (1975), 3A143. · Zbl 0293.05005
[18] N. N. Vorob’ev,Fibonacci Numbers, 2nd ed., Moscow: Nauka, 1964; 3rd ed., 1969.
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