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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] 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) · Zbl 0346.02026 · doi:10.1090/pspum/028.2/0432534
[2] Davis, Martin; Putnam, Hilary; Robinson, Julia, The decision problem for exponential Diophantine equations, Ann. Math., 74, 425-436 (1961) · Zbl 0111.01003 · doi:10.2307/1970289
[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) · doi:10.1070/RM1984v039n02ABEH003092
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[7] Matijasevich, Yuri, On recursive unsolvability of Hilbert’s tenth problem, 89-110 (1973), Amsterdam: North-Holland, Amsterdam
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[9] AH CCCP (1974), 112-123.
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[13] Robinson, Julia, An iterative method of solving a game, Ann. Math., 54, 296-301 (1951) · Zbl 0045.08203 · doi:10.2307/1969530
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[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 · doi:10.1112/jlms/s2-8.3.545
[18] Vorob’ev, N. N., Fibonacci Numbers (1964), Moscow: Nauka, Moscow · Zbl 0143.24201
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