**Martin Davis** was an American mathematician, known for his work on Hilbert's tenth problem.

- Sadly Jerome died of a ruptured appendix at the age of eight, a devastating blow for thirteen year old Martin and his parents.
- Harry and Helen Davis had no formal education but learnt English at a night school for immigrants after arriving in New York.
- The young Davis was educated in public schools in New York, gaining much from the excellent Bronx High School of Science.
- Davis took a course on symbolic mathematical logic in his first year and a reading course on real variable theory with Emil Post in his second year.
- Certainly by the time Davis graduated from the City College with a B.S. in 1948 he knew he wanted to undertake research in mathematical logic.
- As a graduate student at Princeton, Davis was unhappy.
- His thesis On the Theory of Recursive Unsolvability did, however, contain a chapter on Hilbert's Tenth Problem where he introduced the important idea of the Davis normal form.
- Since it played such a major role in Davis's career, perhaps we should say a little more about Hilbert's Tenth Problem at this stage.
- However, certainly Post believed that the problem "begs for an unsolvability proof" and had used these words in his discussions with Davis.
- Let us now return to discussing Davis's career after the award of his doctorate.
- Davis was two years at Urbana-Champaign then spent the two years 1952-54 at the Institute for Advanced Study at Princeton.
- In 1954 he was appointed as an Assistant Professor of Mathematics at the University of California at Davis where he spent a year before accepting a similar position at Ohio State University.
- During these years when Davis was moving around spending time at various institutions, he published a number of important papers such as Arithmetical problems and recursively enumerable predicates (1953), The definition of universal Turing machine (1957), (with Hilary Putnam) Reductions of Hilbert's tenth problem (1958) and (with Hilary Putnam and Julia Robinson) The decision problem for exponential diophantine equations (1961).
- It would not be Davis who would eventually solve the Tenth Problem, rather it was solved in 1970 by Yuri Matiyasevich following further progress by Julia Robinson.
- For his work on Hilbert's Tenth Problem, particularly his remarkable paper explaining the proof, Davis received many honours and awards.
- Finally let us look at some of the highly significant books that Davis has published.
- Another interesting book by Davis is Applied nonstandard analysis (1977).
- Davis republished Computability and unsolvability in 1982 but added his 1973 award winning paper Hilbert's tenth problem is unsolvable (1973) as an appendix.
- In 1983 Davis, in collaboration with Elaine J Weyuker, published Computability, complexity, and languages.
- In 2000 Davis published The universal computer.
- Davis retired from his chair in New York University in 1996 and moved to Berkeley, in California.

Born 8 March 1928, New York City, New York, USA. Died 1 January 2023, Berkeley, California, USA.

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Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive