Editing Julia Robinson (section)

===Hilbert's tenth problem===
[[Hilbert's tenth problem]] asks for an algorithm to determine whether a [[Diophantine equation]] has any solutions in [[integer]]s. Robinson began exploring methods for this problem in 1948 while at the [[RAND Corporation]]. Her work regarding Diophantine representation for exponentiation and her method of using [[Pell's equation]] led to the J.R. hypothesis (named after Robinson) in 1950. Proving this hypothesis would be central in the eventual solution. Her research publications would lead to collaborations with [[Martin Davis (mathematician)|Martin Davis]], [[Hilary Putnam]], and [[Yuri Matiyasevich]].<ref>{{cite book|title=The Decision Problem for Exponential Diophantine Equations|last1=Robinson|first1=Julia|last2=Davis|first2=Martin|last3=Putnam|first3=Hilary|date=1961|publisher=Annals of Mathematics|location=Princeton University}}</ref>

In 1950, Robinson first met Martin Davis, then an instructor at the [[University of Illinois at Urbana-Champaign]], who was trying to show that all sets with listability property were Diophantine in contrast to Robinson's attempt to show that a few special sets—including prime numbers and the powers of 2—were Diophantine. Robinson and Davis started collaborating in 1959 and were later joined by Hilary Putnam, they then showed that the solutions to a “Goldilocks” equation was key to Hilbert's tenth problem.<ref name="sciencenews.org">{{Cite web|url=https://www.sciencenews.org/article/how-julia-robinson-helped-define-limits-mathematical-knowledge|title = How Julia Robinson helped define the limits of mathematical knowledge|date = 22 November 2019}}</ref>

In 1970, the problem was resolved in the negative; that is, they showed that no such algorithm can exist. Through the 1970s, Robinson continued working with Matiyasevich on one of their solution's corollaries, which she once stated that

<blockquote>there is a constant ''N'' such that, given a Diophantine equation with any number of parameters and in any number of unknowns, one can effectively transform this equation into another with the same parameters but in only ''N'' unknowns such that both equations are solvable or unsolvable for the same values of the parameters.<ref name=":0">{{Cite web|url=https://logic.pdmi.ras.ru/~yumat/Julia/|title=My Collaboration with JULIA ROBINSON|website=logic.pdmi.ras.ru|access-date=2018-08-28}}</ref></blockquote>

At the time the solution was first published, the authors established ''N'' = 200. Robinson and Matiyasevich's joint work would produce further reduction to 9 unknowns.<ref name=":0" />