The name of Julia Robinson is inseparable from Hilbert's tenth problem. This was one of the 23 mathematical problems selected by David Hilbert in 1900, problems  which the pending XX century was to inherit from the passing XIX century. The eighth had, at first sight, little in common with the tenth problem. However, when the latter was solved (in the negative) it turned out that the two problems are connected, in a way which was not anticipated by Hilbert.

In my talk I'll briefly outline the history of proving the undecidability  of the tenth problem,  the role played by Julia
Robinson, my collaboration with her and Martin Davis, and a relationship between Hilbert’s  tenth and eighth problems.