On July 29, 1657 they signed the Treaty of Wehlau in Wehlau (Polish: Welawa; now Znamensk), whereby Frederick William renounced a previous Swedish-Prussian alliance and John Casimir recognised Frederick William's full sovereignty over the Duchy of Prussia.
Hilbert, the first of two children of Otto and Maria Therese (Erdtmann) Hilbert, was born in the Province of Prussia - either in Königsberg (according to Hilbert's own statement) or in Wehlau (known since 1946 as Znamensk) near Königsberg where his father worked at the time of his birth.
The treaty consisted of several agreements, including the Treaty of Wehlau signed on 19 September 1657 by the Brandenburg-Prussian and Polish-Lithuanian envoys in Wehlau (Welawa, now Znamensk).
Instead of marching on Wehlau, as was expected, he ordered his forces to cross the Pregel River in safety, near the village of Gross-Jägersdorf (Abandoned in 1945 and away 5 km southwest from Mezhdurechye (Norkitten) and placed on municipality of Svoboda (Jänischken, Jänichen between 1938–1945) in Chernyakhovsky District).