33 years of numerical instability,Part I

BIT has played and plays a great role in the development of concepts concerning numerical (in)stability in initial value problems forODE's and related questions. This development is here seen through the looking-glass of the author, who experienced much of its pains and pleasures. The article is based on a talk given in 1981 at the Zürich symposium to commemorate the tenth anniversary of the death of the eminent Swiss numerical analyst, Heinz Rutishauser. The presentation is mainly chronological with a few digressions. Part I ends at the beginning of the stiff epoch.