  This evocative essay focuses on some landmarks that led the author to the
study of principal curvature configurations on surfaces in $\mathbb R^3$, their
structural stability and generic properties. The starting point was an
encounter with the book of D. Struik and the reading of the references to the
works of Euler, Monge and Darboux found there. The concatenation of these
references with the work of Peixoto, 1962, on differential equations on
surfaces, was a crucial second step. The circumstances of the convergence
toward the theorems of Guti\'errez and Sotomayor, 1982 - 1983, are recounted
here. The above 1982 - 1983 theorems are pointed out as the first encounter
between the line of thought disclosed from the works of Monge, 1796, Dupin,
1815, and Darboux, 1896, with that transpiring from the achievements of
Poincar\'e, 1881, Andronov - Pontrjagin, 1937, and Peixoto, 1962. Some
mathematical developments sprouting from the 1982 - 1983 works are mentioned on
the final section of this essay.
