[1] Szmydt studied at the University of Warsaw in clandestine classes during World War II.

In her 1951 paper, Sur l’allure asymptotique des intégrales des équations différentielles ordinaires, Szmydt applied the topological method by Ważewski to generalizations of Perron's classic results on the asymptotics of systems of solutions of ordinary differential equations.

[4] Szmydt's work on hyperbolic differential equations Sur un problème concernant un systèmes d’équations différentielles hyperboliques d’ordre arbitraire à deux variables indépendantes (1957) proposed a generalised solution for the functional differential equation, which subsumed the Darboux, Cauchy, Picard and Goursat problems as special cases.

[6] Szmydt's textbook Fourier Transformation and Linear Differential Equations (1971) was the first on the topic to be published in the Polish language.

[9] In 1956, Szmydt won the Stefan Banach Prize of the Polish Mathematical Society for her research into topological methods in nonlinear ordinary differential equations.