Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability . Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov .
Petrovsky main matematiko trabaho ay sa teorya ng bahagyang kaugalian equation, ang topology ng algebraic kurva at ibabaw, at mga bagay na maaaring mangyari. Petrovsky din nagtrabaho sa hangganan na halaga para sa problema ng init equation at ito ay inilalapat sa parehong bagay na maaaring mangyari teorya at mga gawain ng Kolmogorov.