[2] She began teaching in the Physics department of the university in 1950 and defended her PhD there, in 1951, under Sergei Sobolev and Vladimir Smirnov.

[2][3] Ladyzhenskaya had a love of arts and storytelling, counting writer Aleksandr Solzhenitsyn and poet Anna Akhmatova among her friends.

[4] She was once a member of the city council, and engaged in philanthropic activities, repeatedly risking her personal safety and career to aid people opposed to the Soviet regime.

[5] Ladyzhenskaya is known for her work on partial differential equations (especially Hilbert's nineteenth problem) and fluid dynamics.

[2] She wrote a student thesis under Ivan Petrovsky[8] and was on the shortlist for the 1958 Fields Medal,[9] ultimately awarded to Klaus Roth and René Thom.