The beautiful Polish student, Marie Sklodowska (1867-1934) (Greer Garson), is the only woman graduate student studying physics in Paris. She attracts the attention of her kindly professor by fainting in class. A father of two daughters, the professor realizes that she is both brilliant and poverty-stricken. He offers her a paid research project, and, without revealing her sex, arranges for her to occupy space in the laboratory of absent-minded Professor Pierre Curie (1859-1906) (Walter Pidgeon).

At first, Curie is annoyed by her presence, but he soon realizes that she is immensely gifted. When she decides to leave Paris (and physics) after standing first at her graduation, Curie is horrified and clumsily proposes marriage to stop her. Their union will be based on respect, reason, and physics, he claims, and she accepts. With his support, she embarks on an obsessive project to isolate what, she realizes, must be an unknown element in the compound pitchblende--a substance that emanates rays like light.

Four years of intense labor with few resources, inadequate facilities, incidental child-bearing, the threat of cancer, and many disappointments lead to the isolation of a minute quantity of radium in 1898. The Curies share the 1903 Nobel prize in physics with Henri Becquerel. Their future seems assured, but tragedy soon strikes: the distracted Pierre is run over by a horse-drawn cab and dies instantly.

Madame's grief is powerful, but she recalls her husband's prophetic words and returns to work. In the final scene, the elderly Madame Curie, now twice Nobel laureate (1911 chemistry), delivers an inspirational lecture on the promise of science to help "mankind" by curing and preventing disease, famine, and war.