We reconstruct Frédéric Joliot and Irène Curie’s discovery of artificial radioactivity in January 1934 based in part on documents preserved in the Joliot–Curie Archives in Paris, France. We argue that their discovery followed from the convergence of two parallel lines of research, on the neutron and on the positron, that were focused on a well-defined experimental problem, the nuclear transmutation of aluminum and other light elements. We suggest that a key role was played by a suggestion that Francis Perrin made at the seventh Solvay Conference at the end of October 1933, that the alpha-particle bombardment of aluminum produces an intermediate unstable isotope of phosphorus, which then decays by positron emission. We also suggest that a further idea that Perrin published in December 1933, and the pioneering theory of beta decay that Enrico Fermi also first published in December 1933, established a new theoretical framework that stimulated Joliot to resume the researches that he and Curie had interrupted after the Solvay Conference, now for the first time using a Geiger-Müller counter to detect the positrons emitted when he bombarded aluminum with polonium alpha particles.