The first historical steps of radioactivity research offer an excellent opportunity to teach a key concept of modern physics: non-deterministic phenomena. However, this opportunity is often wasted because of historical misconceptions and of the irrational fear of radioactive effects. We propose here a lecturing strategy - primarily for undergraduate students - based on interesting historical facts. In particular, on a key conceptual contribution by Marie Curie, an attractive figure for the young women and men of today. Paradoxically, this milestone is almost unknown, whereas it should contribute to her immortal fame -- perhaps as much as the discovery of radium.