On Mars, the strong magnetization in the highland crust of the southern hemisphere and the absence of magnetic anomalies at the Hellas and Argyre impact basins have been taken as signs that the core dynamo that once drove the planet's magnetic field turned off more than 4 billion years (Gyr) ago. Here, we argue instead that the Martian dynamo turned on less than 4 Gyr ago and turned off at an unknown time since then. High spatial resolution magnetometry in both Martian hemispheres is needed to reveal the true history of the Martian dynamo.