The Rydberg formula is emblematic of atomic spectroscopy. We review here the personal background, research accomplishments, and academic career of its discoverer, Janne Rydberg. Although his formula is often introduced as a generalization of the hydrogenic Balmer formula, Rydberg's work was independent of Balmer's, and displayed great ingenuity and a rare ability to recognize hidden patterns in complex numerical data. Although his discoveries attracted wide attention, experimental physics was then considered inseparable from measurement, and the fact that Rydberg's insightful formulations used the data of others impeded his academic career. Although Rydberg did not live to see the full theoretical implications of his discoveries, the vigorous study of Rydberg atoms continues today.