As a schoolboy, Carl Friedrich Gauss reportedly summed the numbers from 1 to 100 in seconds by spotting a hidden pattern. This episode follows the mathematician from a working-class family in Brunswick, through the support of the Duke of Brunswick, to his breakthrough proof that a regular 17-sided polygon could be constructed with compass and straightedge. We also explore his motto, few but ripe, which led him to keep major ideas like non-Euclidean geometry private.

After the Duke was killed fighting Napoleon’s forces, Gauss became director of the Göttingen Observatory and turned to practical problems. He used least squares to predict the reappearance of Ceres, invented the heliotrope, measured Earth’s magnetic field, and helped build an early electromagnetic telegraph with Wilhelm Weber. The episode also examines his dislike of teaching, the deaths of his first wife and infant son, his second wife’s long illness, and his estrangement from his sons.

• The pattern behind the famous sum from 1 to 100
• How a patron helped a working-class prodigy escape his expected path
• Why Gauss withheld revolutionary work and how that slowed mathematics
• How least squares helped astronomers find Ceres again
• The contrast between his mastery of nature and his troubled family life