Galileo saw Neptune in the winter of 1612 and wrote it down as a background star. John Herschel saw it in 1830. James Challis saw it twice in August 1846 during a secret search and logged it as a star. This episode tells the story of how the eighth planet was finally recognized, not through a telescope but through pen-and-ink mathematics, when two men working independently, the shy Cambridge student John Couch Adams and the assertive French astronomer Urbain Le Verrier, reverse-engineered the position of an unseen world from the unexplained wobbles in Uranus's orbit.

We cover Alexis Bouvard's failing prediction tables, the frightening possibility that Newton's laws broke down at great distances, and the brutal inverse problem both men solved by iterating guesses seeded with Bode's Law. We follow George Airy's hush-hush British search, Le Ve ...