A French mathematician predicted an undiscovered planet's exact location using only math — and astronomers found it that very night.
Neptune was mathematically predicted before it was ever seen through a telescope. Urbain Le Verrier calculated its position so precisely that astronomers at the Berlin Observatory found it within one degree of his prediction after less than an hour of searching on September 23, 1846.
Galileo actually observed Neptune twice — on December 28, 1612 and January 27, 1613 — but mistook it for a fixed star near Jupiter. His notebooks even show evidence he noticed the 'star' had moved, yet he never identified it as a planet or published his observations.
The discovery was only possible thanks to a lucky coincidence: a recently completed star chart called Hora XXI hadn't been distributed worldwide yet, but happened to be available at the Berlin Observatory. Student Heinrich d'Arrest suggested comparing it to the sky, and quickly exclaimed, 'That star is not on the map!'
Astronomer Johann Galle nearly didn't get telescope time that night. Observatory director Johann Franz Encke was celebrating his 55th birthday, but graciously permitted use of their Fraunhofer telescope — leading to one of the greatest discoveries in astronomical history.
The discovery sparked a bitter international priority dispute between France and England. John Couch Adams in Cambridge had independently calculated Neptune's position, but his work was never published or acted upon before Le Verrier's publicly announced predictions.
Irregularities in Uranus's orbit had puzzled astronomers since 1821, when Alexis Bouvard published orbital tables showing the planet wasn't following Newton's laws. The mystery could only be explained by the gravitational pull of an unknown, more distant planet.
François Arago memorably declared that Le Verrier had discovered a planet 'with the point of his pen.' The Royal Society awarded Le Verrier the Copley Medal in 1846, and later gave Adams the same honor in 1848.
Just seventeen days after Neptune's discovery, astronomer William Lassell discovered Neptune's largest moon, Triton — turning one groundbreaking find into two.