A planet was found by pure mathematics before anyone pointed a telescope at it

In the 1840s, astronomers noticed Uranus wasn't orbiting quite where Newton's laws predicted. Urbain Le Verrier calculated where an unseen planet's gravity would have to be tugging at Uranus to cause the deviation, and sent his prediction to the Berlin Observatory. On the first night astronomer Johann Galle looked, in September 1846, he found Neptune within about one degree of Le Verrier's predicted position.

— Urbain Le Verrier, Discovery of Neptune — Comptes rendus de l'Académie des sciences, 1846