The discovery of Neptune is a monumental event credited to the collaborative efforts of three key astronomers: Urbain Le Verrier from France, John Couch Adams from England, and Johann Gottfried Galle from Germany. In the early 1840s, astronomers noticed that the orbit of Uranus exhibited irregularities that could not be explained solely by the known gravitational influence of the other planets. This anomaly led Le Verrier and Adams to independently calculate the position of a then-unknown planet that could account for these disturbances. Le Verrier sent his calculations to Galle at the Berlin Observatory, where Galle and his colleague Heinrich Louis d'Arrest utilized a telescope to locate the planet in the night sky. The successful identification of Neptune marked a revolutionary accomplishment for computational astronomy.The actual observation occurred on the evening of September 23, 1846, and occurred shortly after Galle consulted Le Verrier's predictions. This achievement not only validated the methods of celestial mechanics but also strengthened the growing belief in the existence of planets beyond those visible to the naked eye. Such predictions were based on mathematical models derived from Newtonian physics, representing a pivotal moment in the transition towards the application of mathematical reasoning in astronomy. The existence of Neptune was soon confirmed through further observations, proving the efficacy of using gravitation and mathematics to predict the celestial bodies’ positions.