Using the current definition of a planet, Uranus and Neptune are the only two Solar System planets that were discovered
. Mercury, Venus, Mars, Jupiter and Saturn are all visible to the naked eye and have been known since prehistory.
Uranus was discovered by William Herschel
in 1781. It was the first planet discovered by telescope, and the only planet named for a Greek god rather than a Roman god.
It's often said that Neptune
was the first planet discovered mathematically. Using a telescope, Johann Galle actually found the planet, but he searched the area where Urbain LeVerrier had calculated it would be. Interestingly, a number of people had, in fact, seen it before, but not realized it was a new planet.