Neptune was discovered using Math in 1831. After Uranus was discovered in the late 1700's Astronomers notices that it was being pulled out of it's orbit. John Couch Adams of Britain and Urbain Jean Joseph Leverrier of France, used mathematics to predict that the gravity from another planet beyond Uranus was affecting the orbit of Uranus. This gave Astronomers something to look for and the planet was later discovered with a telescope.
You may enjoy:
Discovering Neptune
https://www.youtube.com/watch?v=uzhvAKQ8ng8
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