It’s a tie between John Couch Adams of England and Urbain Le Verrier of France. Both believed that there must be an eighth planet pulling Uranus away from its predicted positions and both were using mathematical methods to correctly predict where this new planet should be. This being an era before email, telephones or even the telegraph, these two men were able to find Neptune completely independently before ever learning about each other’s work! Since they discovered Neptune without knowing about each other’s work, they now share credit for the discovery.
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