Final answer:
Neptune was the first planet discovered through mathematical predictions rather than direct observation, a collaboration of Newtonian physics and mathematics confirming Kepler's vision of a mathematical universe.
Step-by-step explanation:
The first planet discovered via mathematics, rather than direct observation, was Neptune. Historically, the motion of the planet Uranus was observed to deviate from its predicted orbit based on known gravitational forces.
This discrepancy led to the hypothesis of another distant planet exerting its influence on Uranus. Mathematicians and astronomers, such as John Couch Adams and Urbain Le Verrier, independently calculated the expected position of the new planet.
Adams provided his predictions in 1845 to the Astronomer Royal, George Airy. Although the follow-up was delayed, ultimately, Neptune was found very close to the predicted position.
This event marked a triumphant moment combining Newtonian theory, mathematical computation, and observational astronomy.
This method of discovering celestial bodies through calculations continues today in the search for planets around other stars.
Specifically, Neptune's discovery showcased the power of mathematics and physics when applied to the mysteries of the universe, validating Kepler's belief in a mathematically orderly cosmos.