Discovery of Neptune

The planet Neptune is a planet which has been claimed to have been discovered through mathematics alone. Discussions on this topic revolve around a claim that the position of Neptune was predicted and discovered through Newton's Laws of Gravitation, and that it is therefore a confirmation of Newton's theory.

Writer and astronomer Jeffrey Bennett describes this claim (Archive):

Perturbation Theory
According to some sources we find that Neptune was actually discovered, at least in part, on the basis of Perturbation Theory. Perturbation Theory predictions do not use the full laws of Newton, but are based on patterns and epicycles.

https://www.encyclopediaofmath.org/index.php/Perturbation_theory (Archive)

From Perturbation Theory in Celestial Mechanics (Archive) by Dr. Alessandra Celletti we read:

https://en.wikipedia.org/wiki/Urbain_Le_Verrier

See Astronomical Prediction Based on Patterns for information on Perturbation Theory.

Pre-Discovery Observations
Curiously, according to a depiction of its discovery it is described that Neptune was "pre-discovered" and that these observations were "important in accurately determining the orbit of Neptune."

https://en.wikipedia.org/wiki/Discovery_of_Neptune (Archive)

Dishonesty
Science historian Nicholas Kollerstrom states that dishonesty was involved with this claim.

https://en.m.wikipedia.org/wiki/Discovery_of_Neptune (Archive)

Discovered By Luck
Other sources tell us that the planet was discovered by luck.

https://earthsky.org/human-world/today-in-science-discovery-of-neptune (Archive)

http://www.helas.gr/conf/2011/posters/S_5/dallas.pdf (Archive)

https://www.oddsalon.com/jan-2-1860-the-discovery-of-planet-vulcan/

American Journal of Science and Arts
From Vol IV of the American Journal of Science and Arts, November, 1847, we read the following (Archive) from astronomer Sears C. Walker: