On January 2, 1860, French intellectual Urbain Le Verrier stood before the Académie des Sciences and announced his discovery of a new planet named Vulcan. It was small - about 1/17th the size of Mercury, an already diminutive planet - and was proposed to orbit the sun between it and Mercury. He chose the name Vulcan for the Roman god of fire and volcanos, seemingly apt for what would be an extremely warm planet. The problem is that Le Verrier was no astronomer, instead plying his trade as a mathematician, and had observed Vulcan only in his calculations instead of through a telescope.
It had begun when Le Verrier decided to study the motions of the planets using Isaac Newton’s theories of orbital motion as a guideline. When observing Mercury’s movement around the sun, he noticed slight aberrations in its actual path from the course he and Newton had predicted. After comparing the actual movement against his calculated path, Le Verrier reached the conclusion that the only reason for the difference was the existence of an intermediary planet that was altering the gravitational field affecting Mercury. He had earlier used a similar technique to assume the existence of Neptune, and so it was no stretch for Le Verrier to claim discovery of yet another planet.
Le Verrier’s assumption of Vulcan’s existence wasn’t enough proof for him to go to the press with news of a new planet. Instead, he made it known to the astronomical community that he was on the hunt for this possible planetoid and soon received word from an astronomer thinking he may have seen it. Edmond Modeste Lescarbault, a physician and amateur stargazer, had been observing the sun when he spotted a strange object moving across his viewfinder. He measured its transit and reported the findings to Le Verrier, who soon arrived in person (and reportedly uninvited) at Lescarbault’s home to discuss his observation. It was enough proof for Le Verrier, who soon planned his lecture on Vulcan for the Académie.
The problem, which is immediately apparent to the modern observer, is that we know there is no planet Vulcan (outside of Star Trek, that is) and that Mercury is the closest planet to the sun. Even after announcing the new planet, astronomers still had trouble actually spotting it. Reports of seeing Vulcan were always unverified and it became something of a catch all for explaining unexpected sightings of objects transiting the solar surface. For over 50 years there were claims that it had been seen out of the corner of an eye or by accident while looking for other things, but no incontrovertible visual proof had been obtained. Vulcan, which had been born of mathematics and assumptions, would be ultimately disproven by another mathematician using better formulae.
When Albert Einstein put forth his theory of general relativity in 1915, it was the biggest revision to the way we observe and understand our universe since Newton’s laws four centuries earlier. These new theories also served to address the earlier unexplained movements of Mercury, the ones that had spurred Le Verrier to search for another planetary object. When attempting to predict the orbital path of Mercury in Einstein’s model, the observations matched up perfectly without the need to insert the gravitational pull of some intervening body. In essence, a planet theorized to exist without any direct observation was entirely disproven by a revision to the underlying mathematics. The planet of Vulcan was discovered and undiscovered all in a notebook.