The search for a ninth planet began in earnest on 23 September 1846, when German astronomer Johann Gottfried Galle directly observed the eighth, Neptune. But depending on who you ask, the eighth planet had actually been discovered 25 years earlier in 1821, when Alexis Bouvard calculated the orbit of Uranus and determined that gravity from a yet-undiscovered large object—presumably a planet—had disrupted it slightly. That large object was Neptune.
The question of whether there was a ninth was definitively answered in 1930 with the discovery of Pluto, and for 76 years attention focused on discovering a tenth. This search turned out to be successful beyond astronomers’ wildest dreams, as evidence began to surface that there may be hundreds of Pluto-like objects in the outer solar system. And that raised a difficult question: do we really want to live in a solar system where there are too many planets to memorize, and most of them are invisible to us?
In 2006, the International Astronomical Union said no. Pluto was reclassified as a mere "dwarf planet" on the basis that it had not cleared debris from its own orbit, a new planetary criterion that would exclude most of the Pluto-like outer solar system objects but none of the other eight planets, and the search for a true ninth planet began again. And here we are.
Right now, our relationship with the elusive ninth planet is roughly the same relationship astronomers had with Neptune between 1821 and 1846: we’ve got good mathematical reason to think such a planet exists, but we haven’t directly observed it yet. The case was made stronger earlier this month when an article was published in Oxford's Monthly Notices of the Royal Astronomical Society, describing how a team of European astronomers led by Spain’s Carlos de la Fuente Marcos discovered evidence in the outer solar system that the trajectories of extreme trans-Neptunian objects (ETNOs)—small, plentiful Pluto-like objects that we might have called planets before 2006—are disrupted by at least two objects that are much larger, objects that very well may count as planets under our current definition. We may be mere months away from discovering a ninth planet and a tenth.
Of course, that discovery, too, may be temporary; if we find too many of these outer solar system planets, we may need to revise our definition of planetary status yet again to exclude them. In other words, the reclassification of Pluto as a dwarf planet has forced us to confront an uncomfortable fact: that any discovery we make that is too disruptive to our system of classification will simply be reclassified into something less disruptive. This makes sense, because the alternative is to impose on ourselves a system we can no longer use, but it also means that there is a point beyond which—scientifically speaking—we are no longer willing to be surprised.