Note: question text is copied directly from here. This version has an extended resolution date.
In early 2016, two Caltech Professors -- Konstantin Batygin and Mike Brown -- created a major media splash by predicting the existence of Planet Nine, a new, but as-yet unseen planet in the outer solar system. As originally envisioned, their trans-Neptunian world has an orbital period of about 20,000 years and a super-Earth mass more than sufficient to bring the Solar System's planetary inventory back up to nine.
Batygin and Brown's paper, has been downloaded well over half a million times, and presents indirect dynamical evidence for the planet's existence. Its presence is inferred through the gravitational sculpting that it has produced in the trajectories of the most distant Pluto-like worlds that lie beyond Neptune's orbit.
Follow-up papers by a range of authors have added a mixture of credibility, detail, and skepticism to the Planet Nine hypothesis. In the years since the announcement of the hypothesis, Planet Nine has been invoked as an explanation for the generation of highly inclined Kuiper belt objects such as Drac and Niku, it has been argued that it can account for curious orbital commensurabilities among the most distant members of the Kuiper Belt, and it has been hypothesized that it can explain the 6-degree tilt of the planetary orbits relative to the Sun's equator.
The planet, however, remains to be found.
If it does exist, its most likely sky location is probably in one of the two regions of the sky where the Galactic Plane intersects the ecliptic. Confusion from the myriad stars of the Milky Way's disk renders systematic searches difficult in these areas. Nonetheless, new techniques, such as the use of data from NASA's TESS Mission may potentially provide a breakthrough. Additionally, Batygin and co-authors have published an update to their original paper that contains a significant amount of new analysis and remains optimistic regarding the prospects for eventual detection.
Will Planet Nine be discovered before 2030?
For this question to resolve positive, the new Solar System planet must be detected by direct optical observation. The planet should have an inferred radius larger than that of Earth, and an orbital period greater than 5,000 years.