Some astronomers in California claim to have found evidence of a ninth planet* in our solar system. It’s pretty cool if this is true, and it’s all down to maths.
Uranus was not “discovered” as such- astronomers knew it was there but did not know it was a planet until 1781 when William Herschel noticed that it had changed its position over the course of a few days.
After Uranus was discovered (or, rather, confirmed to be a planet), astronomers set about predicting its path in the night sky. The predicted path took into account the pull of gravity by the other planets, and by the sun, but they noticed something peculiar- the observed path did not match any of the predicted paths.
Based on calculations surrounding the anomalies in Uranus’s orbit, astronomers were able to predict the orbit of a planet beyond Uranus and spent the summer of 1846 looking for it- eventually they found it in September of that year, 1 degree out from where frenchman Urbain le Verrier predicted.
However, they felt that Neptune alone could not be affecting Uranus’s orbit, so they searched for another planet- and ended up discovering Pluto. However, they found that Pluto’s mass was not large enough to be causing the extra wobbles in Uranus’s orbit- it was not found out until late in the 20th century that Neptune’s mass was not as big as they thought, meaning Uranus’s wobbles were explained.
This is not just confined to our solar system- by looking at wobbles in the paths of stars, astronomers can ascertain if there is a large planet orbiting it, and can then point their telescopes at it to check out its mass, atmosphere, and so on.
So, maths, and not necessarily direct observation, is used to locate planets, and that’s what’s happened here. The orbits of some of the dwarf objects beyond Pluto do not appear to be entirely normal, so the astronomers have simulated what would happen if there was a planet with a strange orbit affecting them, and this appears to be a feasible solution.
However, they haven’t seen it yet. There might be any number of reasons for the weird orbits, but if they do find another planet in our lifetime, that would be pretty awesome.
*I’m afraid Pluto is not a planet- I’m sorry that the International Astronomical Union has ruined your mnemonic, but it’s only 7% of the mass of all the objects in its region, which disqualifies it.