Stars don't get much more charismatic than Alpha Centauri, as evidenced by the recent announcement of the $100 million Breakthrough Starshot Initiative that aspires to "allow a flyby mission to reach Alpha Centauri in just over 20 years from launch."
Hopefully there'll be a "there" there when the mission barrels through. The current Metaculus odds are running 1 in 3 that a potentially habitable planet will be detected by 2020 in orbit around either Alpha Cen A or Alpha Cen B.
But what about Proxima Centauri? At a distance of 4.25 light years, this binocular-ready red dwarf is currently the closest star to the Sun. It orbits the central Alpha Centauri AB binary with a period of roughly a million years. No planets have been found to orbit it... yet.
The Pale Red Dot consortium has recently used the HARPS instrument to obtain 60 nights of ultra-high precision Doppler radial velocity measurements of Proxima. As explained in detail on the consortium's website, they are following up on a tantalizing Doppler signal that might be due to a terrestrial planet with a mass not dissimilar to Earth's, and an orbital period P>10 days. As of April 1, 2016, they report that their observations are complete, but no news of results has yet emerged.
Prior to Dec. 31, 2017, will a paper appear in the peer-reviewed astronomical literature that announces the detection of a planet orbiting Proxima Centauri?