Two scientists, Tom Westby and Christopher J. Conselice, have published in the Astrophysical Journal that they have calculated the mathematical odds that their are other intelligent alien civilizations out there in the Milky Way. They made the assumption that such life would need a planet very similar to Earth in order to provide the necessary ingredients for life to evolve. This means the proper distance from a star, the proper size, the proper chemical composition, the right type of star, and the proper planet age. They assume that if these factors are reached then it is likely that life would evolve on that planet. So taking these characteristics together the scientists figured out that there are probably about 36 such planets like that in our Milky Way galaxy based on what we have been finding with our exoplanet hunting endeavors in the last several years. Based on the idea of 36 planets, they then calculated that the nearest of those planets would probably be around 17,000 light years away, assumming roughly uniform random locations of these planets throughout the galaxy. This is way too far away for us to have any hope of contacting them under our current understanding of physics.
The Astrophysical Journal: The Astrobiological Copernican Weak and Strong Limits for Intelligent Life