The Fermi Paradox

The Fermi Paradox was officially developed in 1975, after Physicist Enrico Fermi pointed out the seeming contradiction between the scale of the universe and the lack of visible Alien civilizations. This was mathematically represented in Drake's Equation, which attempted to represent all the variables necessary to reach an interstellar civilization, and calculate the likelihood of finding such a civilization.
Drake's equation includes

The rate of star formation,
The fraction of stars that have planets,
The fraction of planets that can support complex molecules,
The fraction of planets that develop life,
The fraction of life that develops to intelligence,
The fraction of intelligent life that develops detectable civilization.

The original estimates with Drake's variables predicted as many as 100,000,000 million and as few as 1,000 civilizations in the Milky way. Later estimates would put the number between 1 out of 10^-12 and 10⁹ civilizations in the Milky way. Given the large variability in the estimates, extensive efforts have been made to streamline the equation. The Fermi institute was founded in Sharanov crater on the far side of the moon for just such a purpose, equipped with a 30 Km liquid mercury telescope nestled in the large crater. This telescope performed a deep survey of nearly the entire Milky way, gathering information on an estimated 84% of the stars in the galaxy. The information from these 337 billion stars varied widely, and of those stars 11% are considered 'unknown circumstances' and merit further investigation. 3% of those planets are classified as 'extreme anomalies' and require intensive study. This means that there are over 1 billion stars in the milky way have unknown circumstances, and warrant extended observation. Since the survey was completed in 346, nearly 20,000 of these 'extreme anomaly' stars have been investigated. Of those, 600 have been investigated an yielded unclear results, and 27 mission have been begun to visit these stars.

Due to the continued lack of clear evidence of alien civilizations, most scientists agree that Humans have arisen very early to the galactic stage, and that civilizations are morel likely to develop in the later years of a galaxy. Most other galaxies intensely observed by telescopes have yielded similar results to the Milky way. General consensus put the chance of observing a civilization any given year (according to the modernized Drake equation) at less that 1 in a trillion per year. This will likely increase dramatically in a few million years.