Given the extreme age of the universe, estimated to be over 13 billion years old, and the immense numbers of stars contained in it, more than a hundred billion in the Milky Way alone, then, if Sol, our sun, and the solar system are typical, there ought to be an abundance of extraterrestrial civilizations throughout the galaxy and the universe as a whole, many, if not most, of whom would be considerably older and more advanced than earth. If this view is correct, then it seems surprising that there has been a complete lack of evidence as to the existence of these civilizations in the form of probes, space crafts and the like.
The question in this form was first advanced in 1950 by Enrico Fermi (1901-1954), physicist and nuclear power pioneer. This paradox was examined in more detail in 1975 by Michael Hart, the astrophysicist, who concluded that even more intriguing than the absence of physical artefacts was the complete absence of any detection of their radio transmission. His conclusion was that the human race was in all probability the only inhabitants of the Milky Way!
In order to try and answer this seeming paradox, Dr. Frank Drake, pioneer SETI investigator and creator of Project Ozma, the first systematic attempt to search for extraterrestrial intelligence, in 1960, formulated an equation that seeks to evaluate the numerous probabilities involved in a search for extraterrestrial intelligence. The equation, which by its very nature is purely speculative, takes account of such factors as the rate of star formation in the galaxy, the number of stars with planets and the numbers of those planets that are habitable, the number of habitable planets that actually develop life and then proceed to develop intelligent communicating life forms, and the expected lifespan of such civilizations.
Given the speculative nature of the factors that are taken into consideration, it is not surprising that reached different conclusions depending on their starting points. Carl Sagan (1934-1996), astrophysicist and astronomer calculated that there could be up to a million such civilizations in the galaxy while Poul Anderson (1926-2001), one of the greatest names in science fiction, in his book "Is There Life On Other Worlds" postulated a possibly billions such civilizations. On the other hand, Frank Tipler, mathematical physicist and cosmologist, less optimistically, suggests that there might actually be less than one such civilization per galaxy! This conclusion is not as odd as it may seem: we know for a fact that there is one such civilization in the Milky Way, ours; however, that does not guarantee that there are any other such civilizations anywhere else, so that the average numbers of such civilizations per galaxy could easily be less than unity.
Of course, the simplest solution to the paradox would be the success of SETI picking up radio transmissions from an extraterrestrial source, but even the absence of such does not necessarily require pessimism. SETI has only been in operation since 1960, while radio transmissions from earth are barely a century old. If an extraterrestrial civilization some 100 light years away did pick up some of the earliest transmissions from earth and did send a message, it would still be on its way. Further, the galaxy is quite a big place, 100,000 light years or so across. If civilizations are concentrated in the densely populated nucleus of the galaxy, even random radio transmissions made by such civilizations before Homo Sapiens constructed his first tool would still be on its way to the relatively deserted portion of the galaxy that we inhabit.
There is also the possibility that they have contacted us and we simply don't know. A radio message that arrived here before Marconi was born would be of absolutely no use to us in determining whether or not there was intelligent communicating life out there. Or, perhaps, we're simply too technologically backward to decipher whatever form of communication they use. Even Leonardo da Vinci, arguably the most intelligent man who ever lived would be hard put to decipher a radio message; he simply didn't have the tools!
A final thought: perhaps they don't want to speak to us. (Just yet, or ever.)