Italian Enrico Fermi was a remarkable scientist, and one of the leading physicists of the 20th century. He contributed greatly in a number of important areas, including quantum theory and nuclear physics, and was often remarked upon for his gentle modesty. Unlike most physicists, he was a master of both theory and experimentation, and won a Nobel Prize for his work on radioactivity. He sadly died in his early 50s of cancer acquired in the course of his work, but — in an amazing testament to his character — considered that price to be worthwhile.
During a lunch-break at the Los Alamos National Laboratory in New Mexico, Fermi and some colleagues – Teller, Konopinsky and York – got into a light discussion about extra-terrestrials. A few minutes later, Fermi suddenly asked “Where are they?” He did some basic estimates regarding life in the universe, and arrived at the conclusion that Earth should already have been visited many times by aliens throughout history and pre-history, and that they — or at least the evidence of their civilisations — should be clearly visible.

Enrico Fermi -- one of science's genuine heroes.
There are some 250 billion stars in our galaxy, and hundreds of billions times that many visible to us. With so many planets out there, there must be a large number of civilisations in our galaxy alone. The Sun is a reasonably young star, so there could very easily be civilisations billions of years old in our galaxy. Why haven’t they colonized it? At least, why can’t we see the evidence of their passage?
The bottom line is that Fermi’s paradox relies on a large set of assumptions, some or all of which might be false:
(a) That we will recognise aliens or their activities when we see them.
(b) That access to the Earth and its surrounding environment is unrestricted – we may be a ‘zoo’, in effect.
(c) That aliens are not already here unofficially, or that governments would tell us if evidence was discovered.
(d) That the Earth is sufficiently interesting to merit even the slightest alien attention.
(e) That interested aliens could and would locate us in the vast gulfs of space if they actually wanted to in the first place.
(f) That we have been looking for long enough – they may have come 500 years ago, for example.
(g) That an alien civilisation is going to want to expand and explore in the first place.
In other words, the unknowns are just too great. Fermi’s paradox is a base for conjecture, but too narrow to provide any evidence for the non-existence of alien life. Besides, you can’t ever really prove a negative anyway. Occam’s Razor suggests that other intelligent life probably is out there somewhere, but unless it actually drops by openly, or we stumble across it whilst exploring some day, we’ll never be able to say either way for sure.
(Note to keep my publisher happy: bits of this post were taken from my book “The Greatest Puzzles Ever Solved”. The related question was whether people were right to take Fermi’s paradox as proof of the non-existence of intelligent alien life in the universe.)





e) is a huge issue in itself! IMHO all others (except maybe a) – hyperintelligent shades of blue, anyone?) are subservient to that.
See Drake’s equation for all the variables we must accept that Fermi was right about for it to be a true paradox.
Summarized, you need to have the right order of magnitude for; the rate of star formation in the galaxy (tick, known); the number of stars with planets and the number that are habitable (tick: and working on it as we speak although ‘habitable’ is a bit anthropocentric); the number of those planets which develop life (uneducated guess: one data sample to work with) and subsequently intelligent communicating life (same); and finally the expected lifetimes of such civilizations (same again).
And until we have something to work with, I’m not going to call it a paradox: more of a big open plain of a question.
We can see detailed views of thousands of galaxies. Not one of them has a visible artificial structure. That means that in several thousands of galactic lifetimes (that’s about 100 trillion galaxy-years) not one single species has ever built a galactic superstructure.
There are no aliens anywhere. We are alone.