Where Is Everybody? -- The Fermi Paradox

From the Hubble telescope

The current calculation out there right now regarding how many stars are in our universe come to a gross count of 10 trillion * 100 billion stars (or 1 with 29 zeros after), living in over 200 billion galaxies (and the number keeps getting larger as our technology improves). So we could be talking about 10^24 planets here, and that's just within our own, known universe.

Of course, the question begs to be asked: Are we alone out here? And if not, where are our cousins?

Nearly 50,000 galaxies in the nearby universe detected by the Two Micron All Sky. Source.

I mean, doing the math, if only 0.1% of the currently estimated billion of habitable planets in our galaxy has intelligent life, and of those only 0.1% have beings with an intelligence like ours or higher, that still leaves 1000 possible planets. Just in the Milky Way alone.

Mapping some of the brightest galaxies.
Source

Therefore, it wouldn't be too much of a stretch of the imagination to think that at least, say, two planets in the Milky Way had advanced intelligent life (and if we crudely extrapolate that to the rest of the known universe, it could potentially mean 400 billion planets with advanced intelligent life)!

So I'm asking again, like Fermi did in 1950 (and many others such as Tsiolkovsky even earlier): Where is everybody?

Because the numbers tell us, probability-wise, that we are not alone, and that quite possibly some civilizations out there are much more advanced than we are, especially that many of them are billions of years older than little planet Earth, and therefore have billions of years of evolutionary (and hopefully technological) advance on us. So why haven't we been visited by them yet, and in a categorically undeniable way (for us puny humans)?

This is called the Fermi paradox, because the numbers highly suggest the possibility of higher alien life in the universe, yet none of "the others" have managed to come over here and otherwise made themselves be known to us. Hence the conundrum.

But of course, one shouldn't think that because we haven't officially come into contact with other alien life doesn't mean that they are out there (and there are plenty of theories that give reasons as to why we don't have any irrefutable proof to it).

Check out a lengthier and more detailed explanation of the paradox here (also contains some neat illustrations).