Might we be alone in the universe?

I think everyone will (or at least should) agree that:

• There is no evidence of intelligent extraterrestrial life (IEL).
• The Drake equation is a framework for estimating the probability of IEL.
• The Drake equation is a mathematical equation - it is mathematics.
• The Drake equation calculates a probability - probability theory is mathematics.
• The variables that must be plugged into the equation are all rough estimates (some are currently SWAGs) and the resulting probability is thus very crude (even in 2018, but we are improving).
• The very nature of an estimate is that it is part fact and part assumption.

In result, the Drake equation simply gives us mathematical formalism to get an idea on the likelihood that IEL exists.   It is rough and involves assumption but it is mathematical and produces probabilities.

So nobody can (yet) say that IEL exist outside of human beings on Earth.   We are the only known hard evidence of intelligent life.    It is possible we are unique in all that exists.   It is also possible there are other forms of intelligent life somewhere in the cosmos.    Currently we do not have good enough data to state with high confidence how likely it is that IEL exists but we do have a mathematical framework for structuring our calculations.

But it is wrong to claim that the Drake equation is not mathematical or that it is nothing but assumption.   Further, the Drake equation originally used Drake's estimates.   Nowadays the equation is used with more sophisticated estimates (e.g. back in 1961 we had no real idea how large our galaxy much less an idea on how many galaxies exist, the likelihood of exoplanets, etc.).    Stay tuned - the estimates will net improve over time.