paper, science fact is proof written on paper with a bit of maths to wrap it all up, but be aware proof is not a synonym for true.
No no no, definitely not. You need the experimental proof as well.
highly highly improbable due to the maths for everything being right for life to exist
The maths works in the other direction. From the sheer number of stars and planets expected, it seems almost a certainty that life should exist, even with incredibly unlikely planets required to support it.