Ive never seen a mathematical formula that PROVES alien life exists. Im not saying its impossible, but the only witnesses to alien visits are at best unreliable people with no hard evidence or ancient people that got visits, then the aliens took off and decided to stop intervening for some reason.
Beyond the expanses seperating stellar systems from eachother, we must also consider how old the universe is. We humans have only been looking up at the stars for thousands of years, a blink of an eye compared to the 13.6 billion years the universe has been around. Even if intelligent life exists in our galaxy and even if it can somehow travel fast enough to contact life, the timing would be very limiting. It would be like releasing a hand ful of fireflies across the US, then expect them to find eachother and blink all at the same time. I dont think its impossible, but we may not ever be lucky enough to know