So what’s the best way to prove that intelligent life exists with math? Well it’s still Drake’s Equation, it just needs to be altered a bit and a more planets with the potential to sustain life need to be discovered…and that’s exactly what has been done.

With NASA’s Kepler Space Telescope constantly on the prowl and discovering potentially habitable planets by tracking their transit of stars, astronomers have come to the conclusion that approximately one in every five stars (1/5) possess planets within their habitable zone. Now it’s just about fixing the equation to deal with the other terms that are a bit broad…such as the probability that advanced life will form.

To do this, Adam Frank and Woodruff Sullivan of the University of Washington, simply altered the math. They eliminated the need for the probability of advanced life forming by calculating the odds against humankind being the only advanced civilization in the universe. They eliminated the need to know the longevity of a civilization by formulating the cosmic archaeological question: *how often does intelligent life evolve throughout cosmic history?*

Calling their new equation the “Archaeological form” of the Drake equation, it now looks a bit simpler, like this:

**N**_{ast} x f_{bt}.

_{ast}x f

_{bt}.

Nast, the number of habitable planets, is defined as N_{ast }= N* x f_{p}x n_{p}, where N* is the total number of stars, f_{p}is the fraction that form planets, and n_{p}is the average of those planets circling in the habitable zones of their parent stars. The second term of the Archaeological form equation, f_{bt}, is defined as the likelihood of an advanced technological civilization arising on one of these habitable planets.

The results suggest that humankind is only likely to be unique if the odds of another civilization developing on a habitable world are less than one in 10^{22}. That’s 100,000,000,000,000,000,000,000 in case you were wondering…which is, to say the least, a bit improbable. If you took 10^{22 }habitable planets…the chances are that more than 1 of them will have life. Frank puts it very nicely as well:

“To me, this implies that other intelligent, technology producing species very likely have evolved before us. Think of it this way: before our result you’d be considered a pessimist if you imagined the probability of evolving a civilization on a habitable planet were, say, one in a trillion. But even that guess, one chance in a trillion, implies that what has happened here on Earth with humanity has in fact happened about 10 billion other times over cosmic history!” – Adam Frank