what would be the point in trying to contact them? If they exist they will be so far distant as to make any form of meaningful dialogue an impossibility.
To illustrate the point, the closest star to us (apart from the sun) that experts believe could have orbiting planets is Alpha Centauri B, which is 4.37 light years away. If a planet did exist in the Alpha centauri system (A big 'if'), and if it was inhabited by life forms (an absolutely huge 'if') that were intelligent enough to have developed radio communication (an almost unimaginably vast 'if') it would take decades to have any kind of a meaningful dialogue.
It's fine for Stephen Hawking to speculate, but let's not lose sight of the fact that even if we did detect life forms on a distant planet the chance of them having developed to the extent where we could communicate is so remote that it's impossible to estimate. That isn't to say that we shouldn't try, and indeed we have been trying for a long time - without any result whatsoever. As far as we've bee able to tell so far there are no radio transmissions that could be originating from an intelligent life form anywhere in the galaxy.
Life might exist in other galaxies of course, but the nearest galaxy to us is a small one ('small' in this context is around 1 billion stars) which is 25,000 light years from our solar system.
That means that even a short radio conversation would take hundreds of thousands of years. hundreds of generations would have lived and died before a response to our first transmission arrived.
Using a mathematical mind to think about aliens is fine, but that's about as far as it's likely to go. When I last looked the evolution of intelligent life didn't seem to have that much to do with mathematics anyway - it was all a matter of luck and trial and error as far as I can see.