From the dawn of time, mankind has looked to the heavens and wondered Are we alone? Our desire for galactic companionship is so strong that we are universally given toward imaginary friends. These interstellar neighbors come in various forms. Some reside in magnificent halls high atop mountain peaks. Others float upon fluffy nimbus clouds in the ultimate gated community. Still others sail about the universe in search of new an exotic orifices to probe. Thus far, these neighbors of ours have proved to be reclusive to say the least. They appear only to the few of us deemed worthy. Worthiness, though, does seem to be subject to a certain degree of relativity. The chosen are selected for their great deeds, their royal lineage, or their wisdom. Other selectees are marked primarily by ownership of a pick-up truck, distinct absence of teeth, and a fundamental lack of language ability. Regardless of the criteria, one thing is constant, we are always on the receiving end of the introduction.
In the age of science, we are trying to change all that. The SETI project, made famous by Carl Sagan's Contact, is keeping an eye out the window for visitors. They are our neighborhood watch and welcome wagon rolled into one. No the universe, of course, is a big place, and we can't look everywhere at once. In an effort to streamline the process, these scientists have to make a lot of guesses. They use their best estimates to guide them, which means excluding some possibilities in favor of others. Despite constant setbacks to our self-esteem, humans tend to be a fairly arrogant species. Even now, in an age when cosmologists are reluctant to place much significance on us at all, the anthropic principle heralds us as unique. We use evolutionary metaphors like ladders and trees, firmly placing ourselves on the highest branches and rungs. In our minds, we are the paradigm by which sentient life ought to be measured.
So we look for class M planets, those that are the most Earth-like. They have a similar temperature range and relative position to a star. The have liquid water and atmosphere. These are the parameters of life. Or are they? Now that science has discovered terrestrial organisms thriving in temperatures well beyond those thought conclusively deadly, and others living deep within the earth eating rock or digesting chemicals thought universally poisonous, how will that affect our search of the skies? Will be recognize a silicon based life-form if we happen upon it? What safeguard can be taken so that we don't overlook our target due to faulty assumptions?
Fortunately, the folks at SETI have a pretty powerful redundancy built into their system. It is the language of mathematics. Despite what science fiction would have us believe, it is unlikely that their are races of humanoids skipping about out there. There is only one hope of a Universal Translator, and that Rosetta Stone is going to be the science of patterns. Any form of life with the technology to send a signal powerful enough to reach us must possess a system of advanced mathematics. That system will be one that we can recognize. It may have more power than ours does, but it will be just as true for us as it is for them. They will not add 2 plus 2 and get 5.
There will be superficial differences, of course. There is no reason to believe that they will use a base-10 system. Even here, we have used base-12, base-60, and with the advent of computers, base-2. This is a minor discrepancy, and is easily overcome. Beyond that we can expect the math to be the same. How can I be so sure? Isn't our mathematics largely a function of how we perceive the world? Yes, and no. Our senses are the windows through which we see the world, and there is no reason to think that alien life would see the world exactly as we do, or for that matter to "see" the world at all. The real question is, could a life form achieve sentience without developing an accurate depiction of the world in which it was evolving. The answer is no. As long as we are talking about life that inhabits a three-dimensional world, we are talking about life that can see, hear, touch, taste, and smell.
At this point, you may feel my arrogance is beginning to show. I will explain. When I say "see," I mean detect electro-magnetic radiation. It may not be in the same range of the spectrum that we think of as being visible. They may have an analog to "bee purple." They may even be able to see the fields themselves, like electric eels or platypuses. When I say "hear" and "touch," I mean sense pressure waves through fluids and solids respectively. When I say "taste" and "smell," I mean assess the chemical components of matter. They may perceive these things differently than we do. They might "see" sound or "smell" time. But regardless of how they paint their picture of the world, it will have to be accurate enough for survival, and that means pattern recognition, and that means math. For life to evolve, each generation has to get better at passing on its genes. That amounts to finding food, avoiding predators, and sometimes locating a mate. All of these things require an internal map of three-dimensional space, and as long as their world occupies the same unbounded three-spherical space that ours does, we can rest assured that their math will be the same as ours.