If aliens landed, how would we know? This thought came to me in an aquarium as I was contemplating a sea anemone, an aquatic creature that looks for all the world like a plant. If we can’t easily distinguish a plant from an animal among terrestrial life forms, why do we assume that an intelligent extraterrestrial would be recognizable as such? It occurred to me, in fact, that an enterprising space alien resembling a sea anemone might simply plant himself in a fish tank at the aquarium in order to observe human civilization closeup without calling undue attention to himself.
Apart from recognizing an extraterrestrial when we saw one, how would we communicate? Again, we have only to look to creatures closer to home to appreciate how daunting this task might be. After decades of work trying to communicate with dolphins – which, like humans, have large brains in relation to their body size  scientists have only begun to decipher the sonic “pictures” these creatures transmit to one another using echolocation. There are still numerous ancient civilizations whose writings remain closed to us because we lack the equivalent of the Rosetta Stone that was used to decipher Egyptian hieroglyphs.
Decades of scanning the heavens for radio signals from extraterrestrials have so far garnered nothing but static – but then an advanced civilization might well regard radio as a hopelessly antiquated form of communication. Even if aliens resorted to ancient technology to reach out to those less advanced than themselves, what kind of message could they send with any assurance that it would be understood?
They might well use mathematics as their Rosetta Stone – not only because any advanced civilization would have to be built on math but also because the universe itself is built on it. “God is a mathematician of a very high order,” wrote the quantum physicist Paul Dirac. “He used very advanced mathematics in constructing the universe.” As it happens, Dirac was an outspoken atheist, and the thought was not original with him. Credit Pythagoras, a Greek mathematician and philosopher, who first put forward the idea in the sixth century BCE. Pythagoras, who made important contributions to astronomy, harmonics and geometry (notably the Pythagorean theorem), founded a sacred brotherhood based on the belief that numbers were divine and that they were "the principle, the source and the root of all things.” Another astronomer, Galileo  who first demonstrated that all bodies fall with uniform acceleration – argued that the universe could not be understood except through the mathematical language in which it was written. Johannes Kepler, discoverer of the laws of planetary motion, chimed in, “Geometry is one and eternal shining in the mind of God.” And Isaac Newton, the greatest mathematician of his day and arguably the greatest of all time, said, “God created everything by number, weight and measure.”
Until recently, those who uncovered the mathematical foundations of the universe all concluded that God was a very clever fellow. Einstein did not believe in a personal God but recognized that a higher intelligence operated in the universe. Now, if Dirac and many of his colleagues are any indication, the scientific community tends to regard itself as being very clever for uncovering the mathematical foundations of a universe but deny there is any divine mathematician at work behind the scenes.
So what would happen if we were to suddenly receive a message from the stars containing a prime number or some other mathematical function, repeated numerous times so its meaning were unmistakable? Would we not conclude there had to be intelligent beings out there somewhere? What other explanation could there be? And if God wanted to signal his presence to us, what better way than to construct an entire universe based on mathematical principles? For Einstein, the most incomprehensible thing about the world is that it is comprehensible, meaning that its mysteries can be solved mathematically. But can there be mathematics without a mathematician? It just doesn’t add up.
