Math has been admitted to be a universal lingua franca through which human would manage to communicate with unknown extraterrestrial civilizations. Since the logic of mathematics is the hard core of any complex world, or say civilizations, scientists have developed multiple theories decoding languages with mathematical algorithm, to prove the feasibility of math as a method to talk to aliens.
There were several achievements in the progress of constructing cosmic languages. Initially, primes were recognized as a almost certainly non-natural origin message which could be a sign of highly intelligence. In 1960, humanity's first attempt of interstellar radio transmission detection was carried out by Frank D. Drake, as the start of Project Ozma. During months of receiving "sounds" from the universe, except for a mistaken alarm due to military experiment, there was no efficient intelligent message or primes message received.
In 1974, human broadcast the most powerful message until then, the Arecibo Message, from Puerto Rico. The broadcast was aimed at targets in the M13, a globular star cluster near the edge of our galaxy, containing 0.3 million stars. Including a concise pictorial content, the message also consists of 1679 bits, 73 lines of 23 characters of 1s and 0s, transmitted by 10 bits per second.
After the pioneer steps of the Arecibo Message, human endeavored to receive radio signals from the and wish to some day hopefully decode them. Although there haven't been any meaningful civilized message that human has ever heard from the galaxy, people are still patiently listening with astronomical radars and equipped themselves with mechanisms of understanding the rationale of alien languages.
Other than being a language, math can also be a tool to estimate the amount of habitable planets, or even active, communicative extraterrestrial civilizations in our galaxy. The famous Drake Equation gave human a general direction of the elements to be aimed at during their observation, though it is still a tremendous technical struggle for current human scientific level.
Additionally, the following equation is based on the Drake Equation for identifying planets where life can generate; the inventors of this equation hoped people's concern about the principles of life be led to the backbone of features of a certain planet.
Mankind had taken wild guesses and coherent theories to assume the likeliness of earthlings with other life forms. Alongside the romantic imaginations and empirical simulations, mankind expresses love for this universe, hoping to one day uncover the mysterious veil of the heavenly bodies, and the transcendental ways of the emergence of life else where in this universe, delicate, intellectual, extraterrestrial.