Carl L. DeVito, Ph.D., is a member of the emeritus faculty in the Department of Mathematics at the University of Arizona. He has developed one of the most widely cited proposals for a language based on plausibly universal scientific concepts and has contributed to several edited volumes on cosmic communication. His other scientific work includes many papers on pure and applied mathematics and four books: Science, SETI and Mathematics (2014), Harmonic Analysis—A Gentle Introduction (2006), Functional Analysis and Linear Operator Theory (1990), and Functional Analysis (1978).
It has often been stated that mathematics would serve as a universal language, one suitable for communication between totally alien societies. Our purpose here is to examine that statement in detail. We shall see that while mathematics is often motivated by scientific applications, it is equally likely to arise from internal sources, sources that have nothing to do with the world of science. Nevertheless, we argue that human mathematics can be understood by any race that has a science, and can be an effective means of mutual communication. There are a number of “philosophies” of mathematics but, in this connection, the views of only two of these need concern us: Extreme Platonists and Strict Formalists. The difference between them is apparent in how they answer the following question: Are the natural numbers, 1, 2, 3, 4, … merely creations of the human mind or do they exist independently of us? The Platonic view is that these objects, and indeed all mathematical objects, really exist, perhaps in some hyperworld. In this view the mathematician is rather like the scientist. He, or she, discovers objects that are “out there.” So if an alien intelligence exists then they, too, could discover the same mathematical objects that we have found, for instance, real and complex numbers, functions, topological spaces, etc.
The strict formalist, however, has a very different view. To her, or him, mathematics is a kind of game played by specific rules. Somewhat like chess. An unsolved problem gives a kind of goal, and solving such a problem constitutes a “win.” So, to a strict formalist, while five fingers, five cars, and five dollars certainly exist, the number 5 does not. It is a creation of the human mind and an alien, however intelligent, might have no knowledge of 5 or of any other human mathematical object.
My own position is a strange combination of the two. I think the natural numbers do exist independently of us. The rest of mathematics, however, might not exist anywhere but in our minds. But since, as we shall see, all of mathematics can be based on the notion of natural number, all of our mathematics could, in principle, be communicated to any intelligent alien who understands these numbers, certainly to any race whose members can count. It will become apparent, however, that the world of mathematics is not the world of physical reality. It is an artificial world, a world of abstractions and idealizations that human mathematicians have created over many centuries. It may be more reflective of our minds than we realize and may say more about human nature than it does about the real world. Still, one must not forget that human mathematics has an uncanny habit of becoming useful either in explaining some aspect of reality or modeling that reality. So as strange as it might appear to an alien he, or she, or it will be able to appreciate its value.