Mark Balaguer is Professor of Philosophy, California State University, Los Angeles. His research interests are in philosophy of mathematics and language. Mark’s major book is Platonism and Anti-Platonism in Mathematics. He received his PhD Philosophy from City University of New York Graduate Center.

Balaguer describes mathematics as follows: “Mathematics is very different from what you thought it was when you were in high school. Most people think that mathematics is about solving problems, and they talk about being good at math, so it’s like a skill. But real mathematics is a theory. It is a theory about the world in the same way that physics and biology are. It looks like mathematics is the study of structures. Take the structure of the natural numbers. It starts with zero, then one, two, three and it goes on forever. And we know some basic things about the sequence of natural numbers. Every number has a successor, a unique successor, and, except for zero, every number has a unique predecessor. From these basic laws, mathematicians start thinking about more advanced questions about what this structure is like. They start proving theorems, which are simply claims about the nature of this structure. For example, Euclid proved that there are infinitely many prime numbers [numbers that have no factors or divisors other than one and themselves]. This is completely non-obvious. As you go up, the prime numbers get more and more sparse. And it could have been the case that at some extremely large number the prime numbers just stop. But it turns out that they do not. They go forever. And that’s what Euclid proved.”