What is mathematics? It's neither physical nor mental, it's social. It's part of culture. It's part of history. It's like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That's what math is.

For mathematician Reuben Hersh, mathematics has existence or reality only as part of human culture. Despite its seeming timelessness and infallibility, it is a social-cultural-historic phenomenon. He takes the long view. He thinks a lot about the ancient problems. What are numbers? What are triangles, squares and circles? What are infinite sets? What is the fourth dimension? What is the meaning and nature of mathematics?

In so doing he explains and criticizes current and past theories of the nature of mathematics. His main purpose is to confront philosophical problems: In what sense do mathematical objects exist? How can we have knowledge of them? Why do mathematicians think mathematical entities exist forever, independent of human action and knowledge?