The “artificial mathematician” objection: Exploring the (im)possibility of automating mathematical understanding

Abstract

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice-not just as a method of inquiry but as a fellow inquirer.