The Cultural and Evolutionary History of the Real Numbers

The cultural history of the real numbers began with the positive integers. Kronecker is often quoted as saying, "God made the integers; all else is the work of man," by which he meant that the system of real numbers had been erected by mathematicians on the intuitively obvious foundation provided by the integers. Taken as a statement about the cultural history of mathematics, this is beyond dispute. But if this is taken as a claim about the psychological foundations of arithmetic reasoning, then we suggest that here, as in many other areas of psychology, introspection and intuition are poor guides to the inner workings of the mind.