High School Identities

Abstract

In 1969, Polish mathematician and logician, Alfred Tarski asked if all the identities true in the set of natural numbers involving the constant 1, addition, multiplication, and exponentiation can be derived from the eleven axioms that are taught at the high school level (High School Identities). In 1981 Alex Wilkie negatively solved this problem by constructing an identity that cannot be proved using these axioms. In this paper we survey results connected with Tarski’s problem.