Interview with Heisuke Hironaka Heisuke Hironaka is one of the premier algebraic geometers of the twentieth century. He is best known for his 1964 work on the resolution of singularities of algebraic varieties over a field of characteristic zero, for which he received the Fields Medal in 1970. The fundamental nature of this problem was apparent to many mathematicians in the first part of the twentieth century, notably Oscar Zariski, who solved the problem for curves and surfaces and had a profound influence on Hironaka. Taking a strikingly original approach, Hironaka created new algebraic tools and adapted existing ones...