From the Heidelberg Laureate Forum:
"Awarded the Fields Medal 'for his work in algebraic geometry, including the resolution of certain singularities and torus imbeddings with implications in the theory of analytic functions, and complex and Kähler manifolds.'…
Hironaka focused his efforts on algebraic geometry. His heart was caught by one problem in particular, the resolution of singularities. It was the fruit of those efforts with the resolution of singularities that landed him at Harvard in 1957 to study under Oscar Zariski… A standout bond that he forged was with Alexander Grothendieck, who received the Fields Medal in 1966. Grothendieck encouraged him to come to Paris and their collaboration made great steps towards to Hironaka being able to prove the problem of resolution of singularities…It was Hironaka’s induction skills and selectively compiling the knowledge he had acquired in Kyoto, Cambridge and Paris that eventually led to his proof."
Fields Medalist, 1970