Hironaka initially studied physics, chemistry, and biology, but his third year as an undergraduate, he chose to move to taking courses in mathematics.

The group, informally known as the Akizuki School, discussed cutting-edge research developments including the resolution of singularities problem for which Hironaka later received the Fields Medal.

[5] Hironaka's algebra background, developed under Akizuki, allowed him to bring fresh insights into mathematics discussions in Harvard, which placed a greater emphasis on geometric perspectives.

In 1958–1959, Alexander Grothendieck visited Harvard University and was another important influence on Hironaka, inviting him to the Institut des Hautes Études Scientifique (IHES) in Paris.

Then, soon after getting his first teaching position at Brandeis, he realized that if he combined his commutative algebra experience from Kyoto, geometry of polynomials from Harvard, and globalization technique from IHES, he had everything he needed to solve the problem.

[3] In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.

[10] Hironaka received a Fields Medal, the highest honor in mathematics, at the International Congress of Mathematicians at Nice in 1970 at 39, just under the 40 year age limit.

[15] Hironaka married Wakako Kimoto in 1960, a Brandeis Wien International Scholar who entered Japanese politics through her election to the House of Councillors in 1986.