The Japanese government awarded Heisuke Hironaka, Byerly Professor of Mathematics, two cultural prizes Wednesday, including the prestigious Order of Culture.

Hironaka was one of five persons to receive the Order of Culture, which is awarded annually. In addition, the 44--year-old professor was the youngest of ten named "Persons of Cultural Merit," an award that carries a lifetime annual pension of $8,000.

According to Koichi Matsumoto, an official at the Japanese Embassy in Washington D.C., the prizes are "given to those individuals who have made significant achievements in the fields of art or science."

A selection committee appointed by the Minister of Education chooses the recipients, Matsumoto said yesterday.

Hironaka has been away from Japan for the last 18 years except for a visit during the academic year 1972-73 when he was on leave from Harvard. He has been a professor here since 1968.

Hironaka received his B.A. and M.A. degrees from Kyoto University and a Ph.D. from Harvard in 1960, and then taught for eight years at Brandeis University and another four years at Columbia University before coming to Harvard.

Hironaka teaches algebraic geometry and complex analytic geometry.

Discussing his future plans, Hironaka said yesterday, "I like America, but I like life in Japan too. I miss Kyoto very dearly, but I cannot say if I will go back."