Among the newly elected members are Secretary of State Hillary Rodham Clinton, director Clint Eastwood and musician Sir Paul McCartney.
Chau, who teaches at the University of Chicago, won the Fields Medal in 2010. That is the mathematics version of the Nobel Prize.
Since the prize was founded by the International Mathematical Union in 1936, only three Asian mathematicians had won it before Chau. All were from Japan.
The 40-year-old mathematician received his doctorate degree from Université Paris-Sud in 1997. He returned to Viet Nam upon the government's request to help implement the national 2010-2020 math development program after accepting a professorship at the University of Chicago.
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