In 1929 Hildebrandt received the Chauvenet Prize for his 1926 expository article The Borel theorem and its generalizations.
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He has received numerous awards, among them the Gordon Bell Prize and Householder Prize (1990), the Chauvenet Prize (1998), the Edgerly Science Partnership Award (1999), the SIAM Activity Group on Linear Algebra Prize (2000), and the Lester R. Ford Award, (2005, with Gilbert Strang).
He has received various awards including the Chauvenet Prize (1993), Fellowship in the Royal Society of Canada (1994), Fellowship in the American Association for the Advancement of Science (2002), an honorary degree from Limoges (1999), and foreign membership in the Bulgarian Academy of Sciences (2003).
In 1993, Bailey received the Sidney Fernbach award from the IEEE Computer Society, as well as the Chauvenet Prize and the Hasse Prize from the Mathematical Association of America.