# Walter Baily, influential mathematician, 1930-2013

Walter Baily, a globetrotting University of Chicago mathematician whose research extended the range of algebraic geometry, died Jan. 15 at the Brandel Care Center in Northbrook. He was 82.

Baily co-authored a seminal concept with Swiss mathematician Armand Borel that introduced what came to be known as the Baily-Borel Compactification. “This is, probably, Baily’s best-known and his most influential work,” said Martin Karel, professor emeritus of mathematics, Rutgers University at Camden.

They first published the concept in the *Bulletin of the American Mathematical Society* in 1964, and then followed up with a more detailed treatment in the *Annals of Mathematics* in 1966. The method is still an important tool for studying certain arithmetic aspects of representation theory and number theory, said UChicago mathematics professor Niels Nygaard.

Baily’s son, Walter Toshi Baily, remembers how his father never tried to stand above others. “He was extremely humble. That’s one of the things I really remember and respect about him,” Toshi Baily said.

Baily also encouraged his students to be independent, noted Karel, PhD’72, who received his UChicago doctorate in mathematics under Baily’s supervision. “While I was his student, Walter offered his advice and ideas to me gently and was patient with me,” Karel said. “Walter and his wife Yaeko warmly welcomed me and entertained me at their home many times.”

Baily was born July 5, 1930, in Waynesburg, Penn. He received his bachelor’s degree from the Massachusetts Institute of Technology in 1952 and his master’s degree and PhD from Princeton University in 1953 and 1955 respectively. He then served a year each at MIT and Princeton as an instructor before moving to Chicago.

“Walter’s admiration for his PhD adviser, Kunihiko Kodaira, fostered a deep love of Japanese culture and the Japanese language, which he spoke fluently,” Nygaard said.

As a graduate student, Baily also honed his ideas in conversations with Salomon Bochner, who spent much of his career on the Princeton mathematics faculty. Karel characterized Bochner as “certainly an imposing figure in mathematics at the time.” When Karel visited Bochner years later, Bochner told him that Baily “would come into his office and ‘think out loud.’”

Baily joined the UChicago faculty as an assistant professor in mathematics in 1957, attaining the rank of professor in 1963. During these years, he traveled often to Japan to give guest lectures. His host during many of his early visits was University of Tokyo mathematician Shokichi Iyanaga, one of Japan’s leading mathematicians.

During one of Baily’s visits to Tokyo he met his future wife, Yaeko Iseki. “Professor Iyanaga acted as the official matchmaker between my mother and father,” Toshi Baily said. The Bailys recently celebrated their 50th anniversary, having married in Tokyo on Jan. 7, 1963.

“For many years Walter and Yaeko maintained a residence in Tokyo and they would spend part of every summer in Japan,” Nygaard noted.

Baily also was a frequent visitor to Moscow and St. Petersburg. “Walter had a great love for Russian culture, music and literature, and he also spoke Russian fluently,” Nygaard said.

Baily was a member of the American Mathematical Society and of the Mathematical Society of Japan. He was a winner of the William Lowell Putnam Mathematical Competition in 1952. His honors also include receiving an Alfred P. Sloan Fellowship in 1958, and giving an invited talk at the 1962 International Congress of Mathematicians in Stockholm, Sweden.

He retired as a professor emeritus in 2005. “Walter was a revered colleague in the mathematics department. He spent many joyful hours of good conversation with his colleagues at the Quadrangle Club, where he was a lifelong member,” Nygaard said.

Baily is survived by his wife, Yaeko Baily, Chicago; his son Walter Toshi Baily; a daughter-in-law, Atsuko Baily; and two grandchildren, Lisa and Emmy Baily, all of Tokyo.

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