Andrew Gleason, professor *emeritus* of the Mathematics Department, perhaps best known for his contribution to solving Hilbert’s Fifth problem, died Oct. 17 of complications following surgery. He was 86. Shing-Tung Yau, chair of the department, said, “Andrew was a great mathematician who solved many important problems in mathematics. He also provided a great service to the University as chairman of the Society of Fellows and as chairman of the department for a period of time. One-time president of the American Mathematics Society, he was a leader of the world’s math community. He trained countless graduate students, and proved an inspiration to them and others.”

Born in Fresno, Calif., Andrew Mattei Gleason moved with his family to New York while he was in high school. After graduating from Yale University in 1942, he enlisted in the Navy and served as a cryptanalyst during World War II, seeking to break Japanese and German codes. He re-enlisted in 1950 and served as a code breaker in the Korean War for three years.

“Many mathematicians were code breakers, because it took a mathematical mind,” said his wife Jean Berko Gleason, whom he married in 1959.

In 1946, Gleason was appointed a Junior Fellow of the Society of Fellows, a select group of young scholars who are given three-year fellowships to pursue their studies without formal requirements at Harvard.

During this period, Gleason set about solving Hilbert’s Fifth, a problem that mathematician David Hilbert formulated in 1900. Gleason solved a key aspect of the problem with three others, winning the Newcomb Cleveland Prize from the American Association for the Advancement of Science in 1952.

By solving the problem, Gleason and his team made a tremendous advance in the understanding of symmetries, which are the basis of Hilbert’s Fifth, said Clifford H. Taubes, former chair of the Mathematics Department.

“His biggest contribution was to solve this problem,” said Taubes. “Solving the problem said things were simpler than they could have been. Now [other mathematicians] … can focus on other parts of symmetry.”

In 1969, Gleason was named the Hollis Professor of Mathematics and Natural Philosophy, an endowed chair at Harvard.

He served as head fellow of the Society of Fellows, helping select junior fellows from 1989 to 1996. He taught mathematics at Harvard until he retired in 1992.

Gleason also worked on developing new mathematics curricula for students, particularly calculus courses. He was concerned with how children learn, as well.

“He loved working with children; he was always engaged in math curriculum reform. He was interested in how children thought. He wanted children to understand how mathematics worked,” Jean Gleason said.

Gerhard Gade University Professor Barry Mazur said of his longtime colleague, “His ardent interest in basic things — in things that really matter — his intellectual generosity, and the clarity of his thought, made a deep impression on everyone who knew him.”

Shlomo Sternberg, the George Putnam Professor of Pure and Applied Mathematics, recalled Gleason warmly: “Andrew Gleason was a world famous mathematician by the mid-1950s. Among mathematicians he was famous for his contribution to the solution of Hilbert’s Fifth problem. Among theoretical physicists and philosophers concerned with the foundations of quantum mechanics, he was famous for ‘Gleason’s theorem,’ elucidating a key point in quantum logic.

“So when my wife, Aviva, and I arrived at Harvard in 1959, we were a bit in awe of him. But Jean and Andy Gleason were very warm and kind to us over these many years, and we frequently turned to them for sagacious advice. Andy had a very broad range of interests including mathematics education at a national level. We will miss him, and we extend our sympathies to Jean and to their daughters.”

Among his many interests, Gleason had a passion for astronomy. “He loved looking at the stars. He knew every star in the sky and could tell you their names,” Jean Gleason said. “Early on, he was planning on becoming an astronomer but then he learned how cold it was” to sit outside and watch.

In 2006, Gleason sailed along the coast of Turkey to see a solar eclipse and also traveled to the United Kingdom, France, and Kenya to view celestial events.

In addition to his wife, Gleason leaves three daughters: Katherine of New York, Pam of Wagener, S.C., and Cynthia of Framingham, Mass.; and a sister, Anne Eudey of Walnut Creek, Calif.

A memorial service is scheduled for Nov. 14 at 2 p.m. in the Memorial Church, Harvard Yard. A reception will follow at Loeb House, 17 Quincy St., from 3 to 5 p.m.