''In graduate school," he once wrote, ''I became seduced by the beauties of pure mathematics."

Dry and daunting to non-acolytes, the field for Dr. Mackey held the allure many find in the fine arts.

''He would always talk about mathematics in this aesthetic way," said his daughter, Ann Sturgis Mackey. ''He loved it."

A deep thinker whose work in representation theory, group actions, and functional analysis helped bring closer together the fields of math and physics, Dr. Mackey died March 15 of complications from pneumonia. He was 90, had lived in Cambridge, and was Landon T. Clay professor emeritus at Harvard University.

By his own description a ''gregarious loner" who spent hours alone each day in his study or office, Dr. Mackey was sought out by many to share a meal or a conversation, in part because of his bracing sense of ethics.

''He was a gentle man, but he was the most intellectually honest person I've ever known," said Clifford Taubes, chairman of Harvard's math department. ''He wouldn't let people get away with cozy preconceptions. Here, I'm not just talking about mathematics, but aspects of life, your beliefs. You'd get into these conversations about politics and things in everyday life and he'd say, 'Well, why do you believe that?' You really had to back up what you were saying."

In notes for a eulogy she plans to deliver at tomorrow's memorial service, his daughter wrote that although her father's embrace of honesty sometimes nudged over the boundaries of tact, ''He never wished to be unkind, and would often agonize about how to uphold the truth without giving serious offense."

Dr. Mackey was born in St. Louis. His family moved to Florida, and then to Houston when he was 10. There he remained for 12 years until graduating from what was then Rice Institute. In autobiographical writings, he described each choice that led him to mathematics as a ''compromise" or ''soul struggle." His father wanted him to pursue a career in business. The compromises, spurred by a chemistry book that captured his fancy at 15, involved majoring in chemical engineering, then physics, and finally mathematics as a graduate student at Harvard, from which he received a master's and a doctorate.

''I wanted somehow to combine the logical precision of mathematics with the (apparently) richer content of physics," he wrote in 1982 to one of his daughter's friends, who was herself torn between math and physics.

In a sense, Dr. Mackey split the difference. Dipping into physics, he took aspects of quantum mechanics and placed them ''on firm mathematical footing," Taubes said.

''He was one of these bridge figures who pulled these two fields closer together," said David Mumford, a professor of applied mathematics at Brown University.

Dr. Mackey was elected to the American Academy of Arts & Sciences, the National Academy of Science, and the American Philosophical Society. He lectured widely and taught at other colleges around the world, including as George Eastman visiting professor at Oxford University and Walker Ames professor at the University of Washington. He used a Humboldt Foundation research grant to visit the Max Planck Institute in Germany.

''Mathematical Foundations of Quantum Mechanics," published in 1963, was the most widely known of his several books.

In the written copy of a 1982 speech ''What Do Mathematicians Do?" Dr. Mackey wrote that ''if a non-mathematician listens to these people talk or attempts to read their journals, he confronts an incomprehensible jargon." By contrast, colleagues often hailed his prose as crisp and clear.

Dr. Mackey did not have a telephone in his office or his study at home. He would work on math for 45 minutes of each hour, then read in another field for 15 minutes to cleanse his intellectual palate. He kept a written record of each minute he worked, each penny he spent -- a mathematical version of Thoreau's examined life.

Math, he found, could be applied to other pursuits. He invented what his daughter called a ''numeric notational system" to teach himself piano, and spoke an abbreviated form of French that cleared away the clutter of assigning gender to nouns.

When he became a father at 47, he gave up driving at the request of his wife, Alice, who said ''he had a tendency to go left when right was right."

Each morning and evening he set aside time to read and play games with his daughter and would not allow work to intrude.

''He was a great believer in quality time and he really embraced it," his daughter said. ''When he was with me, he was really, truly with me."

After his daughter went to bed, he would read aloud to his wife while she did needlepoint -- biographies, nonfiction, and the classics of English literature.

''When he was not working, he was totally attentive to the person he was with," his wife said. ''People would say, 'He really listened to me.'. . ."

In addition to his wife and his daughter of Hastings-on-Hudson, N.Y., Dr. Mackey leaves a sister, Madge Mackey Wintz of Houston; and a grandson and granddaughter.

By Bryan Marquard

April 28, 2006 © Copyright 2006 Globe Newspaper Company.