Robert J. Zimmer, a mathematician who as president of the University of Chicago championed diversity not only quantitatively, in the recruitment of students and faculty, but also by protecting free expression on campus with a protocol that was later embraced by dozens of colleges across the country, died on Tuesday at his home in Chicago. He was 75.

His wife, Shadi Bartsch-Zimmer, a classics professor at the university, said the cause was glioblastoma multiforme, a virulent form of brain cancer.

Mr. Zimmer, who presided over the university from 2006 to 2021, was instrumental in shepherding what became known as the Chicago Principles, a set of guidelines recommended by the Committee on Free Expression, a faculty group he appointed in 2014.

Those guidelines have become a bulwark against what critics perceive as the stifling of academic freedom by colleges where students are able to insulate themselves against discomforting viewpoints — practices that are often lumped together as “cancel culture.”

“Concerns about civility and mutual respect can never be used as a justification for closing off discussion of ideas, however offensive or disagreeable those ideas may be to some members of our community,” the faculty committee concluded.

In August 2016, during Mr. Zimmer’s presidency, the university informed incoming freshmen: “We do not support so-called trigger warnings, we do not cancel invited speakers because their topics might prove controversial, and we do not condone the creation of intellectual safe spaces where individuals can retreat from ideas and perspectives at odds with their own.”

Some campus critics suggested that Mr. Zimmer was motivated by complaints from conservative alumni. But, he told The Wall Street Journal, in responding to a national trend, he was upholding the university’s traditional values.

“What you’re seeing is a kind of drift of discourse,” he said. “You see actions by a lot of people which seem to indicate that they feel that they can, in fact, legitimately stifle the expression of others whose views they fundamentally disagree with.”

Daniel Diermeier, who was the university’s provost when Mr. Zimmer was its president and is now the chancellor of Vanderbilt University, said in an email: “Whether controversies over speakers, policies on disruptive conduct or his refusal to use the endowment for political purposes, the University of Chicago, under his leadership, remained committed to its principles during volatile times and a role model on free expression around the world.”

Mr. Zimmer was a prodigious fund-raiser. During his tenure as president, the university received six gifts of $100 million or more. He oversaw an increase in financial aid for undergraduates and the elimination of loans, as a way to enable students to graduate without debt.

He also initiated an engineering program; invested in graduate studies in humanities, social sciences and the arts; established the Urban Education Institute, which operates a public school in Chicago and conducts research on instruction; and opened satellite campuses in Beijing, Hong Kong and Delhi, India.

Applications to the undergraduate college more than tripled, to more than 32,000 in 2018 from fewer than 10,000 in 2006.

Robert Jeffrey Zimmer was born on Nov. 5, 1947, in Manhattan to Dr. Max Zimmer, a family practitioner in the West Village, and Harriet (Brokaw) Zimmer, who managed her husband’s medical office.

Growing up in a diverse neighborhood, he learned the value of tolerance. Having been raised in the McCarthy era, his son Benjamin said, “when there was one form of cultural suppression, when he saw a manifestation of that from another direction, he thought it was something he should stand up for, particularly at a university where it was part of its foundational ethos.”

After graduating from Stuyvesant High School in Manhattan, Mr. Zimmer earned a bachelor’s degree in mathematics from Brandeis University in 1968 and master’s and doctorate degrees, both also in mathematics, from Harvard University in 1971 and 1975.

“I actually started college as a physics major,” Mr. Zimmer once confessed. “I switched to mathematics when I tried unsuccessfully for 45 minutes to get an oscilloscope to show a sine wave.”

As a mathematician and an author, he specialized in “ergodic theory, Lie groups and differential geometry,” according to a university biography.

He taught at the United States Naval Academy from 1975 to 1977 and began teaching at the University of Chicago in 1977. He was named a full professor in 1980. He also taught for two years at the University of California, Berkeley.

At Chicago, he served as the chairman of the math department, the deputy provost for research and the vice president for research of the Department of Energy’s Argonne National Laboratory in Lemont, Ill., which the university oversees. From 2002 to 2006, he was a math professor and provost at Brown University. He then returned to the University of Chicago as its 13th president.

His marriage in 1974 to Terese Schwartzman, the former director of strategic initiatives for the Urban Education Institute, ended in divorce. In addition to his wife, Professor Bartsch-Zimmer, who is the director of the university’s Institute on the Formation of Knowledge and whom he married in 2011, and his son Benjamin, the chief executive of a biotechnology firm, Mr. Zimmer is survived by two other sons from his first marriage: David, a lawyer, and Alex, a filmmaker. He is also survived by a brother, Richard B. Zimmer; his mother, Harriet (who is 104 and still lives in the West Village apartment where Mr. Zimmer was raised); and two grandchildren.

At the end of the 2021 academic year, while recovering from brain surgery, Mr. Zimmer stepped down as president to become chancellor. He retired and was named chancellor emeritus in July 2022.

As a private institution, the University of Chicago was under no obligation to abide by the First Amendment’s guarantee of free speech. But, Bret Stephens wrote in a New York Times opinion essay in 2017, the real crux of Mr. Zimmer’s case for free speech, offensive or not, was that it was “our salvation from intellectual mediocrity and social ossification.”

According to Mr. Stephens, Mr. Zimmer balked at the notion that unfettered free speech would jeopardize the cause of inclusion because it might upset, among others, some of the people who were seeking to be included.

“Inclusion into what?” Mr. Zimmer had wondered in a speech that year. “An inferior and less challenging education? One that fails to prepare students for the challenge of different ideas and the evaluation of their own assumptions? A world in which their feelings take precedence over other matters that need to be confronted?”

For Mr. Zimmer, the mathematician, that kind of education wouldn’t count.