One by one, the glass ceilings of academia are vanishing. Elizabeth Garrett, president-elect of Cornell University, will become the first woman to lead that school when she takes office in July. But in the Ivy League, such firsts have become almost commonplace.

What may be more significant: Garrett’s ascension will mean women are at the helm of half of the eight Ivy League schools. She joins Christina H. Paxson of Brown University (who took office in 2012), Drew Gilpin Faust of Harvard University (2007) and Amy Gutmann of the University of Pennsylvania (2004).

Garrett said this is no accident. Women are rising in the ranks of faculty and administration at colleges across the country. In 2010, she became the first female provost at the University of Southern California.

“There are more of us in the pipeline to take on these jobs as leaders,” Garrett said Tuesday in a visit to The Washington Post newsroom. She recalled that when she was in law school at the University of Virginia in the 1980s, she had to make a point of hunting for a class taught by a female professor. Now, she said, there are far more women on the law faculty at U-Va. and elsewhere. Women also are making progress, at various rates, in other disciplines.

“It certainly is not a battle that has been won,” Garrett said. “But it is a battle that we’re winning.”

(Worth noting: There were also four female presidents in the Ivy League after Faust took office at Harvard in 2007.)

Garrett, 51, was named to the Cornell presidency in September. She will succeed the outgoing David J. Skorton, who is about to become secretary of the Smithsonian Institution. Garrett is a legal scholar and expert on presidential politics, tax policy and the legislative process. One of the eye-catching lines on her resume: She clerked for the late U.S. Supreme Court Justice Thurgood Marshall. This week, Garrett stopped by the court in a swing through Washington. She met with, among others, Justices Ruth Bader Ginsburg (a Cornell alumna) and Elena Kagan (a former faculty colleague at the University of Chicago). The Cornell Glee Club joined her.

Garrett said she is getting up to speed on Cornell, a complex institution with operations in Ithaca, New York City and Qatar. The university is privately run but has a public mission that traces back to its founding in 1865, under a landmark law that provided federal land grants to establish colleges for agriculture and other practical educational purposes.

“It’s uniquely American in its spirit,” Garrett said of Cornell. She noted that the university admitted women and African Americans in its earliest years. “It has a very profound egalitarianism.”

Garrett said she is enthusiastic about the development of Cornell Tech, a technology-oriented graduate school that will soon occupy a new campus on Roosevelt Island in New York City. A temporary campus opened in Google’s building in the Chelsea neighborhood of Manhattan in 2012. She said it could become “an exemplar for higher education.”

Garrett also offered her views on a few higher education issues.

On student safety, which has become a prominent topic as reports of campus sexual assault are on the rise nationwide, she said university leaders must draw a firm line: “Assault, intolerance, bigotry and harassment will not be tolerated,” she said, pounding a table for emphasis. “Will not be tolerated in any form.” She said Cornell plans to participate in a joint campus initiative with other members of the prestigious Association of American Universities to survey students on sexual assault and other campus climate questions. She said she puts great stock in sexual assault prevention programs, including those that teach bystanders to intervene in troublesome situations.

Regarding Greek student organizations, which have come under scrutiny at Cornell and elsewhere because of hazing and other problems, Garrett noted that she joined the sorority Chi Omega when she was an undergraduate at the University of Oklahoma. She said the public should not overlook that fraternities and sororities provide students with numerous positive experiences, including charitable activities.

Asked about President Obama’s plan to rate colleges on measures of value and access, starting this year, Garrett sounded skeptical. “As it’s currently formulated,” she said, “I’m not sure that it’s structured in a way that will provide meaningful information.” She added: “I do not think this rating system will accomplish what the administration hopes to.”

But she said she supports the idea of providing consumers with better data to navigate the market.

At USC, Garrett worked for a president – C.L. Max Nikias – who declined to join the movement to offer free education through what are known as massive open online courses, or MOOCs. Cornell, though, provides MOOCs through a Web site called edX. The edX venture is overseen by the Massachusetts Institute of Technology and Harvard University. Garrett said that in her new position she will not be against MOOCs. “It’s great that Cornell is experimenting,” she said.