The benefits to Saudi Arabia from these relationships are clear. The kingdom gets access to the brain trust of America’s top academic institutions as it endeavors to modernize its economy, an effort Prince Mohammed has named Vision 2030. Perhaps as important, the entree to schools like M.I.T. serves to soften the kingdom’s image. Saudi Arabia is an absolute monarchy, hostile to women’s and L.G.B.T.Q. rights and without protections for a free press or open expression, but its associations beyond its borders can make it seem almost like an honorary Western nation. Another way to view the Saudi relationship with American universities is as a form of branding; its recent moves to sponsor prominent sporting events serve the same purpose. “It’s a way of spreading soft power,” says Jordan, the former ambassador, “in the same way the U.S. has done for years around the world.”

On his trip to Cambridge last year, Prince Mohammed spent a full day along the two-mile corridor that is arguably America’s most hallowed academic ground. After the morning at M.I.T., he made the short trip in his motorcade to Harvard, where he participated in what was called a faculty round table, followed by a reception with local college presidents.

No one asked him about Yemen or about much of anything else. An administrator at Harvard who helped arrange the crown prince’s event there described it as “a show, a meet-and-greet — there was not a big give-and-take or an opportunity for questions.” It was a repeat of how Prince Mohammed spent his time at M.I.T. “They asked to come, and we agreed to host them,” says Richard Lester, the associate provost. I asked if he knew the reasons for the crown prince’s visit. “I think one of them undoubtedly was that there was a P.R. value associated with the visit,” he said. “And they may have also been genuinely curious about what we do here.”

Administrators at universities with ties to Saudi Arabia emphasize their role as a liberalizing influence. The University of New Haven, a private school that has a criminal-justice program, helps educate Saudi law-enforcement officers. The program has come under scrutiny because of the kingdom’s notoriously harsh and autocratic justice system. New Haven’s president, Steven H. Kaplan, told me that his institution had created a curriculum based on American constitutional law that would make Saudi students less likely to be involved in any activities like rounding up, torturing or executing dissidents. “We are helping implement the kind of change that will instill in citizens there the kind of values that would cause them to resist and oppose such horrible acts,” he said. He acknowledged that he had no way of knowing for sure what activities students were involved in once they graduated.

To critics, the universities are selling their good names. Sally Haslanger, an M.I.T. philosophy professor, refers to the university conferring “symbolic capital” on the Saudi regime. “M.I.T.’s name, integrity, credibility and scientific excellence have power,” she told me, “and we have used it to burnish the reputation of Mohammed bin Salman and his regime.”

On a Frigid night in late February, about 100 people filed into a basement auditorium in the Cambridge Public Library for a program titled “Whose University Is It?” Two dozen speakers, a mix of professors, students and community members, addressed a range of what they considered dubious relationships between local universities and foreign or corporate interests. Halfway through the evening, Ruth Perry, a professor of literature at M.I.T., led the crowd in a version of the folk anthem “Which Side Are You On?” with lyrics she had rewritten for the occasion. One verse went: “A crown prince comes to visit/To take us by the hand/No partnering with killers/In Middle Eastern lands.” Another verse said, “Our schools get Judas cash.”

The debate over Saudi involvement in American higher education echoes the movement a generation ago that pushed universities to divest from apartheid-era South Africa, and more recently, calls from some quarters for schools to disassociate from Israel in protest of its occupation of the Palestinian territories. Faculty members and students — as well as the surrounding communities in urban centers like Cambridge — often want universities to reflect their own sense of moral clarity and outrage. University administrators, in almost all cases, resist.