If her assumptions are correct, the college, with a $42 million operating budget, needs to set aside at least $168 million before it can enroll the next freshman class. This isn’t likely to happen. Dr. Nelson is adamant that the only way out of this conundrum is to cancel that class and merge Hampshire with a much wealthier “strategic partner.” Otherwise, she told a group of prominent alumni, donors and former administrators this week, Hampshire will be forced to close within the next three or four years.

As she explained it, the demographic changes threatening Hampshire’s future are a serious concern to all but the most well-endowed universities. Increasingly, America’s colleges and universities will be competing more and more fiercely for fewer and fewer applicants from a rapidly shrinking pool of high school graduates. This reality has almost every school with an endowment less than $500 million quaking in its boots right now, she said.

Since November, Dr. Nelson has been having secret discussions with potential partners. Perhaps the best fit is the nearby University of Massachusetts at Amherst, a member of the Five College Consortium that includes Hampshire, Amherst, Smith and Mount Holyoke. Students in the consortium can already take classes and use the resources at any of those schools — an arrangement that has been particularly advantageous to students at Hampshire, with its relatively limited curriculum and small library. But whatever the perceived benefits of a merger, nobody denies it would inflict severe pain. Many of the school’s faculty and staff members would probably lose their jobs.

Within the extended Hampshire community, there is emphatic disagreement with the course Dr. Nelson appears to have set. Kenneth Rosenthal, the college’s official historian and its first treasurer, believes it would be a grave mistake for Hampshire to jump into an asymmetrical partnership out of a panicked reaction to the financial challenges of the moment. And he thinks it would be an even bigger mistake for Hampshire to forgo enrolling new students in September, which would ensure the inevitability of a merger.

Mr. Rosenthal points out that Hampshire owns several hundred acres of valuable land that could be commercially developed. “Half the colleges in the country would love to have this kind of problem,” he said. “Plenty of alumni have put Hampshire in their wills, but because the oldest of them are only 66 or 67 years old, they haven’t started dying yet. That’s problematic in the short term, but not in the long term.”

Be that as it may, it seems foregone that Dr. Nelson will soon announce that no new students will be enrolled at Hampshire for the next academic year. Soon thereafter, she will likely propose some kind of lopsided merger with a securely endowed educational institution.

Hampshire’s iconoclastic educational model is widely admired and deservedly praised. Given what lies ahead, however, it is not at all clear how much of the Hampshire philosophy — to say nothing of the Hampshire soul — will survive.

Jon Krakauer is the author of “Into the Wild” and “Missoula: Rape and the Justice System in a College Town.”

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