Harvard University struck a respectful but firm tone in a letter to the Trump administration on Monday, arguing that the university and the administration shared the same goals, though they differed in their approaches. It was latest move in an extraordinary back-and-forth between the school and the federal government in recent weeks.

The letter from Alan M. Garber, Harvard’s president, was sent a week after the Trump administration said it would stop giving Harvard any research grants.

Last month, the university took the government to court over what it has called unlawful intrusion into its operations. But on Monday, Dr. Garber’s tone was softer, saying he agreed with some of the Trump administration’s concerns about higher education, but that Harvard’s efforts to combat bigotry and foster an environment for free expression had been hurt by the government’s actions.

Dr. Garber said he embraced the goals of curbing antisemitism on campus; fostering more intellectual diversity, including welcoming conservative voices; and curtailing the use of race in admissions decisions.

Those goals “are undermined and threatened by the federal government’s overreach into the constitutional freedoms of private universities and its continuing disregard of Harvard’s compliance with the law,” Dr. Garber said in the letter to Linda McMahon, the secretary of education.

The university’s response came one week after Ms. McMahon wrote to Harvard to advise the university against applying for future grants, “since none will be provided.” That letter provoked new worries inside Harvard about the long-term consequences of its clash with the Trump administration.

“At its best, a university should fulfill the highest ideals of our nation, and enlighten the thousands of hopeful students who walk through its magnificent gates,” Ms. McMahon wrote. “But Harvard has betrayed its ideal.”

Rolling through a roster of conservative complaints about the school, Ms. McMahon fumed about the university’s “bloated bureaucracy,” its admissions policies, its international students, its embrace of some Democrats and even its mathematics curriculum.

Ms. McMahon referred to Harvard as “a publicly funded institution,” even though Harvard is private and the vast majority of its revenue does not come from the government. She suggested that the university rely more on its own funds, noting that Harvard’s endowment, valued at more than $53 billion, would give it a “head start.” (Much of Harvard’s endowment is tied up in restricted funds and cannot be repurposed at will.)

“Today’s letter,” Ms. McMahon wrote, “marks the end of new grants for the university.”

In Dr. Garber’s letter on Monday, he said that the university had created a strategy to combat antisemitism and other bigotry, and had invested in the academic study of Judaism and related fields. But he said the university would not “surrender its core, legally-protected principles out of fear of unfounded retaliation by the federal government.”

He denied Ms. McMahon’s assertion that Harvard was political.

“It is neither Republican nor Democratic,” he said of the university. “It is not an arm of any other political party or movement. Nor will it ever be. Harvard is a place to bring people of all backgrounds together to learn in an inclusive environment where ideas flourish regardless of whether they are deemed ‘conservative,’ ‘liberal,’ or something else.”

Although Harvard is the nation’s wealthiest university by far, officials there have warned that federal cuts could have devastating consequences on the campus and beyond. During Harvard’s 2024 fiscal year, the university received about $687 million from the federal government for research, a sum that accounted for about 11 percent of the university’s revenue.

The government can block the flow of federal money through a process called debarment. But the procedure is laborious, and the outcome may be appealed. Experts on government contracting said Ms. McMahon’s letter indicated that the administration had not followed the ordinary procedure to blacklist a recipient of federal funds.

Harvard officials are aware that, even if they challenge the administration’s tactics successfully in court, Mr. Trump’s government could still take other steps to choke off money that would be harder to fight.

The federal government often sets priorities for research that shape agencies’ day-to-day decisions about how and where federal dollars are spent. Some academics worry that the government might pivot away from fields of study in which Harvard has deep expertise, effectively shutting out the university’s researchers. Or the administration could simply assert that Harvard’s proposals were incompatible with the government’s needs.

Jessica Tillipman, an expert on government contracting law at George Washington University, said that it can be difficult to show that the government is using a back door to blacklist a grant recipient.

“You basically have to demonstrate and point to concrete evidence, not just a feeling,” she said.

Still, she said, Ms. McMahon’s letter could offer Harvard an opening to contest a protracted run of grant denials.

“It’s not as hard to prove,” Ms. Tillipman said, “when you have a giant letter that said, by the way, we aren’t giving you these things anymore.”

In August 2021, a mysterious package from Sarasota, Fla., showed up in Nicole Archer’s mailbox in Manhattan.

Dr. Archer hurried upstairs to her cramped Chelsea apartment with the thick envelope in hand and tore it open at her dining table, revealing a legal document she had wondered about for months.

She knew that a beloved college professor had bequeathed her something in her will. She was expecting a modest gift — enough money for a fancy dinner, perhaps, or one of the beaded bracelets the professor liked to make by hand.

But when Dr. Archer, 49, saw the number on the last page — $100,000 — she thought there must be a misplaced decimal point.

“I truly, honestly believed that I read it wrong,” she said. “I remember following the number with my finger, making sure I understood how many zeros it was.”

At about the same time, 30 other people across the country received similar letters, sent at the behest of a professor whose class they had taken years earlier.

Over 50 years of teaching art history at New College of Florida, Prof. Cris Hassold had carved out an influential but complex legacy. She referred to her students as her children. She hired them to clean her home — a disturbing hoarder’s den. At times, she humiliated them in class.

But the students who knew her best described her as a singular force of good in their lives. “The cult of Cris,” as one described it, lives on in her 31 favorite students, who inherited her intensity, her quirks and, in the end, her life savings.

A Backdrop of Counterculture

New College, a small public honors college in Sarasota, on Florida’s Gulf Coast, was known for attracting gifted students who could not afford a private liberal arts school but who sought a rigorous course load in a relaxed, sunny environment.

It became a center of counterculture where gender studies courses filled up quickly and students wandered the campus barefoot, experimented with drugs and organized sex parties.

Courses were demanding. Professor Hassold detested textbooks and assigned 150 pages of weekly reading from dense, primary sources by writers and critics like André Breton and Rosalind Krauss.

Inside the dining room of the century-old Old Caples Mansion, which looks out onto palm trees and the vibrant blue hues of the Sarasota Bay, Professor Hassold would draw the shades, shutting out the sunshine in favor of focused darkness. A dozen students each semester would sit around a table for hours, discussing the postwar femme fatale or analyzing a painting’s brushstrokes.

Andrea Bailey, 47, who is now the director of American Women Artists, a nonprofit organization, was confident in her ability to write about art — until she enrolled in one of Professor Hassold’s art classes in 1995. Ms. Bailey kept one especially scathing review of her take on a van Gogh painting.

“Her conclusion that the woman in ‘The Straw Hat’ is an aristocrat is simply wrong,” Professor Hassold wrote in Ms. Bailey’s academic file on Dec. 8, 1995. “I do not understand how she could have read about the works and gotten it so muddled.”

The students who were not intimidated by Professor Hassold’s withering style were the ones most likely to be granted admission to her inner circle.

Dr. Archer is now an associate professor of art history and gender studies at Montclair State University in New Jersey. She recalled walking into one of those dimly lit sessions in 1995 as an ambitious but directionless freshman and seeing Professor Hassold behind a pile of oranges that she had harvested for the students in her surrealism class.

“Doesn’t your family eat all of the oranges?” a student asked.

“I don’t have a family,” Professor Hassold said.

“You’re not married?”

“What would I do with a husband?” Professor Hassold, who grew up in Louisville, Ky., scoffed in her Southern drawl. “That would just be a pain in the neck.”

The offhand comment stuck with Dr. Archer. “It was kind of like the most amazing moment I had ever had,” she said. “She is just herself. It was a type of woman I had never met.”

A Home That Revealed a Secret Past

The professor and her students strengthened their bond during long, informal dinners.

Over potstickers at the Cheesecake Factory or French onion soup at a local bistro, Professor Hassold gossiped with them about rival art professors or recalled adventures with old boyfriends in New York. She expressed dismay over her belief that New College was losing its liberal, countercultural spirit — a shift that would become more pronounced decades later.

Professor Hassold was always digging into her students’ aspirations.

“What do you want to do and how do you get there?” her students remembered her asking. “Who do you like to read? Where do they teach? They teach abroad? How do you save up the money to go?”

These dinners, Dr. Archer recalled, “were these fun spaces where you could imagine a life for yourself without restrictions.”

Many students wondered, however, why Professor Hassold never invited them into her home.

Ryan White, who enrolled in Professor Hassold’s film noir class as a freshman in 2003, would come to understand. After he grew close to her over the semester and the following years, she asked him to help her mow her front lawn — an apocalyptic jungle of ferns and shrubs — and tidy up inside her home.

Mr. White, 45, who now runs a New York City-based knife sharpening company, recalled that it was a “nightmare.”

Cans of food, muffin tins, office supplies and a library’s worth of art history books cluttered every corner of her home. Stacks of papers spilled onto her bed. A guest bathroom had been rendered useless for a decade because boxes of papers prevented the door from opening.

Her neighbors had complained, and welcomed the effort by Mr. White and other students to clean up her property, delivering lemonade as a gesture of gratitude.

“I’m going to need this someday,” Professor Hassold would say as she held up an old article, Mr. White recalled, perhaps one about Stéphane Mallarmé’s impact on cubism.

“You haven’t seen it in 40 years,” Mr. White would respond.

Katie Helms, 47, of Kingston, N.Y., who graduated from New College in 2003, gained insight into Professor Hassold after they fell into a deep conversation about their parents.

Ms. Helms, now a business consultant and doctoral student in education, made a habit of reading Professor Hassold’s hundred-page assignments multiple times, making her one of Professor Hassold’s favorites.

One night as they drove to dinner, Ms. Helms said, Professor Hassold recalled returning home from the University of Louisville to find that her mother had thrown away all of her daughter’s belongings. Ever since then, Professor Hassold held onto everything.

It was likely just one factor behind a hoarding problem that eventually rendered her home unlivable. Instead of parting with the detritus, Professor Hassold built a second home on her property.

“She wasn’t very good at letting things, or people, go,” Dr. Archer said.

‘She Adopted Us’

The youngest of 12, Ms. Helms received little attention growing up. That changed when she met Professor Hassold. For the first time, Ms. Helms felt unconditional acceptance for everything from her smoking habit to her queer identity.

“I’ll never get the kind of acknowledgment from my parents that I got from her,” Ms. Helms said, her voice cracking with emotion. “I think about her almost every day.”

When their time in Professor Hassold’s classroom ended, many students worked for her as teaching assistants and sought her out for career advice. When they returned to Sarasota later in life, they would make dinner plans with their old mentor.

As Dr. Archer put it, “she had a collection of students in the same way that she had endless collections of books.”

Professor Hassold retired in 2016 at 85. In her final years, she told some of her former students that she planned to leave them something when she died. She didn’t have much family apart from a brother and a few nieces. This was not a woman who lived luxuriously — driving a beat-up Toyota Corolla and cycling through a modest wardrobe. The students were touched, but they weren’t expecting much.

“She didn’t have a family, but we were her family,” Mr. White said. “She adopted us, and we adopted her.”

Bittersweet Endings

In April 2020, Professor Hassold had a stroke at the grocery store and collapsed.

In July of that year, as she was making some progress in her recovery, a fall on the bathroom floor left her needing hospice care. At the peak of the coronavirus pandemic, cordoned off from the world, Professor Hassold died on July 15, 2020. She was 89.

Her former students held a virtual memorial service, crying and laughing over Zoom as they shared stories. Many joked that they had secretly hoped she would die in the classroom, her happy place. But they took solace that she died before New College became unrecognizable.

In the years after her death, Gov. Ron DeSantis of Florida set his sights on transforming the school into a bastion of conservative values. The school shuttered its gender studies program and began recruiting students from Christian schools. Professor Hassold’s students were sure she would be appalled by how it changed.

In August 2021, Professor Hassold’s former students received a package of legal documents that revealed her biggest secret. She had amassed a $2.8 million estate and was dividing it among the 36 people closest to her — 31 of whom were former students, according to documents shared by Steve Prenner, the executor of her estate and a former student.

Some of the students were shocked, particularly those who could not recall when they had last spoken to her.

Professor Hassold had allotted the money based on how close she had been to each student, and how much she believed they needed the money, according to the former students. The payments ranged from around $26,000 to $560,000.

Ms. Helms used part of the roughly $26,000 that she received to help her recover from surgery. Other former students used the money for a down payment on a house, to travel or simply to pay down debts and cover their bills.

It suddenly made sense, Ryan White thought as he opened his letter, why she worked until she was 85, lived so frugally and hid away at times. It was partly the post-Depression era in which she was raised, as well as her fierce independence. But perhaps she had been saving up with her students in mind all along.

“She wanted to give as much away as she could,” said Mr. White, who also received around $26,000.

After Dr. Archer opened her letter, she stepped out into the Manhattan summer and bought a bottle of sherry — a tribute to her Professor Hassold, who loved to drink it.

She thought of what she might do with the $100,000 the letter promised her — open a savings account, maybe buy a home someday, and commit to her career in academia.

For Dr. Archer, the money felt like a message from her mentor:

“Here’s a little something to help you be you.”