Burroughs did not issue a ruling on Monday, but in questioning from the bench, she asked the Trump administration how it could make “ad hoc decisions” when “there’s no documentation, no procedure” justifying the funding cuts on the basis that Harvard failed to combat antisemitism.

Harvard sued the Trump administration over the cuts in April, and lawyers for both the university and the government appeared in US District Court to argue that Judge Allison D. Burroughs should issue a summary judgment in the case in their respective favor.

The Trump administration’s legal case for cutting nearly $3 billion in federal aid to Harvard University was met with skepticism on Monday from a federal judge who described the government’s arguments as “a bit mind-boggling” during a high-stakes hearing in Boston.

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Harvard alumni rally outside a Boston court where Harvard University will argue against the Trump administration’s funding cuts

“The consequences for that in terms of constitutional law are staggering,” Burroughs said.

Harvard has argued that the Trump administration violated its constitutional rights and that the cuts are a significant blow to critical scientific research.

Michael Velchik, a Department of Justice attorney appearing on behalf of the government, argued that the government has the right to cancel Harvard’s grants because of its determination that the university has failed to root out antisemitism on campus, which he said is a priority of the Trump administration.

“Harvard claims the government is anti-Harvard. I reject that,” Velchik said. “The government is pro-Jewish students at Harvard. The government is pro-Jewish faculty at Harvard.”

Burroughs, who said she is Jewish and agreed that there were some missteps on campus, pressed Velchik to connect the concerns about antisemitism with the cancellation of funds and why the administration could make wholesale cuts instead of making decisions grant-by-grant.

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After Harvard publicly resisted the Trump administration’s demands in April, the government has cut its federal funding, attempted to ban international students from campus, and threatened the university’s accreditation. Harvard has made some reforms on campus that align with the Trump administration’s priorities and restarted negotiations with the government, but no resolution has been reached.

The case has enormous consequences not just for Harvard but more broadly for higher education, with several other prestigious colleges targeted by the administration with hundreds of millions of dollars in funding cuts. In Harvard’s case, the university says the Trump administration’s recent actions will cost the school more than $1 billion annually.

The funding cuts have disrupted studies ranging from experimental cancer treatments to the prevention of near-fatal food allergies.

Steven Lehotsky, a lawyer representing Harvard, argued Monday that the government’s termination of the university’s research grants violated Harvard’s First Amendment rights. He pointed to the Trump administration’s April 11 letter — which demanded Harvard overhaul its governance, admissions policies, and hiring procedures — adding that “no private university could accept” those terms.

Lehotsky said that the case is “about the federal government’s control over the inner-workings of America’s oldest institution of higher education.”

Harvard has also argued that the Trump administration skirted a legal process to cancel funding under Title VI of the Civil Rights of 1964, which prohibits discrimination “on the basis of race, color, or national origin.” Lehotsky at one point quoted “Sentence first — verdict afterwards,“ a line from the Queen of Hearts in the book “Alice’s Adventures in Wonderland,” to illustrate how he believes the government took action before legally justifying its decisions.

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The Trump administration did assert that Harvard violated Title VI in a notice it released last month, which Lehotsky argued proves that the government knew that process was available to try and cancel funds, but chose not to follow it.

Velchik, meanwhile, said that the government was not using the Title VI process in this case and argued that the administration had the authority under federal regulations regarding grants. Because of that, Velchik argued that the case should be tried in federal claims court as opposed to federal district court, which Burroughs sharply questioned.

Burroughs is a familiar face for Harvard. She is presiding over the university’s other high-profile case against the Trump administration, which challenges the government’s efforts to bar Harvard from hosting international students. Burroughs has blocked those efforts until the case is decided, and the government has appealed her decision.

The judge also oversaw the Harvard admissions lawsuit in 2018, where the group Students for Fair Admission argued that the university’s admissions process discriminated against Asian Americans. Burroughs ruled in favor of Harvard at the time, but the Supreme Court overturned the decision in a 2023 landmark ruling that outlawed race-based affirmative action in higher education admissions.

In a post on his social media network Truth Social, President Trump said Monday that Burroughs is “a TOTAL DISASTER” and an “automatic ‘loss’ for the People of our Country,” an example of Trump’s string of attacks on judges who have checked the executive branch’s power.

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On Monday, Burroughs also heard from lawyers representing Harvard’s chapter of the American Association of University Professors, which sued the Trump administration over the funding cuts. Burroughs, who is also overseeing the association’s case, said she was considering staying that case until a decision in Harvard’s suit, but the association pushed back, arguing that it wants its case to continue because it worries Harvard will settle with the Trump administration.

It’s unclear when Burroughs will make a ruling in Monday’s case, but Harvard has asked for a decision by Sept. 3, which represents a deadline set by the government for Harvard to begin submitting documents to wind down grants.

The American Association of University Professors was among the protesters outside the court in Boston on Monday. Heather Diehl/For The Boston Globe

As the hearing wrapped up around noon, dozens of Harvard students, faculty, and alumni gathered outside of the John Joseph Moakley Courthouse in support of the university and its researchers.

The rally was organized by the Crimson Courage, a group of Harvard alumni that has called on Harvard to continue resisting Trump.

Community organizer and Harvard alumnus Lew Finfer, who helped coordinate the protest, said the funding cuts not only have disastrous consequences for scientific research, but also for families whose lives were directly impacted by studies focused on cancer, Alzheimer’s, and other diseases.

“Having family … who have had cancer and died of cancer and have Alzheimer’s, the fact that people are trying to do something about it — [the research] always feels personal, as it would to anyone if they heard heard about these things,” Finfer said.

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“It’s not just research,” Finfer added. “It’s people’s lives.”

James McAffrey, 22, a Harvard undergraduate who co-founded a student group advocating resistance against the Trump administration’s attacks on the university, said during the protest that he feels a personal responsibility to speak out in support of the university.

“I haven’t had research funding cut. I’m not at risk of being deported,” he said Monday. “Which is why I feel even more committed to speaking out … because there’s so many of my peers that can’t say what they think and that’s not right in an America built on freedom of speech.”

Aidan Ryan can be reached at aidan.ryan@globe.com. Follow him @aidanfitzryan. Sadaf Tokhi can be reached at sadaf.tokhi@globe.com.