In the long-running rivalry between Donald J. Trump and late-night television, the stage is often less a forum for dialogue than a showcase for contrast. That dynamic was on display again this week when Mr. Trump, appearing on a prime-time talk show, repeated a familiar claim about his intelligence — and was met with a pointed response from the host, Jimmy Kimmel.

Mr. Trump, speaking with the confidence that has long defined his public persona, told the audience that he possessed a “very high IQ” and described himself as a genius unmatched by experts. The remarks echoed assertions he has made for years, both on the campaign trail and in interviews, where he has frequently characterized himself as exceptionally intelligent and uniquely qualified.

The studio audience reacted with a mixture of applause and uneasy laughter.

Mr. Kimmel, seated behind his desk, responded not with a raised voice or overt mockery but with a question.

“That’s a lot,” he said evenly. “What’s the actual score?”

The inquiry, simple and specific, shifted the tone of the exchange. Numbers, Mr. Kimmel noted, are measurable. They offer clarity where rhetoric can blur. If Mr. Trump’s intelligence had been tested, what was the documented result?

Mr. Trump brushed off the question, saying such records were private but widely known to affirm his brilliance. The host paused, then reached into his desk drawer and produced a sheet of paper he said was drawn from historical school records. According to Mr. Kimmel, the document showed a standardized IQ score of 96 from Mr. Trump’s time at the New York Military Academy in the 1960s.

The camera zoomed in as Mr. Kimmel read the figures aloud, citing percentile rankings in verbal and mathematical categories. A murmur spread through the audience.

A score of 96 falls slightly below the statistical average of 100, the benchmark commonly used in IQ testing. Mr. Kimmel repeated the number slowly.

“Below average,” he said.

Mr. Trump immediately objected, calling the document inaccurate and dismissing it as “fake news.” He insisted that teachers, doctors and associates had long attested to his intelligence. His voice rose as he waved off the claim.

Mr. Kimmel did not escalate. “Below average is a number,” he replied. “And numbers are facts.”

The exchange was emblematic of the relationship between Mr. Trump and late-night television hosts, who have often used satire to challenge his statements. Over the past decade, programs hosted by Mr. Kimmel, Stephen Colbert and others have regularly scrutinized the former president’s rhetoric, blending comedy with pointed political commentary.

What distinguished this moment was not merely the punchline but the framing. Rather than trading insults, Mr. Kimmel emphasized the distinction between self-description and documentation.

“Intelligence isn’t measured by volume or repetition,” he said at one point, as Mr. Trump attempted to interject. “It’s proven over time.”

The audience responded with sustained laughter and applause, some rising to their feet as the tension broke.

Whether the document Mr. Kimmel referenced was authentic could not be independently verified during the broadcast, and representatives for Mr. Trump did not immediately provide comment afterward. Historically, Mr. Trump’s academic records have remained private, and discussions of his IQ have largely been confined to his own public claims.

Still, the moment resonated beyond the studio.

Within minutes, clips circulated across social media platforms, where users replayed the exchange and debated its implications. Supporters of Mr. Trump criticized the segment as disrespectful and partisan, arguing that late-night hosts routinely target him for ratings. Critics praised Mr. Kimmel for confronting what they view as inflated self-assessments with empirical scrutiny.

The broader theme — the tension between assertion and evidence — has been central to American political discourse in recent years. Mr. Trump has often relied on confident repetition to reinforce his narrative, a strategy that proved effective in both business branding and electoral politics. His opponents, including media figures, have countered by emphasizing documentation and fact-checking.

In this instance, the visual contrast was stark: a former president insisting on his exceptional intellect, and a comedian calmly holding up a sheet of paper.

Late-night television occupies a peculiar space in American culture, at once entertainment and commentary. While hosts are not journalists in the traditional sense, their monologues and interviews often shape public perception, especially among younger viewers. A well-timed joke can crystallize a critique more memorably than a policy paper.

By the end of the segment, Mr. Kimmel softened his tone, addressing the audience directly.

“Confidence can sell a lot of things,” he said. “But numbers don’t bend.”

For viewers at home, the exchange underscored a recurring feature of the Trump era: the collision between personal narrative and verifiable data. Whether one saw the moment as a fair challenge or an unfair ambush depended largely on prior loyalties.

What was clear, however, was the power of the format. In less than ten minutes, a boast became a question, a question became a prop, and a prop became a punchline. And in the space between laughter and protest, the debate over image and evidence played out once again under bright studio lights.