Mr. Daniels, 69, is the most innovative university president in America. Like his counterparts at other schools, he believes higher education has been “a competitive advantage” for the U.S.—“a nice little export industry, if you add up all the dollars that come here to purchase the education of students from other places.” He regards the rumbling in Washington about curbing visas for foreign students to be “very shortsighted.” But he also thinks American higher education has grown fat and complacent. He’s making inventive, even radical changes in the way his institution finances itself and imparts an education.

Mr. Daniels kicks off our conversation with a morality tale: “I’ll speak to an audience of businesspeople and say: Here’s the racket that you should have gone into. You’re selling something, a college diploma, that’s deemed a necessity. And you have total pricing power.” Better than that: “When you raise your prices, you not only don’t lose customers, you may actually attract new ones.”

For lack of objective measures, “people associate the sticker price with quality: ‘If school A costs more than B, I guess it’s a better school.’ ” A third-party payer, the government, funds it all, so that “the customer—that is, the student and the family—feels insulated against the cost. A perfect formula for complacency.” The parallels with health care, he observes, are “smack on.”

Mr. Daniels takes a different approach. In 2001-03, he ran the White House budget office for President George W. Bush, who dubbed him “The Blade” for his cost-cutting skills. Mr. Daniels brought his paring knife to Purdue. Examples of his efficiencies include replacing full-time dining-hall employees with student workers, scrapping the vast fleet of university-owned buses in favor of a private contractor, and saving $61 million on capital projects through what the university calls “innovative construction management.”

His most eye-catching achievement has been to keep costs down for students. By graduation day in 2020, tuition won’t have risen in eight years. “We’re able to say,” he says, “that the total cost in nominal dollars of going to Purdue will be less in 2020 than it was in 2012.”

Mr. Daniels says widespread adoption of Purdue’s “affordability campaign” would improve higher education. “Everybody is worried,” he says, furrowing his brow. “What are we at? A trillion and a half of student debt, twice as much as the total credit-card debt. It’s a social and economic problem.” He offers up a list of life’s milestones that people delay because of college debt: “marriage, household formation, child raising, homeownership, business-start formation—all of these things are being pressed down by college debt.” The “obvious first step,” Mr. Daniels replies, “is don’t charge so darn much in the first place.”

Yet he is notably reticent about encouraging other institutions to follow his lead. “It feels as though not a week goes by when there’s not an invitation to go talk about the subject to somebody’s board of trustees or state regents,” he says. “I’ve turned down every one of those. We don’t—I don’t—proselytize. We don’t assert that anything we’ve done here fits any school but ours.”

Even so, he’s happy to explain how he did it. When he arrived at Purdue in January 2013, the university had raised tuition 36 years in a row—typical for American higher ed, where an increase in tuition “was just considered an annual rite of spring.” Mr. Daniels suggested a one-year pause “to indicate some sensitivity to what was a growing concern about the cost of it all.”

He feared Purdue would pay a price in the perverse marketplace if it didn’t raise tuition, which goes up annually across the nation by 2% to 3%. Instead he was pleasantly surprised to find his school in a “position of differentiation—what every marketer hopes for.” Purdue “acquired a reputation as a place where you’re less likely to get socked with an annual surprise.” In consequence, it has had “record applications, from higher- and higher-quality students.”

Other costs, such as room and board, have also been held constant, and the price of textbooks has fallen by about 30%. A “duopoly” of two large bookstores had “owned the market at Purdue,” Mr. Daniels says. “We invited Amazon onto campus, and they set up their first bricks-and-mortar facilities anywhere.”

Another innovation, introduced in 2016, is the Income Share Agreement, an alternative to traditional student loans under which a student receives funding for his education in exchange for a percentage of income for up to 10 years after graduation. Like many modern economic innovations, the idea had its origins in a paper by Milton Friedman, published in 1955. Friedman asked why it shouldn’t be possible for an investor “to ‘buy’ a share” in a student’s earning prospects.

Under Purdue’s version of the agreement, credit is extended to students by a university-affiliated nonprofit and is available to all majors and all classes except freshmen. Students don’t owe anything while at university, for a six-month “grace period” thereafter—and after graduation if they’re unemployed or earn less than $20,000 a year. The total repayment is capped at 2.5 times the principal.

The Income Share Agreement, Mr. Daniels says, “isn’t a substitute for heavily subsidized loans—you can’t beat those. But it’s a pretty good one for the expensive loans that many students have to layer on. I always say, think of it as working your way through school after you leave, after you get the degree.”

Critics call it a form of indenture, but Mr. Daniels says they have it “absolutely backwards.” If you want indentured servitude, he bridles, “look at the government loan program. You can’t even get out in bankruptcy. The debt compounds, year on year. Whether life goes well or not, you still owe exactly the same amount.” In the case of the study-now-pay-later contracts, “if something goes wrong or life goes poorly, you owe nothing, or very little.”

Mr. Daniels’s “dog eat dog” quip doesn’t describe the atmosphere on Purdue’s campus. It’s a happy place, and the Boilermakers still glow from their epic football defeat of Ohio State in late October. He is a popular and accessible president who uses the treadmill in the student gym and sits amid ordinary fans at football games. There’s a trope at every game—“Where’s Mitch?”—in which the camera pans across the crowd to find the president in the stands.

The one great source of turbulence during Mr. Daniels’s tenure may prove his most successful innovation. In a bold move for a public university, Purdue in 2017 purchased Kaplan University, an online for-profit distance-learning institution. It was relaunched this year as a nonprofit, Purdue University Global, after Mr. Daniels overcame bitter resistance from some professors, who feared a dilution in the quality of a Purdue education. In November 2017, more than 300 faculty members signed a petition opposing the deal, citing concerns about academic standards, integrity and freedom.

Mr. Daniels says he has won over most of his critics: “There are far more faculty who are looking to see if there’s a program that they could originate for Purdue Global. It’s taken a while, but our faculty have come to understand the importance of our mission here.”

The online university now enrolls 29,000 students. Its aim is to serve working adults nationwide who wish to complete college degrees but don’t have the time or geographical proximity to enroll in ordinary classes. Expanding access to education, Mr. Daniels says, is “in the genetic code of this place—it’s just who we are.” He sees it as a successor of the “two great domestic educational policy achievements of America’s first 250 years”—the GI Bill of 1944, which helped World War II veterans go to college, and the Morrill Act of 1862. The latter established land-grant universities, including Purdue, on federal land across rural America to focus “on agriculture and the mechanic arts.” The aim: bring education to citizens who didn’t have easy access.

Today “there are 35 to 40 million Americans by most counts who started college and didn’t finish,” Mr. Daniels says. “We’re not talking about people who stopped at high school, but those who went and spent some money—probably borrowed some money—and then didn’t complete a degree. There are twice as many of them as all the 18- to 24-year-olds in America.”

They suffer economically for want of a degree: “In this economy, in this world, getting those people a credential is enormously important, especially to a society which keeps wringing its hands about the quality of its workforce.” In his ambition, “the typical student at Purdue Global is a 33-year-old working adult—much more likely to be a woman, and as likely as that to be a minority—probably with family obligations.”

The acquisition of Kaplan was, as he puts it, a “matter of kismet.” Mr. Daniels was determined to enhance Purdue’s online educational offerings but frustrated by his inability to do so. “Every year, between Christmas and New Year’s Day, I write a little self-evaluation and give it to the board,” he says. “Three years in a row, the worst grade I gave myself was for online education.” Purdue faced a make-or-buy decision: “Should we invest and build an online presence internally, or should we try to acquire it?”

In early 2017, a common friend connected Mr. Daniels to Donald Graham, chairman of the Graham Holdings Co. , which had sold the Washington Post to Jeff Bezos in 2013 and still owned Kaplan University. “Don called me,” Mr. Daniels recalls, “and he said to me, ‘This will probably be the shortest call of your day, but I don’t suppose, by any chance, you want to buy Kaplan.’ ” Fifteen minutes later, “we had a deal.”

Next year marks Purdue’s 150th anniversary, and the university is commemorating the occasion with a lecture series, “150 Years of Giant Leaps.” The title is inspired by Neil Armstrong, Purdue’s most famous alumnus, who visited the moon during the university’s centennial year. Purdue boasts two dozen astronauts among its alumni, more than any other civilian university—including the last man on the moon, Eugene Cernan, as well as the first.

Mr. Daniels, for his part, likes it here on Earth, especially in his own small corner of Indiana. In April this year, Purdue’s trustees approved an extension to his contract that allows him to serve indefinitely, requiring either party to give one year’s notice. They sold it as a reward for his innovations. Mr. Daniels sees these innovations as small steps for Purdue. But if others were to follow some of his ways, we could well have a giant leap for American higher education.

Mr. Varadarajan is executive editor at Stanford University’s Hoover Institution.

Correction
An earlier version of this article misstated the enrollment at Purdue University Global. And Purdue has more astronaut alumni than any other civilian institution.