Brian Caffo teaches a public health course at Johns Hopkins University that he calls a “mathematical biostatistics boot camp.” It typically draws a few dozen graduate students. Never more than 70.

This fall, Caffo was swarmed. He had 15,000 students.

They included Patrycja Jablonska in Poland, Ephraim Baron in California, Mohammad Hijazi in Lebanon and many others far from Maryland who ordinarily would not have a chance to study at the elite Johns Hopkins Bloomberg School of Public Health in Baltimore. They logged on to a website called Coursera and signed up. They paid nothing for it.

These students are a sliver of the more than 1.7 million who have registered with Coursera since April. The phenomenon of free online education puts big issues on the table: the growth of tuition, the role of a professor, the definition of a student, the value of a degree and even the mission of universities.

“Massive open online courses,” or MOOCs, have caught fire in academia. They offer, at no charge to anyone with Internet access, what was until now exclusive to those who earn college admission and pay tuition. Thirty-three prominent schools, including the University of Washington and Stanford University, have enlisted to provide classes via Coursera.

For his seven-week course — which covers advanced math and statistics in the context of public health and biomedical sciences — Caffo posts video lectures, gives quizzes and homework, and monitors a student discussion forum. On the first day, the forum lit up with greetings from around the world. It was heady stuff for a 39-year-old associate professor who is accomplished in his field but hardly a global academic celebrity.

“I can’t use another word than unbelievable,” Caffo said. Then he found some more: “Crazy ... surreal ... heartwarming.”

For universities, the word for it is revolutionary. And higher education’s elite is in the vanguard.

In addition to for-profit Coursera, MOOC providers include a fledgling nonprofit competitor, edX, which has drawn hundreds of thousands of users to free online courses from Harvard University, the Massachusetts Institute of Technology and the University of California at Berkeley. On Oct. 15, the University of Texas system joined them.

“We want to dramatically increase access to learning for students worldwide while, at the same time, reinventing campus education,” said Anant Agarwal, president of edX.

A third high-traffic MOOC platform, for-profit Udacity, declares that “higher education is a basic human right.”

The courses pose questions for top universities: Are they diluting or enhancing brands built on generations of selectivity? Are they undercutting a time-tested financial model that relies on students willing to pay a high price for a degree from a prestigious institution? Or are they accelerating the onset of a democratized, globalized version of higher education?

MOOC students, for the most part, aren’t earning credit toward degrees. Educators say that before credits can be awarded, they must be assured that there are adequate systems to prevent cheating and verify student identities. But at the very least, these students can claim to have been educated by some of the world’s most prestigious universities.

“Students and families that are being asked to pony up $150,000 or $200,000 for a credential are going to start asking, ‘What’s the value of this thing?’ ” said Richard A. DeMillo, director of the Center for 21st Century Universities at Georgia Tech, which is part of the Coursera venture.

In a tech-crazed culture, many developments are heralded as “disruptive” to this or that industry. Sometimes their influence fades. But MOOCs just might merit the label.

“The real question is, if you start to get very good online MOOCs, why do you need a university?” said Joseph A. Burns, dean of faculty at Cornell University. “And what does an Ivy League university bring to the table? ... The campus ideal, he said, “of a teacher and five students crowded around their feet on a sunny lawn or something like that — that’s gone.”

Burns predicted that Cornell will join the MOOC movement. Some distinguished professors, he said, are fired up about the prospect of teaching 100,000 students instead of 20.

Steven Knapp, president of George Washington University, said his school will hold off for now. He worries about quality control.

“It’s like teaching a stadium,” Knapp said. “You could teach a lecture course in a stadium, but how engaged would the students be sitting in the top row?”

Exactly how MOOC platforms will make money without charging tuition remains to be seen. There is talk of selling branded certificates to students who pass a course. Another idea is to provide job-placement services.

“Quite a few employers have contacted us, unsolicited, asking to hire our top students,” said Coursera co-founder Andrew Ng, a Stanford University computer scientist. He said companies seem willing to pay for recruiting help. With student consent, Ng said, Coursera has begun making introductions to a few employers.

The company also has struck a deal with Antioch University, based in Ohio, that will enable tuition-paying students to take Coursera courses for credit at that school.

Still, Ng said, Coursera has so far generated almost no revenue. It is relying on venture capital. “Right now, we are more focused on getting the product right first than in monetizing,” Ng said.

For universities, MOOCs deliver worldwide exposure now and offer the possibility of cash flow in the future. Contracts with Coursera indicate that 6 percent to 15 percent of gross revenue from a given course, plus an additional share of profit, would go to the partner schools. Universities are responsible for the upfront costs of producing their courses.

Educators also believe that MOOCs will yield insights about student learning that can be applied on campus. Large lecture courses might morph if students can receive more content online, freeing up class hours for them to work with professors on projects.

Burck Smith, chief executive of StraighterLine, which sells low-price online courses, contends that MOOCs are overhyped. He said universities that give their product away are likely to face challenges similar to those newspapers confronted when they launched open-access websites.

“Free content has never really been a successful business model,” Smith said.

“People ask me all the time, ‘Why do you give it away for free?’” said Michael Klag, dean of Johns Hopkins’ public health school. “The reason, of course, is it’s consistent with our mission.” Also, he said, “it does build our brand.”