The wave of enthusiasm for online education is unearthing some hard and interesting computational problems that Daphne Koller would love to solve. But first she has to find the time.

Last January, Koller and her colleague Andrew Ng took leave from faculty positions at Stanford University’s artificial-intelligence lab to create Coursera, a venture-financed online-education startup with offices five miles from campus.

Since then, Coursera’s growth has been rapid and all consuming. The company has posted more than 200 free classes taught by professors at 33 top universities, such as the University of Pennsylvania and Caltech. More than 1.5 million students have signed up, and about 70,000 new students—the equivalent of four or five Stanfords—join every week.

Koller, 44, now spends her average day “probably on a plane somewhere” headed to pitch Coursera to university administrators and faculty. The last 10 months have transformed her from a celebrated expert in statistics into the co-CEO of a large and complex educational website whose money-making plans are still nascent.

“As I drive home, I sometimes think this is somebody else’s life,” she says. She calls the experience “surreal.”

So far, tearing down the paywalls around higher education has been the simple part. What’s more challenging is making online classes like “A History of the World Since 1300” and “Algorithms I” match the quality of their in-person equivalents. That means racing to set up live forums for class discussions, keeping the site from crashing amidst the crush of students, and urgently seeking ways to make classes more interactive and to automate grading as much as possible.

Given such technical challenges, it’s not an accident that many of the people behind recent efforts to put college courses online come from computer science labs. Another Stanford researcher, Sebastian Thrun, resigned to create the startup Udacity. At MIT, the former head of the AI department, Anant Agarwal, now runs edX, another of the organizations offering “massive online open courses,” or MOOCs (see “The Crisis in Higher Education”).

“We saw the opportunity and the technology and had the ability to leverage it,” says Koller. But putting classes online is only part of what the AI researchers intend with MOOCs. By following the progress of millions of students online, it may be possible to develop new insights into how people learn and tailor classes on an individual level. “What we have here is an unprecedented level of detail and scale of data,” she says.

Koller is a third-generation PhD who grew up in Jerusalem, where her father was a well-known botanist. She is no stranger to experimenting with new forms of teaching: more than a decade ago, Stanford began broadcasting one of her classes for adult-education students. Eventually, Koller began telling all her students to watch the lectures at home. “All of a sudden, the idea kind of just popped into my brain that it didn’t make sense for me to go into class every week teaching the same lecture that I’ve been teaching for 15 years, the same jokes at the same time,” she says.

Attending class became optional, a time for one-on-one interaction. Even so, twice as many students began showing up. In 2011, she and Ng helped Stanford open three classes online to the public at large. This year, they raised $22 million from investors to start Coursera and create a Web platform any school could use.

Like its technology, Coursera’s business model is a work in progress. One idea considered has been a job board to connect employers to students who have taken specific Coursera classes. Another is to charge students who want to earn an official credit. In November, Antioch University in Los Angeles said it would begin letting its students take two Coursera classes for credit, splitting the modest revenues with the company.

Classes on the site are still of uneven technical quality. A course on Greek and Roman mythology is little more than a talking professor green-screened against bullet points and pictures of temples. But Koller believes this is just the beginning. By collecting an unprecedented amount of data about how students are learning, and analyzing it automatically in real time, educators could realize their dreams of personalized education at a large scale. “The goal is to design personalization, and to identify where someone is struggling and what might be helpful to them,” she says.

Some of Koller’s own academic research, published this February, illustrates how this might work. She and several collaborators applied machine-learning techniques to study an introductory programming class. The researchers created mathematical descriptions of the students themselves, looking for models that would explain their advances and setbacks. One discovery: success in the course was predicted by a student’s approach to solving the first assignments, not by right or wrong answers.

So far, Koller has had little time to pursue this or many other potential avenues for research, but Coursera has started to wade into the realm of “big data.” For instance, staffers have begun testing to compare different video presentation styles, even down to the way colors are displayed. By showing different students different formats—and tracking who keeps watching—they hope to discover which ones decrease the likelihood that a student will tune out.

Automation becomes more difficult—yet also more important—the further Koller gets from her familiar ground of math and computer science. Multiple-choice questions, computer code, and math problems can be graded by a machine. But what about an essay, a drawing, or a question whose correct answer could be “Obama,” “Barack Obama,” or “the president”?

These are still hard problems for computer science. For its growing number of classes in liberal arts and social sciences, Coursera has instead devised a peer grading system, in which a computer assigns classmates to give one another feedback. One popular class that uses this system is Modern & Contemporary American Poetry, taught by University of Pennsylvania professor Al Filreis. It consists of a lively discussion, organized much like a call-in radio show, with questions taken from the phones, forums, and Twitter.

Around 30,000 students signed up—making one-on-one teaching impossible. From the class discussion forums, it’s clear not everyone is thrilled with the peer grading approach. In another class, the one on Greek and Roman mythology, confusion caused delays and mid-course changes to the grading system.

Despite such problems, Koller says, her conversations with potential university partners are becoming progressively easier. Online learning used to be synonymous with shady diploma mills that offered a questionable product. Now it suggests something much better and more technologically sophisticated. “There’s been a huge transition in people’s thinking,” she says.