There may be no brand more venerable than the Ivy League. Individually and together, its eight members connote the pinnacle of scholarship. No university has emerged to challenge its intellectual supremacy in more than a century. On that timeline, Caltech, founded in 1891, is a start-up.

But now there is the Minerva Project. Ben Nelson, former CEO of the online photo service Snapfish, is building a school he asserts will be more rigorous than Harvard or Yale. "It will be harder to get into Minerva than any other university," says Nelson. "You'll have the same criteria for your grades, essay, and application. But you'll get no brownie points for how good an athlete you are, for how much money your parents can donate, or for what state you were born in." While Nelson is raising the floor established by elite universities in terms of who qualifies for admission, he is also raising the ceiling in terms of how many to admit. Like virtually every other higher-education start-up, Minerva, based in San Francisco, will live online. That means Nelson can swing wide his doors to tens of thousands of top-drawer students, many of them international. "Harvard allows 2,000 students into the admission cycle, of whom 200 are not American," says Nelson. "Clearly, that's not a good representation of the smartest people in the world."

The company, a for-profit, expects to admit its first class of several hundred in the fall of 2014 or 2015. Tuition will cost less than $20,000--half the price of the Ivy League. In April, Benchmark Capital invested $25 million, the largest seed round in its history. "The idea of giving kids a world-class, credentialed education is the most ambitious goal we've seen in this space," says Kevin Harvey, a Benchmark general partner.

Minerva isn't Nelson's first stab at transforming education. Twenty years ago, at the University of Pennsylvania, he enrolled in a class about the history of universities. "I studied Penn and Franklin and Hopkins," says Nelson. "Then I looked around and said, 'This is not what it's supposed to be.' " His chief criticism: Schools were training people to be successful but not to become the kind of leaders who could move the world forward. So he joined the student government and spent the next four years loudly advocating for change.

Post-Snapfish, Nelson thought again about education reform. He still wanted to improve elite education, but his more pressing concern was to expand it. Since Nelson's graduation, top schools had adopted needs-blind admission policies, and students around the world increasingly coveted a U.S. education. The result was far more demand from worthy students than the Ivies and their prestigious brethren could handle. "Admissions officers at elite universities will tell you that they could take everyone they've accepted, reject them, then accept the next tier 10 times over and not be able to tell the difference in quality," says Nelson.

Minerva will be global in more than its student body. Nelson plans to establish dormitory clusters in cities around the world. After their freshman years, students will be strongly encouraged to spend each semester in a different location. Students unable to participate in this movable feast must demonstrate proficiency in three languages to graduate.

Minerva's curricular innovations emerge from a distinction Nelson draws between knowledge dissemination and intellectual development. Knowledge, he maintains, is free and ubiquitous on the Internet, with nonprofits like Khan Academy and schools like Stanford posting thousands of lectures and lessons. So Minerva will offer no introductory classes. Rather, students are expected to master the basics of every subject on their own. During their freshman year, all students will follow the same core curriculum focused on subjects including multimodal communications and complex-systems analysis. That foundation laid, every subsequent course can be taught at a very high level. "If you were to look at sophomore-junior-senior years at Minerva, they will be equivalent to junior-senior-and-master's years at most other elite universities," says Nelson.

He is also upending the pedagogic convention whereby tenured faculty deliver weekly lectures, followed by discussion sections presided over by beleaguered grad students. The school will bestow Minerva Prizes--characterized by Nelson as Nobel awards for teaching--on star academics at top universities. Prizewinners will "curate" classes for Minerva. That will entail creating original course materials; the professors can also invite their respected peers to contribute specialized expertise. Classes will gather online to view and discuss the material, overseen by the full-time faculty--all of whom will be Ph.D.'s or the equivalent and all of whom will receive both salaries and stock options.

Nelson's vision has already resonated at the highest levels of traditional academe. Former Harvard president and Treasury Secretary Larry Summers offered to chair Minerva's advisory board after a single meeting with its founder. Another adviser is Bob Kerrey, a former U.S. senator, Nebraska governor, and president of the New School. "What he's got is one of the best private-education ideas I've ever heard," says Kerrey. "I think he's going to be successful, and as a consequence, university presidents across the country are going to be able to say to their boards and their faculties, 'We have to change.' He's going to have a very, very positive impact on all of higher education in America."

For Nelson, that impact will be measured by how many brilliant students he can endow with what he calls the Minerva brain and establish in roles in which they can make a difference. Toward that end, he is creating a department to help graduates raise money and make connections for new businesses and other projects. The department will also perform many functions of a traditional publicist--promoting the accomplishments of alumni so alumni can concentrate on their actual work. "We want to create an ethos where what's rewarded is doing as opposed to self-promotion," says Nelson. "It's the difference between graduating people who are focused on themselves and graduating people who are focused on moving the world forward."