And yet, five years in, “radical innovation” has yet to emerge. Many fellows have been financially successful, raising some $450 million for companies that are valued at $2.45 billion. Some are disrupting the fields of photonics, artificial intelligence and educational technology. But the biggest hits have been the most pedestrian. One fellow, Ritesh Agarwal, raised $225 million to build an online market for budget hotels in India; another, Ben Yu, scored a hit with a topical energy spray.

“Peter Thiel promised flying cars, we got caffeine spray instead,” wrote the technology writer and entrepreneur Vivek Wadhwa.

To have a lasting impact, Mr. Thiel must move past the first iteration of Silicon Valley and toward the hardware and science revolutions that will usher in Silicon Valley 2.0. We already have enough OKCupids. We don’t have enough of the desperately needed inventions — nuclear fusion energy or cancer cures — that emerge when credentialed scientists tinker away for years on expensive machines that have nothing to do with Snapchat. Of course, this sort of tinkering most often happens in the academic institutions that Mr. Thiel reviles, despite their role in the foundational breakthroughs — such as the internet — that enabled Mr. Thiel to build his $2.7 billion fortune.

As his fellowship program matures, each class begins to look a little more like the creator himself; there are fewer ambitious research projects, and more of the kind of tech start-ups that fed Mr. Thiel’s appetite for investing. Such a drift may have been inevitable. But there’s also the fact that hard science is … well, hard.

“It’s true that civilization won’t get to the next level if we’re just doing thin software solutions,” Mr. Thiel acknowledged. “But we need to consider not just whether an idea can change the world, but also whether it’s feasible and has a clear path to market.”

Mr. Thiel’s fellow PayPal founder, Elon Musk, has managed to do both, parlaying his dot-com profits into space exploration, solar power and electric cars.

One wonders if Mr. Thiel has the motivation to extract his wagon wheels from the profitable ditch that he has dug, or if he is content to stand atop the vehicle and rant. Like his presidential candidate, the more he rants, the less clear it is what exactly he stands for. Just as his investments in invasion-of-privacy lawsuits show that his much-trumpeted commitment to free speech may dissolve when he himself feels affronted, his role in the founding of Palantir, a secretive data-mining company employed by nearly every American military and spy agency, suggests that he’s not as anti-government as he might like to believe.