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When Jacob Barnett was two years old, doctors told his mother Kristine that her son would probably never be able to talk, read, or even tie his shoes. He had moderate to severe autism, they informed her.

Indeed, Barnett seemed to have gone silent. Over about six months, the toddler had lost all communication skills and eye contact—he wouldn't even say "mommy" anymore. Per the experts' recommendations, Kristine put Barnett into an intensive therapy program, and into a preschool for kids with special needs.

For dozens of hours per week, professionals would work with him, trying to get him to do what he couldn't or wouldn't do. But he wasn't getting any better. After a while, Kristine went against everyone's advice and pulled him out of special education. She figured that her son would be better off if he spent those hours focused instead on what he could do—what he wanted to do.

Jacob Barnett, 18.

Jacob Barnett, 18.

So Kristine started teaching him herself, honing in especially on his outsized passion for math and science.

To say that this approach got her son talking again is an understatement. Suddenly, at age three, he spoke four languages. He could answer complicated astrophysics questions, despite the fact that no one had taught him the subject matter.

Around that age, he was also completing 5,000-piece puzzles, teaching himself Braille, making elaborate string diagrams in neat mathematical patterns, and faithfully recreating street maps on the floor using Q-tips—early evidence of his photographic memory.

At age eight, Barnett audited a physics class at Indiana University–Purdue University Indianapolis. His mom sat with him in the lecture hall, so people assumed that she was a student who didn't have a babysitter. But after Barnett started speaking up in class—and after he got an A on the final—the university invited him to enroll.

First, he had to complete the curriculum for grades six through 12, which he did in just over a year. Teaching himself high school math was the easiest part—he absorbed all of algebra, geometry, and calculus in two weeks. The fact that he remembers literally every math problem he's ever encountered helped. (He sees them pictorially in his mind's eye.)

At 10, he was officially a college student. At 13, he became a published physicist. At home, his parents couldn't stock paper fast enough to keep up with how fast he was writing equations. So he'd move on to whiteboards, then to windows.

"I've always had a deep curiosity to understand how the world works," he says. "It has been both fascinating and humbling to believe that life's diverse patterns could emerge from simple mathematical expressions."

Rumors swirled that he'd soon be a Nobelist, and some even thought that Barnett was on his way toward disproving Einstein's theory of relativity.

Barnett, though, doesn't call himself a genius. In his mind, he's only done what he believes anyone can do—transitioned from learning to thinking to creating. He feels so strongly about the idea of moving beyond rote learning, in fact, that, when he was 13, he gave a TEDx talk (currently creeping up on eight million YouTube views) called "Forget What You Know."

During the talk (Barnett wore a red shirt with phi on it), he made it clear that he's a huge proponent of taking breaks from learning and having time to think: "When you think, you must think in your own creative way—not accepting everything that's already out there," echoing his mother's skepticism of experts.

Barnett's work is already stretching our understanding of the universe. "I enjoy defining the boundaries of my understanding of the world and pushing them farther," he says. One of his favorite findings is that of a fermion-doubling problem in loop quantum gravity. "I demonstrated," he explains, "that the theory appears to have an inconsistency with the standard model of particle physics."

After college, Barnett moved from his native Indiana to Waterloo, Canada, for graduate school at the Perimeter Institute, a physics hotspot where many of the world's top thinkers in the subject, including Stephen Hawking, have taught. (By some metrics, it's easier for a physicist to get into Harvard University, Stanford University, or the Massachusetts Institute of Technology than into Perimeter.)

Barnett was Perimeter's youngest student ever admitted, and submitted his master's thesis at 15. Today, he's still at Perimeter and the University of Waterloo, getting his Ph.D. "My current research," he says, "is devoted to studying problems with many particles in an extension of standard quantum mechanics. In particular, I'm studying how entangled a state of such a system is when it has minimal energy."

Barnett's mentor and advisor at Perimeter is Lee Smolin, the famous physicist who has been called a "necessary troublemaker." "He's done an excellent job at shaping me into a young scientist," Barnett says, "encouraging me to develop my own research tastes while answering questions and bringing me up to date on various physics topics."

Barnett himself may be on the road to becoming a career academic, but then again, he may not. "The most notable childhood dream job I had," he says, "was pretty predictable for a child prodigy. I wanted to become a professor." For now, though, "my only long-term goals are to be happy, and to be doing something I find challenging and rewarding," Barnett says. "Right now, physics is at the pinnacle of those goals, but perhaps in the future I will be motivated by something else."

"I don't feel like it's possible for me to tell you where I'm going to be in 50 years, 10 years, or even five years, for that matter," he continues. "These are lengths of time I haven't been around long enough to appreciate. Ten years ago I was in third grade. Due to my autism, I had just started communicating. It would've been impossible to guess that I would be a graduate student in physics now."

But Barnett would never curse his autism for causing his early hardships. "I'm very happy to be autistic," he said during an interview when he was 15. "If I was not autistic, I would not be at the place I am right now. Autism is my way of thinking. It's my way of viewing the world. It's because of that that I'm able to do what I'm able to do best."

Regardless of where he ends up—whether on the Nobel podium or elsewhere—Barnett will have defied his early childhood prognosis. As for tying his shoes, though, he's partial to sandals. But that's not because he can't arrange laces in a bow. It's because he has better things to think about.

Explore the complete list of this year's 30 top thinkers under 30 here.