Paul Steinhardt (BS ’74) once imagined a kind of crystal that was not supposed to exist in nature. Decades later, with the help of an Italian mineralogist, he found one. Tracing its origins would take Steinhardt, his son Will (BS ’11), and an international team of researchers to one of the most remote parts of the world, and open new mysteries about the formation of the solar system.


In the fall of 2008, Luca Bindi sat in his lab at the Museum of Natural History at the University of Florence in Italy, poring over data analysis. Then the head of mineralogy, Bindi was conducting a series of X-ray analyses on a selection of micromounts, tiny rock samples displayed in showcases in the museum’s main exhibition hall, specks only a bit larger than grains of sand. One of the samples, catalog number 46407/G, made him sit up straight. If he was reading the data correctly—and he was pretty sure he was—46407/G exhibited properties strongly indicative of an incredibly rare type of matter: a quasicrystal. 

If so, it would be the first natural quasicrystal ever discovered. 

Quasicrystals were not supposed to exist naturally. In fact, up until three decades ago, they weren’t supposed to exist at all. The laws that govern the structure of crystals dictate that they exhibit certain properties, including specific symmetries. Quasicrystals defy such boundaries, with compositions unlike any of their brethren. Their initial discovery in 1984 stirred deep controversy and overturned existing preconceptions about matter. Still, they are exceedingly rare, and had only been made in laboratories under tightly controlled conditions. So it then became the common wisdom that nature must not have elected to make them. If this sample was actually a quasicrystal, and if it was naturally made, it would contradict what had for nearly a century been considered a fundamental law.

Sample 46407/G might change the way we look at the world.

Bindi put his findings into an email a few days later. “The results are incredibly promising,” he wrote—the science-speak equivalent of “Eureka!”


Forbidden Symmetries

Across the Atlantic, Bindi’s email pinged the inbox of Paul Steinhardt (BS ’74), a theoretical physicist and cosmologist at Princeton University. Steinhardt is a warm but quiet man, pensive and careful with his words. As the director of the Princeton Center for Theoretical Science, he is also regarded as one of the nation’s leading cosmologists, widely known for developing the first working model of cosmic inflation (and then decades later recanting it in favor of a radically different theory). 

Steinhardt also happens to be one of the world’s foremost authorities on quasicrystals; three decades ago, he practically coined the term.

So what exactly is a quasicrystal?

When most people think of a crystal, they conjure up images of jewelry cases filled with multihued minerals with sharp, angular edges. It turns out that these shapes are the result of their atomic structures, which arrange into neat, regular, and repeating geometrical patterns. Now think of tiles spread across the surface of a floor: Depending on the shape of the tiles, the pattern produces certain symmetries. While there are thousands of crystals, their shapes can be grouped into only four specific symmetries—either two-, three-, four-, or six-fold.

The first hints of this were discovered more than a century ago in 1912, when the German physicist Max von Laue sent beams of X-rays through crystals, capturing beautiful portraits of the resulting diffraction patterns. This quickly opened the door to further discoveries about the makeup of matter. X-ray crystallography, as it became known, offered a new method that allowed researchers to peer into the dazzling and complex atomic structures of minerals, viruses, proteins, and even DNA. Yet compared with other forms of matter, crystals proved to be nature’s minimalists, and the understanding of their rigid architecture and symmetry was considered a closed case.

“It was so fundamental, you learned it in elementary school,” said Steinhardt. “Two, three, four, or six folds—period. That was it.”

There are, of course, other symmetrical compositions in the universe. The tiling on a soccer ball, composed of pentagons and hexagons, includes five-fold symmetries. Mosques throughout the Middle East display Girih tiling with two-, five-, and 10-fold symmetries that produce ornate patterns dizzying in complexity and beauty. In 1976, mathematical physicist Roger Penrose proposed a set of just two tiles that could cover a plane infinitely in nonperiodic fashion, full of five-fold symmetries.

But to have such exotic formations occur within crystals…that was forbidden by the laws of material science as we knew them. Such a crystal would be impossible.

Turns out, Steinhardt has a problem with the word “impossible.”

“I think that when someone says ‘impossible,’ I always want to know: Do you mean it violates the laws of physics?” Steinhardt asks. “Or do you mean that it would be very, very interesting?”

Steinhardt decided to put the crystal law to the test. In the early 1980s, while a faculty member at the University of Pennsylvania, he and fellow researcher Dov Levine developed a theoretical framework arguing that solids with forbidden symmetries could occur, at least in principle. They termed this new phase of matter “quasiperiodic crystals,” or “quasicrystals.” By sheer coincidence, around the same time another materials scientist, Dan Shechtman, who was at Johns Hopkins University, stumbled upon just such a formation lurking within an aluminum-manganese alloy and published his findings in 1984, just a few months before Steinhardt and Levine published their own paper. 

“Shechtman had a sample without a theory,” Steinhardt says. “We had the theory without a sample.” 

The name stuck, but that was all. The reaction from the scientific community was swift and withering. The very idea of quasicrystals, most experts argued, was so heretical to the laws of crystallography that Shechtman, Steinhardt, and their colleagues had to be in error. “There are no such thing as quasicrystals,” two-time Nobel laureate and Caltech professor Linus Pauling (PhD ’25) famously declared, “only quasi-scientists.” Pauling labored to explain the strange patterns with another theory, but the evidence mounted as more examples of quasicrystals continued to be found. Within a decade, the tide of scientific thinking began to turn. “I think Pauling thought that such an extraordinary claim required extraordinary evidence,” Steinhardt said. “In the end, I believe he felt that he served by pushing us to eliminate all other options and strengthen our case.”

In 1998, Steinhardt moved from Pennsylvania to the physics department at Princeton, and his primary attention drifted to other research interests. He also focused on his role as a father to his four young children. 

Still, one issue continued to trouble him: Hundreds of quasicrystals had been discovered by researchers around the world, but all had been created in a lab. Why had none been found to occur naturally? 

“These things could be made, but only under very controlled processes,” Steinhardt said. “But what if nature had already figured out another way to make them?” If so, might one already be hiding within some existing collection? He just had to figure out how to find the needle in a very, very large haystack.

The Internet offered a solution. For a number of years, mineralogists had been cataloging their samples in an international database. This included information from routinely performed powder-diffraction tests, a kind of quick and dirty version of the type of X-ray diffraction test used to detect quasicrystals. Powder diffractions weren’t enough to make a positive identification, but they could be used to rule out samples. In 2001, Steinhardt and fellow physicist Peter Lu published an open invitation, along with a methodology, for researchers to help them search their collections. No one responded. 

Years passed. Steinhardt’s children grew, went on to high school, and then began to think about college. Then, in 2007, one mineralogist offered to help: Luca Bindi in Florence.