One atom thick, graphene is the thinnest material known and may be the strongest. Illustration by Chad Hagen

Until Andre Geim, a physics professor at the University of Manchester, discovered an unusual new material called graphene, he was best known for an experiment in which he used electromagnets to levitate a frog. Geim, born in 1958 in the Soviet Union, is a brilliant academic—as a high-school student, he won a competition by memorizing a thousand-page chemistry dictionary—but he also has a streak of unorthodox humor. He published the frog experiment in the European Journal of Physics, under the title “Of Flying Frogs and Levitrons,” and in 2000 it won the Ig Nobel Prize, an annual award for the silliest experiment. Colleagues urged Geim to turn the honor down, but he refused. He saw the frog levitation as an integral part of his style, an acceptance of lateral thinking that could lead to important discoveries. Soon afterward, he began hosting “Friday sessions” for his students: free-form, end-of-the-week experiments, sometimes fuelled by a few beers. “The Friday sessions refer to something that you’re not paid for and not supposed to do during your professional life,” Geim told me recently. “Curiosity-driven research. Something random, simple, maybe a bit weird—even ridiculous.” He added, “Without it, there are no discoveries.”

On one such evening, in the fall of 2002, Geim was thinking about carbon. He specializes in microscopically thin materials, and he wondered how very thin layers of carbon might behave under certain experimental conditions. Graphite, which consists of stacks of atom-thick carbon layers, was an obvious material to work with, but the standard methods for isolating superthin samples would overheat the material, destroying it. So Geim had set one of his new Ph.D. students, Da Jiang, the task of trying to obtain as thin a sample as possible—perhaps a few hundred atomic layers—by polishing a one-inch graphite crystal. Several weeks later, Jiang delivered a speck of carbon in a petri dish. After looking at it under a microscope, Geim recalls, he asked him to try again; Jiang admitted that this was all that was left of the crystal. As Geim teasingly admonished him (“You polished a mountain to get a grain of sand?”), one of his senior fellows glanced at a ball of used Scotch tape in the wastebasket, its sticky side covered with a gray, slightly shiny film of graphite residue.

It would have been a familiar sight in labs around the world, where researchers routinely use tape to test the adhesive properties of experimental samples. The layers of carbon that make up graphite are weakly bonded (hence its adoption, in 1564, for pencils, which shed a visible trace when dragged across paper), so tape removes flakes of it readily. Geim placed a piece of the tape under the microscope and discovered that the graphite layers were thinner than any others he’d seen. By folding the tape, pressing the residue together and pulling it apart, he was able to peel the flakes down to still thinner layers.

Geim had isolated the first two-dimensional material ever discovered: an atom-thick layer of carbon, which appeared, under an atomic microscope, as a flat lattice of hexagons linked in a honeycomb pattern. Theoretical physicists had speculated about such a substance, calling it “graphene,” but had assumed that a single atomic layer could not be obtained at room temperature—that it would pull apart into microscopic balls. Instead, Geim saw, graphene remained in a single plane, developing ripples as the material stabilized.

Geim enlisted the help of a Ph.D. student named Konstantin Novoselov, and they began working fourteen-hour days studying graphene. In the next two years, they designed a series of experiments that uncovered startling properties of the material. Because of its unique structure, electrons could flow across the lattice unimpeded by other layers, moving with extraordinary speed and freedom. It can carry a thousand times more electricity than copper. In what Geim later called “the first eureka moment,” they demonstrated that graphene had a pronounced “field effect,” the response that some materials show when placed near an electric field, which allows scientists to control the conductivity. A field effect is one of the defining characteristics of silicon, used in computer chips, which suggested that graphene could serve as a replacement—something that computer makers had been seeking for years.

Geim and Novoselov wrote a three-page paper describing their discoveries. It was twice rejected by Nature, where one reader stated that isolating a stable, two-dimensional material was “impossible,” and another said that it was not “a sufficient scientific advance.” But, in October, 2004, the paper, “Electric Field Effect in Atomically Thin Carbon Films,” was published in Science, and it astonished scientists. “It was as if science fiction had become reality,” Youngjoon Gil, the executive vice-president of the Samsung Advanced Institute of Technology, told me.

Labs around the world began studies using Geim’s Scotch-tape technique, and researchers identified other properties of graphene. Although it was the thinnest material in the known universe, it was a hundred and fifty times stronger than an equivalent weight of steel—indeed, the strongest material ever measured. It was as pliable as rubber and could stretch to a hundred and twenty per cent of its length. Research by Philip Kim, then at Columbia University, determined that graphene was even more electrically conductive than previously shown. Kim suspended graphene in a vacuum, where no other material could slow the movement of its subatomic particles, and showed that it had a “mobility”—the speed at which an electrical charge flows across a semiconductor—of up to two hundred and fifty times that of silicon.

In 2010, six years after Geim and Novoselov published their paper, they were awarded the Nobel Prize in Physics. By then, the media were calling graphene “a wonder material,” a substance that, as the Guardian put it, “could change the world.” Academic researchers in physics, electrical engineering, medicine, chemistry, and other fields flocked to graphene, as did scientists at top electronics firms. The U.K. Intellectual Property Office recently published a report detailing the worldwide proliferation of graphene-related patents, from 3,018 in 2011 to 8,416 at the beginning of 2013. The patents suggest a wide array of applications: ultra-long-life batteries, bendable computer screens, desalinization of water, improved solar cells, superfast microcomputers. At Geim and Novoselov’s academic home, the University of Manchester, the British government invested sixty million dollars to help create the National Graphene Institute, in an effort to make the U.K. competitive with the world’s top patent holders: Korea, China, and the United States, all of which have entered the race to find the first world-changing use for graphene.

The progress of a technology from the moment of discovery to transformative product is slow and meandering; the consensus among scientists is that it takes decades, even when things go well. Paul Lauterbur and Peter Mansfield shared a Nobel Prize for developing the MRI, in 1973—almost thirty years after scientists first understood the physical reaction that allowed the machine to work. More than a century passed between the moment when the Swedish chemist Jöns Jakob Berzelius purified silicon, in 1824, and the birth of the semiconductor industry.

New discoveries face formidable challenges in the marketplace. They must be conspicuously cheaper or better than products already for sale, and they must be conducive to manufacture on a commercial scale. If a material arrives, like graphene, as a serendipitous discovery, with no targeted application, there is another barrier: the limits of imagination. Now that we’ve got this stuff, what do we do with it?