The Mütter Museum in Philadelphia houses an array of singular medical specimens. On the lower level the fused livers of 19th-century conjoined twins Chang and Eng float in a glass vessel. Nearby, visitors can gawk at hands swollen with gout, the bladder stones of Chief Justice John Marshall, the cancerous tumor extracted from President Grover Cleveland’s jaw, and a thighbone from a Civil War soldier with the wounding bullet still in place. But there’s one exhibit near the entrance that elicits unmatchable awe. Look closely at the display, and you can see smudge marks left by museumgoers pressing their foreheads against the glass.

The object that fascinates them is a small wooden box containing 46 microscope slides, each displaying a slice of Albert Einstein’s brain. A magnifying glass positioned over one of the slides reveals a piece of tissue about the size of a stamp, its graceful branches and curves resembling an aerial view of an estuary. These remnants of brain tissue are mesmerizing even though—or perhaps because—they reveal little about the physicist’s vaunted powers of cognition. Other displays in the museum show disease and disfigurement—the results of something gone wrong. Einstein’s brain represents potential, the ability of one exceptional mind, one genius, to catapult ahead of everyone else. “He saw differently from the rest of us,” says visitor Karen O’Hair as she peers at the tea-colored sample. “And he could extend beyond that to what he couldn’t see, which is absolutely amazing.”

Throughout history rare individuals have stood out for their meteoric contributions to a field. Lady Murasaki for her literary inventiveness. Michelangelo for his masterful touch. Marie Curie for her scientific acuity. “The genius,” wrote German philosopher Arthur Schopenhauer, “lights on his age like a comet into the paths of the planets.” Consider Einstein’s impact on physics. With no tools at his disposal other than the force of his own thoughts, he predicted in his general theory of relativity that massive accelerating objects—like black holes orbiting each other—would create ripples in the fabric of space-time. It took one hundred years, enormous computational power, and massively sophisticated technology to definitively prove him right, with the physical detection of such gravitational waves less than two years ago.

Einstein revolutionized our understanding of the very laws of the universe. But our understanding of how a mind like his works remains stubbornly earthbound. What set his brainpower, his thought processes, apart from those of his merely brilliant peers? What makes a genius?

Philosophers have long been pondering the origins of genius. Early Greek thinkers believed an overabundance of black bile—one of the four bodily humors proposed by Hippocrates—endowed poets, philosophers, and other eminent souls with “exalted powers,” says historian Darrin McMahon, author of Divine Fury: A History of Genius. Phrenologists attempted to find genius in bumps on the head; craniometrists collected skulls—including philosopher Immanuel Kant’s—which they probed, measured, and weighed.

None of them discovered a single source of genius, and such a thing is unlikely to be found. Genius is too elusive, too subjective, too wedded to the verdict of history to be easily identified. And it requires the ultimate expression of too many traits to be simplified into the highest point on one human scale. Instead we can try to understand it by unraveling the complex and tangled qualities—intelligence, creativity, perseverance, and simple good fortune, to name a few—that entwine to create a person capable of changing the world.

Intelligence has often been considered the default yardstick of genius—a measurable quality generating tremendous accomplishment. Lewis Terman, the Stanford University psychologist who helped pioneer the IQ test, believed a test that captured intelligence would also reveal genius. In the 1920s he began tracking more than 1,500 Californian schoolkids with IQs generally above 140—a threshold he labeled as “near genius or genius”—to see how they fared in life and how they compared with other children. Terman and his collaborators followed the participants, nicknamed “Termites,” for their lifetimes and mapped their successes in a series of reports, Genetic Studies of Genius. The group included members of the National Academy of Sciences, politicians, doctors, professors, and musicians. Forty years after the study began, the researchers documented the thousands of academic reports and books they published, as well as the number of patents granted (350) and short stories written (about 400).

But monumental intelligence on its own is no guarantee of monumental achievement, as Terman and his collaborators would discover. A number of the study’s participants struggled to thrive, despite their towering IQ scores. Several dozen flunked out of college at first. Others, tested for the study but with IQs that weren’t high enough to make the cut, grew up to become renowned in their fields, most famously Luis Alvarez and William Shockley, both of whom won Nobel Prizes in physics. There’s precedent for such underestimation: Charles Darwin recalled being considered “a very ordinary boy, rather below the common standard in intellect.” As an adult he solved the mystery of how the splendid diversity of life came into being.

Scientific breakthroughs like Darwin’s theory of evolution by natural selection would be impossible without creativity, a strand of genius that Terman couldn’t measure. But creativity and its processes can be explained, to a certain extent, by creative people themselves. Scott Barry Kaufman, scientific director of the Imagination Institute in Philadelphia, has been bringing together individuals who stand out as trailblazers in their fields—people like psychologist Steven Pinker and comedian Anne Libera of the Second City—to talk about how their ideas and insights are kindled. Kaufman’s goal is not to elucidate genius—he considers the word to be a societal judgment that elevates a chosen few while overlooking others—but to nurture imagination in everyone.

These discussions have revealed that the aha moment, the flash of clarity that arises at unexpected times—in a dream, in the shower, on a walk—often emerges after a period of contemplation. Information comes in consciously, but the problem is processed unconsciously, the resulting solution leaping out when the mind least expects it. “Great ideas don’t tend to come when you’re narrowly focusing on them,” says Kaufman.

Studies of the brain offer hints at how these aha moments might happen. The creative process, says Rex Jung, a neuroscientist at the University of New Mexico, relies on the dynamic interplay of neural networks operating in concert and drawing from different parts of the brain at once—both the right and left hemispheres and especially regions in the prefrontal cortex. One of these networks fosters our ability to meet external demands—activities we must act on, like going to work and paying our taxes—and resides largely in outer areas of the brain. The other cultivates internal thought processes, including daydreaming and imagining, and stretches mainly across the brain’s middle region.

Jazz improvisation provides a compelling example of how neural networks interact during the creative process. Charles Limb, a hearing specialist and auditory surgeon at UC San Francisco, designed an iron-free keyboard small enough to be played inside the confines of an MRI scanner. Six jazz pianists were asked to play a scale and a piece of memorized music and then to improvise solos as they listened to the sounds of a jazz quartet. Their scans demonstrate that brain activity was “fundamentally different” while the musicians were improvising, says Limb. The internal network, associated with self-expression, showed increased activity, while the outer network, linked to focused attention and also self-censoring, quieted down. “It’s almost as if the brain turned off its own ability to criticize itself,” he says.

This may help explain the astounding performances of jazz pianist Keith Jarrett. Jarrett, who improvises concerts that last for as long as two hours, finds it difficult—impossible, actually—to explain how his music takes shape. But when he sits down in front of audiences, he purposefully pushes notes out of his mind, moving his hands to keys he had no intention of playing. “I’m bypassing the brain completely,” he tells me. “I am being pulled by a force that I can only be thankful for.” Jarrett specifically remembers one concert in Munich, where he felt as if he had disappeared into the high notes of the keyboard. His creative artistry, nurtured by decades of listening, learning, and practicing melodies, emerges when he is least in control. “It’s a vast space in which I trust there will be music,” he says.

One sign of creativity is being able to make connections between seemingly disparate concepts. Richer communication between areas of the brain may help make those intuitive leaps possible. Andrew Newberg, director of research at the Marcus Institute of Integrative Health at Thomas Jefferson University Hospitals, is using diffusion tensor imaging, an MRI contrast technique, to map neural pathways in the brains of creative people. His participants, who come from Kaufman’s pool of big thinkers, are given standard creativity tests, which ask them to come up with novel uses for everyday objects like baseball bats and toothbrushes. Newberg aims to compare the connectivity in the brains of these high achievers against that of a group of controls to see if there is a difference in how effectively the various regions of their brains interact. His ultimate goal is to scan as many as 25 in each category and then pool the data so he can look for similarities within each group as well as differences that may appear across vocations. For instance, are certain areas more active in a comedian’s brain compared with a psychologist’s?

A preliminary comparison of one “genius”—Newberg uses the word loosely to distinguish the two groups of participants—and one control reveals an intriguing contrast. On the subjects’ brain scans, swaths of red, green, and blue illuminate tracts of white matter, which contain the wiring that allows neurons to transmit electrical messages. The red blotch on each image is the corpus callosum, a centrally located bundle of more than 200 million nerve fibers that joins the two hemispheres of the brain and facilitates connectivity between them. “The more red you see,” Newberg says, “the more connecting fibers there are.” The difference is notable: The red section of the “genius” brain appears to be about twice as wide as the red of the control brain.

“This implies that there’s more communication going on between the left and the right hemispheres, which one might expect in people who are highly creative,” says Newberg, stressing that this is an ongoing study. “There’s more flexibility in their thought processes, more contributions from different parts of the brain.” The green and blue swaths show other areas of connectivity, stretching from front to back—including dialogue among the frontal, parietal, and temporal lobes—and may reveal additional clues, says Newberg. “I don’t know yet what else we might find out. This is just one piece.”

Even as neuroscientists try to understand how the brain fosters the development of paradigm-shifting thought processes, other researchers are wrestling with the question of when and from what this capacity develops. Are geniuses born or made? Francis Galton, a cousin of Darwin, objected to what he called “pretensions of natural equality,” believing that genius was passed down through family bloodlines. To prove it, he mapped the lineages of an array of European leaders in disparate fields—from Mozart and Haydn to Byron, Chaucer, Titus, and Napoleon. In 1869 Galton published his results in Hereditary Genius, a book that would launch the “nature versus nurture” debate and spur the misbegotten field of eugenics. Geniuses were rare, Galton concluded, numbering roughly one in a million. What was not unusual, he wrote, were the many instances “in which men who are more or less illustrious have eminent kinsfolk.”

Advances in genetic research now make it possible to examine human traits at the molecular level. Over the past several decades, scientists have been searching for genes that contribute to intelligence, behavior, and even unique qualities like perfect pitch. In the case of intelligence, this research triggers ethical concerns about how it might be used; it is also exceedingly complex, as thousands of genes may be involved—each one with a very small effect. What about other kinds of abilities? Is there something innate in having an ear for music? Numerous accomplished musicians, including Mozart and Ella Fitzgerald, are believed to have had perfect pitch, which may have played a role in their extraordinary careers.

Genetic potential alone does not predict actual accomplishment. It also takes nurture to grow a genius. Social and cultural influences can provide that nourishment, creating clusters of genius at moments and places in history: Baghdad during Islam’s Golden Age, Kolkata during the Bengal Renaissance, Silicon Valley today.

A hungry mind can also find the intellectual stimulation it needs at home—as in suburban Adelaide, Australia, in the case of Terence Tao, widely considered one of the greatest minds currently working in mathematics. Tao showed a remarkable grasp of language and numbers early in life, but his parents created the environment in which he could flourish. They provided him with books, toys, and games and encouraged him to play and learn on his own—a practice his father, Billy, believes stimulated his son’s originality and problem-solving skills. Billy and his wife, Grace, also sought out advanced learning opportunities for their son as he began his formal education, and he was fortunate to meet educators who helped foster and stretch his mind. Tao enrolled in high school classes when he was seven years old, scored 760 on the math section of the SAT at age eight, went to university full-time when he was 13, and became a professor at UCLA at 21. “Talent is important,” he once wrote on his blog, “but how one develops and nurtures it is even more so.”