The Mutter 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 the bladder stones of Chief Justice John Marshall, 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. 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. These remnants of 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. Einstein's brain represents potential, the ability of one exceptional mind to catapult ahead of everyone else.

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 100 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?

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. 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 California 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. 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 the Termites published, as well as the number of patents they were granted (350) and short stories they wrote (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, 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 hint 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 perform, 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 University of California, 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. "I'm bypassing the brain completely," he tells me. "I am being pulled by a force that I can only be thankful for."

Even as neuroscientists try to understand how the brain fosters paradigm-shifting thought processes, other researchers are wrestling with the question of when and from what this capacity develops. Are geniuses born or made?

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.

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.

Natural gifts and a nurturing environment can still fall short of producing a genius, without motivation and tenacity propelling one forward. These personality traits, which pushed Darwin to spend two decades perfecting On the Origin of Species and Indian mathematician Srinivasa Ramanujan to produce thousands of formulas, inspire the work of psychologist Angela Duckworth. She believes that a combination of passion and perseverance — what she calls "grit" — drives people to achieve. Duckworth, herself a MacArthur Foundation "genius," says the concept of genius is too easily cloaked in layers of magic, as if great achievement erupted spontaneously with no hard work. She believes there are differences when it comes to individual talent, but no matter how brilliant a person is, fortitude and discipline are critical to success.

Nor does it happen on the first try. "The No. 1 predictor of impact is productivity," says Dean Keith Simonton, professor emeritus of psychology at UC Davis and a longtime scholar of genius. Big hits emerge after many attempts. "Most articles published in the sciences are never cited by anybody," says Simonton. "Most compositions are not recorded. Most works of art aren't displayed." Thomas Edison invented the phonograph and the first commercially viable light bulb, but these were just two of the 1,000-plus U.S. patents he was awarded.

Some geniuses never get the chance to be productive. Throughout history women have been denied formal education or deterred from advancing professionally. Mozart's older sister, Maria Anna, a brilliant harpsichordist, had her career cut short by her father when she reached the marriageable age of 18. Half the women in the Terman study ended up as homemakers. People born into poverty or oppression don't get a shot at working toward anything other than staying alive. "If you do believe that genius is this thing that can be singled out and cultivated and nurtured," says McMahon, "what an incredible tragedy that thousands of geniuses or potential geniuses have withered and died."

Sometimes, by sheer good fortune, promise and opportunity collide. If ever there was an individual who personified the concept of genius in every aspect, it was Leonardo da Vinci. Born in 1452 to unmarried parents, Leonardo began life in a stone farmhouse in Italy's Tuscan hills. From these simple beginnings, Leonardo's intellect and artistry soared like Schopenhauer's comet. The breadth of his abilities — his artistic insights, his expertise in human anatomy, his prescient engineering — is unparalleled.

Today an international group of scholars and scientists is tracing the artist's genealogy and hunting down his DNA to learn more about his ancestry and physical characteristics, to verify paintings that have been attributed to him — and, most remarkably, to search for clues to his extraordinary talent.

Genealogists are tracking down Leonardo's living relatives on his father's side for cheek swabs. Anthropologists are seeking access to remains believed to be Leonardo's at Château d' Amboise, a castle in France's Loire Valley where he was buried in 1519. Historians and geneticists are experimenting with techniques to obtain DNA from fragile Renaissance-era paintings and paper.

The quest to unravel the origins of genius may never reach an end point. For some, that is as it should be. "I don't want to figure it out at all," says Keith Jarrett when I ask if he is comfortable not knowing how his music takes hold. "If someone offered me the answer, I'd say, 'Take it away.'"

In the end it may be that the journey is illuminating enough and that the insights it reveals along the way — about the brain, about our genes, about the way we think — will nurture glimmers of genius in not just the rare individual but in us all.

Excerpted from an article that originally appeared in National Geographic. Reprinted with permission.