A happy genius is the gift of nature: it depends on the influence of the stars, say the astrologers, on the organs of the body, say the naturalists; ’tis the particular gift of heaven, say the divines, both Christians and heathens. How to improve it, many books can teach us; how to obtain it, none; that nothing can be done without it all agree.

–John Dryden, A Parallel of Poetry and Painting

I have met six Nobel Prize winners, and none has come close, in my view, to qualifying as a genius. Three won the prize for economics. They were all supremely confident and no doubt highly intelligent, but, I thought, insufficiently impressed by the mysteries of life. Another won his for physics, but in my company he wished to talk only about Shakespeare, on which he was commonplace and extremely boring. Another was a laureate for biology; he seemed to me, outside the laboratory, a man without the least subtlety. The last won his Nobel Prize for literature, and the most profound thing about him was the extent to which he had screwed up his personal life. Somehow it is always sensible to remember that in 1949 the Nobel Prize in medicine was given to Antonio Egas Moniz, a Portuguese surgeon, for developing the procedure known as the lobotomy.

Genius is rare. Schopenhauer thought a genius was one in a hundred million. In this realm if in no other, that most pessimistic of philosophers may have been optimistic. Distinguishing between a man of learning and a genius, Schopenhauer wrote: “A man of learning is a man who has learned a great deal; a man of genius, one from whom we learn something which the genius has learned from nobody.” A genius is not merely brilliant, skillful, masterly, sometimes dazzling; he is miraculous, in the sense that his presence cannot be predicted, explained, or accounted for (at least thus far) by natural laws or scientific study. The definitions for genius may be greater than the actual number of true geniuses who have walked the earth. My own definition is as follows: Be he a genius of thought, art, science, or politics, a genius changes the way the rest of us hear or see or think about the world.

The word genius, like many another (superstar, icon, fabulous), has undergone much inflation in recent decades. Quarterbacks and shortstops and singers are called geniuses, so, too, successful hedge-fund operators and chefs. “We are lucky to be living in an age of genius,” the editors of Esquire proclaimed in 1999 when they ran an issue devoted to the subject. Their candidates for genius included, among others, the actor Leonardo DiCaprio, the basketball player Allen Iverson, the designer Tom Ford, the foreign-policy pundit Fareed Zakaria, the chef Thomas Keller, a computer scientist named Bill Joy, and Jeff Bezos of Amazon.com. Handsome, skillful, talented, fraudulent, immensely successful, whatever else they are, none of these men is a genius, not even close.

The first question about genius is, in the root sense, existential: Does genius truly exist? Although he himself had earlier fallen for what he took to be the genius of Richard Wagner, in his later writings Friedrich Nietzsche thought not, referring in his Late Notebooks to “the superstition of our [the 19th] century, the superstitious belief in genius.” In Human, All Too Human, he wrote: “Because we think well of ourselves, but in no way expect that we could ever make the sketch to a painting by Raphael or a scene like one in a play by Shakespeare, we convince ourselves that the ability to do so is quite excessively wonderful, a quite uncommon accident, or, if we still have a religious sensibility, a grace from above.” The genius, whether in science or art, was for Nietzsche not in the least miraculous if only because he didn’t really exist.

Nietzsche held that the belief in genius, along with being irrational generally, was of most danger to those who come to believe in their own. As a case in point, he cites Napoleon, whose certainty about his own genius “turned into an almost mad fatalism, robbed him of his quick, penetrating eye, and became the cause of his downfall.” Nietzsche’s own dubiety about genius did not stop a cult of genius from forming around him, with many acolytes in the approved German manner, even before he was dead.

A distinction needs to be made between genius and talent. “Talent is like the marksman who hits a target, which others cannot reach,” wrote Schopenhauer. “Genius is like the marksman who hits a target, which others cannot see.” Mere talent cannot hope to rival genius, but neither can genius dispense with talent. “Talent without genius isn’t much,” wrote Paul Valéry, “but genius without talent is nothing.” On good days, I am talented. Shakespeare was a genius every day.

Who is and who is not an authentic genius is a question always up for dispute. Dante, Shakespeare, and Tolstoy are on most lists. So, too, among the ancients, Homer, Socrates, Plato, Aristotle. Bach, Beethoven, and Mozart are the indisputable musical geniuses. Leonardo da Vinci and Michelangelo and Raphael make the cut in the visual arts. So in science do Euclid, Galen, Galileo, Kepler, Newton, and Darwin. In politics, Pericles, Alexander the Great, Julius and Augustus Caesar, Napoleon, Winston Churchill, and Mahatma Gandhi would seem to qualify, with Lenin and Hitler and Stalin and Mao Zedong falling into the category of evil geniuses.

Secondary geniuses may be added into the mix, those figures who, however glittering their brilliance, have not affected the world in the same fundamental way as have primary geniuses: figures such as Descartes and Pascal, Spinoza and Kant, Titian and Rembrandt and possibly Picasso, Haydn and Handel and Schubert, Dostoyevsky and Dickens. Was Balanchine a genius? Was Matisse? Stravinsky? Or were they merely—some merely—great artists?

With the names Karl Marx and Sigmund Freud we enter the murky waters of geniuses who are today perhaps better thought the intellectual equivalent of false messiahs. Marx and Freud each made people see the world very differently than before they wrote, but we now know that they made them see it falsely. Most people no longer believe in either the Class Struggle or the Oedipus Complex. Marx’s and Freud’s license to genius has, in effect, expired.

If you think you are a genius, you probably aren’t. “I have nothing to declare except my genius,” Oscar Wilde is supposed to have told the agent at customs on Ellis Island when he visited America in 1882. Gertrude Stein announced that the Jews produced only three geniuses, Jesus, Spinoza, and herself; and in that ventriloqual work, The Autobiography of Alice B. Toklas, she has Miss Toklas say that she has met three geniuses in her life, Alfred North Whitehead, Pablo Picasso, and Gertrude Stein. Neither Wilde nor Stein remotely resembled a genius, certainly not by any strict definition. Such genius as they possessed was chiefly for self-promotion.

Most people would cite Albert Einstein as the last modern genius, and those with an interest in professional philosophy might add Ludwig Wittgenstein to the relatively recent genius list. As candidates for the title, Einstein and Wittgenstein have the added allure of having been, not to put too fine a point on it, goofy, for the modern taste in geniuses seems to run in that vein. In an earlier era, geniuses were felt to be not goofy but strange if not mad. Nietzsche’s last years were cloaked with insanity, which seemed to add to his authority. The world’s first acknowledged genius, Socrates, was strange in many ways. An exceedingly ugly man, with astonishing powers of concentration, he was entirely uninterested in honor, wealth, or even minimal material comforts, risked his life in battle, chose to spend his days arguing that he knew nothing while demonstrating that his interlocutors knew even less, and accepted the verdict of the Athenian assembly that he was the enemy of the state and therefore willingly took the hemlock.

Sockless, in his sweatshirt, with his wild hair and doofus mustache, Einstein walked the streets of Princeton looking like nothing so much as the fifth Marx Brother. Wittgenstein, the scion of a wealthy and wildly neurotic Viennese family, shed his vast personal fortune and went in for corporal punishment when he taught young children in Austria. Jewish, homosexual, hot-tempered, he was, as Bertrand Russell averred, “the most perfect example I have known of genius as traditionally conceived; passionate, profound, intense, and domineering.”

Genius as traditionally conceived is the subject of Darrin M. McMahon’s Divine Fury: A History of Genius (Basic Books, 360 pages), a work at once erudite and intellectually penetrating and immensely readable. A historian at Florida State University, McMahon has written what he terms “a history in ideas,” by which he means “a long-range intellectual history that examines concepts in multiple contexts across broad expanses of time.” Tracing the history of how people have thought about genius from the ancient world to our day, he has, in his own words, teased “out genius’s intimate connection to the divine, a connection that few analysts of the subject have explored.” Providing many mini-portraits of genius figures along the way, he persuasively argues that genius has never been entirely shorn of the notion of divinity, even in boldly secular ages, and how central the conception of genius has been to the way different ages have apprehended the world.

Socrates never spoke of his genius, but he did refer to his daimon, a spirit that resided within him offering instruction only on what he must not do. For the ancient Greeks, thinkers and artists were believed neither to discover nor create but to unveil what already existed. Their genius led them to these unveilings. No one was a genius, but a privileged few had genius, which was in the providence of the gods and functioned, as it did for Socrates, as a guardian spirit. As such, genius could be good or evil. One was either born with genius or not; it could not be acquired, but inhabited only those souls the gods inspired—in-spire, Professor McMahon notes, means to breathe into—to extraordinary deeds.

McMahon doesn’t quite say so, but geniuses tend to emerge in those areas of life dominant in specific cultures at specific times. For the Greeks, the main games were philosophy and art. For the Romans, it was military exploits and administration, and the only two Romans up for genius whom McMahon mentions prominently are Julius and Augustus Caesar. During the Middle Ages, devotion and piety, with an emphasis on asceticism and personal sacrifice, won the genius laurels, and the genius that occupied the souls of men and women was thought to be imbued by angels. Augustine of Hippo and Thomas Aquinas were both made saints. (“Genius,” wrote the Russian philosopher Nikolai Berdyaev, “is another kind of sainthood.”) For the Renaissance, it was art, chiefly visual art, painting and sculpture and architecture, that rang the gong. For the modern age, beginning with the 18th century, scientific geniuses predominate. For our own age, the main game, once thought to be invention—Thomas Edison and Henry Ford held genius status for a while—has yet to be determined, especially with so much science now being done not individually but in teams. Hence the paucity of agreed-upon geniuses in our day. Those master marketeers of the digital age, Bill Gates and Steve Jobs, need not apply.

The dividing line for our understanding of genius was the 18th century. In an emerging secular age, Descartes and Voltaire removed the tutelary-angel aspect from the conception. McMahon reminds us that it was only “in the eighteenth century that Shakespeare was declared a genius.” Men were no longer thought to have genius but to be geniuses. John Locke and Thomas Hobbes took things a step further, arguing that geniuses were not born but made. The English essayist Joseph Addison divided geniuses between the natural (Homer, Pindar, Shakespeare) and what he called the “imitative” geniuses, or geniuses of learning (Aristotle, Francis Bacon, John Milton).

The Enlightenment, operating on the suppositions of liberalism, held that if the educational franchise were only sufficiently extended, genius would be a possibility for all. “To improve social conditions, widen access to education, and enhance human possibilities,” according to McMahon, “was to extend the frontiers of the republic of genius, enhancing the potential of all.” Being in the right place at the right time was thought a necessity for establishing one’s genius. Genius was being demystified.

The cult of genius was central to the French Revolution. Voltaire, Mirabeau, and Rousseau were taken as geniuses by the revolutionaries, and Napoleon was later thought to be the genius child of the revolution. Hegel came up with the notion of “the world-historical individual,” of whom Napoleon fitted the mold perfectly. Goethe kept a bust of Napoleon in his study. Beethoven wrote the Eroica with Napoleon in mind, though subsequently bailed out of the Napoleon cult.

The Romantics preferred their geniuses daring like Lord Byron; mystical like William Blake; and tragic like poor John Keats. For them, geniuses, simultaneously heroes and martyrs, were blessed with gifts for revelation, and cursed by being at odds with the culture of their time. The ideal type of genius for the romantic was the poet. Percy Shelley called poets “the unacknowledged legislators of the world”; they were also prophets, who showed and revealed the sacred. Romantic critics—William Hazlitt, Samuel Taylor Coleridge, Ralph Waldo Emerson—made the genius out to be above the law, a law unto himself, and in his own way a god.

For the Romantics, so for the Germans: Where God had been, genius now stood. Genius for Germans became religion by other means, in the sense that the German people took their bearings from their supposed geniuses. Goethe, Schiller, Hegel, von Humboldt, Wagner, Nietzsche; the candidates for genius among them were not few. The one work of fiction with a genius as its hero, Thomas Mann’s composer Adrian Leverkühn in Doctor Faustus, was, of course, a rich product of German culture.

The worship of genius on the part of the Germans would one day exact a heavy price. Some of McMahon’s most brilliant pages persuasively set out how the genius cult helped pave the way to power for Adolf Hitler. Even Hitler’s failure as an artist played into his reputation and self-regard as a genius. “Far from abandoning his interest in art,” McMahon writes, “Hitler, via politics, pursued aesthetics by other means.” In Mein Kampf, Hitler announced his own entrance onto the world stage as a genius: “Geniuses of an extraordinary kind do not admit consideration of normal humanity.” Even Hitler’s madness tended to certify him as a genius, for by the early decades of the 20th century, everyone knew that geniuses were “touched,” in all meanings of the word.

Another step in the post-Enlightenment demystification of genius was to attempt scientifically to measure it. Here the conflict was between those who took geniuses as miracles of nature and those who took them as the product of their nurture. Eugenicists and others began studying genius in an attempt to locate and then quantify it. Much nuttiness followed: The measuring of skulls and brainpans (cranioscopy) and the studying of bumps on heads (phrenology) were for a time thought to supply the key. People even began grave robbing to secure the skulls of long-dead geniuses. The Italian criminologist Cesare Lombroso studied the interrelation of genius, madness, and degenerative disease, producing wild conclusions about the longevity of geniuses and the paucity of the production of genius in topographically flat countries. Climate conditions were added into the mix; in one such treatise, the cold northern European countries were said to be more productive of genius than the warm southern European ones.

In the second half of the 19th century, the eugenicist Francis Galton, a cousin of Charles Darwin’s, sought and failed to prove that genius was hereditary. If it were, then we should have to regret the many geniuses who were childless, when they might have created a rich gene pool. (In the 1980s, an American optometrist named Robert K. Graham, himself distinctly no genius, began a Nobel Prize–winners sperm bank, known as the Repository for Germinal Choice, which, as McMahon notes, “closed its vaults in 1997.”) In fact no two geniuses—if one holds to a strict standard—have ever showed up in the same family. Galton was a nature-trumps-nurture man, and his ideas for breeding higher intelligence, and hence increasing the prospects of genius, never really got off the ground, though as we sadly know Hitler, in later years, ran with them.

McMahon calls all these various social- and pseudo-scientific attempts to understand genius “geniology.” The best known was the invention, by the Frenchman Alfred Binet in 1906, of the educational diagnostic tool known as Intelligence Quotient, or IQ. McMahon writes: “The immediate goal was to classify those falling below normalcy, but it was readily apparent that an exam of this sort could be used to do the opposite, too, identifying and ranking individuals whose mental ages were above average.” IQ was derived by dividing mental age by actual age and then multiplying by 100. What IQ chiefly showed was a propensity, or want thereof, for solving abstract problems. (The Scholastic Aptitude Test similarly predicts nothing more than one’s chances of doing well in college.) Chess players, mathematics wizards, memory freaks tended to score highest on IQ tests.

IQ, those who believed in it felt, was innate, and derived from heredity. A man named Lewis Terman was a true believer in the accuracy of IQ. He thought that by using the results of IQ testing carefully, society could be improved, by early marking out the brightest of children and encouraging and ultimately utilizing their talents. “It should go without saying,” Terman wrote, “that a nation’s resources of intellectual talent are among the most precious it will have. The origins of genius, the natural laws of its development, and the environmental influences by which it may be affected for good or ill are scientific problems of almost unequaled importance in human welfare.”

In what is known as a longitudinal study, Terman discovered 1,000 children who scored 140 or more on IQ tests (140 was thought to be potential genius level) and arranged to track them through their later lives. None did anything extraordinary, while two children tested at the same time who did not make the 140 IQ cut went on to win Nobel Prizes. In his acknowledgments, McMahon notes that he was someone who early in life was told his intelligence-test results showed him “not the recipient of gifts.” He goes on to write: “There is evidence to suggest that an exaggerated belief in the strength of one’s innate capacities can actually harm a child’s development, sapping motivation and initiative. And there is even more evidence to show how damaging it can be to tell young people that, according to the numbers, they just don’t measure up.” I was myself luckily never tested for my IQ. Had I been, I might today be managing your local Jiffy Lube.

Intelligence, as anyone who has thought at all about it will long ago have concluded, is multi-valent, or of many kinds. Howard Gardner, the Harvard developmental psychologist and the leading investigator of intelligence in our day, has concluded that there are at least seven types of intelligence: linguistic, logical-mathematical, musical, bodily-kinesthetic, spatial, interpersonal, and intrapersonal. (He later added an eighth, naturalist intelligence, or that of people with a gift for observing nature.) Each of us is likely to be better endowed in one or another of these than in the others. “No two people,” Gardner concludes, “have exactly the same intelligence in the same combination.”

Genius, meanwhile, remains the least understood of all kinds of intelligence. The explanation for the existence of geniuses and accounting for their extraordinary powers have thus far eluded all attempts at scientific study. The intelligence of genius is still, so to say, off the charts. “As yet little is known about the genetics and neurobiology of creative individuals,” Gardner writes. “We know neither whether creative individuals have distinctive genetic constitutions, nor whether there is anything remarkable about the structure and functioning of their nervous systems.”

I find it pleasing that science cannot account for genius. I do not myself believe in miracles, but I do have a strong taste for mysteries, and the presence, usually at lengthy intervals, of geniuses is among the great ones. Schopenhauer had no explanation for the existence of geniuses, either, but, even while knowing all the flaws inherent in even the greatest among them, he held that geniuses “were the lighthouses of humanity; and without them mankind would lose itself in the boundless sea of error and bewilderment.” The genius is able to fulfill this function because he is able to think outside himself, to see things whole while the rest of us at best see them partially, and he has the courage, skill, and force to break the logjam of fixed opinions and stultified forms. Through its geniuses the world has made what serious progress it has thus far recorded. God willing, we haven’t seen the last of them.