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A genius is a person who displays exceptional intellectual ability, creativity, or originality, typically to a degree that is associated with the achievement of new advances in a domain of knowledge. A scholar in many subjects (e.g. Gottfried Wilhelm Leibniz or Leonardo da Vinci ), or a scholar in a single subject (e.g. Albert Einstein or Charles Darwin) may both be referred to as a genius. There is no scientifically precise definition of genius, and the question of whether the notion itself has any real meaning has long been a subject of debate, although psychologists are converging on a definition that emphasizes creativity and eminent achievement.

Etymology
In ancient Rome, the genius (plural in Latin genii) was the guiding spirit or tutelary deity of a person, family (gens), or place (genius loci). The noun is related to the Latin verb genui, genitus, "to bring into being, create, produce". Because the achievements of exceptional individuals seemed to indicate the presence of a particularly powerful genius, by the time of Augustus the word began to acquire its secondary meaning of "inspiration, talent". The term genius acquired its modern sense in the eighteenth century, and is a conflation of two Latin terms: genius, as above, and ingenium, a related noun referring to our innate dispositions and talents.

Galton
The assessment of intelligence was initiated by Francis Galton (1822–1911) and James McKeen Cattell. They had advocated the analysis of reaction time and sensory acuity as measures of "neurophysiological efficiency" and the analysis of sensory acuity as a measure of intelligence.

Galton is regarded as the founder of psychometry. He studied the work of his older half-cousin Charles Darwin about biological evolution. Hypothesizing that eminence is inherited from ancestors, Galton did a study of families of eminent people in Britain, publishing it in 1869 as Hereditary Genius. Galton's ideas were elaborated from the work of two early 19th-century pioneers in statistics: Carl Friedrich Gauss and Adolphe Quetelet. Gauss discovered the normal distribution (bell-shaped curve): given a large number of measurements of the same variable under the same conditions, they vary at random from a most frequent value, the "average," to two least frequent values at maximum differences greater and less than the most frequent value. Quetelet discovered that the bell-shaped curve applied to social statistics gathered by the French government in the course of its normal processes on large numbers of people passing through the courts and the military. His initial work in criminology led him to observe "the greater the number of individuals observed the more do peculiarities become effaced..." This ideal from which the peculiarities were effaced became "the average man".

Galton was inspired by Quetelet to define the average man as "an entire normal scheme"; that is, if one combines the normal curves of every measurable human characteristic, one will in theory perceive a syndrome straddled by "the average man" and flanked by persons that are different. In contrast to Quetelet, Galton's average man was not statistical, but was theoretical only. There was no measure of general averageness, only a large number of very specific averages. Setting out to discover a general measure of the average, Galton looked at educational statistics and found bell-curves in test results of all sorts; initially in mathematics grades for the final honors examination and in entrance examination scores for Sandhurst.

Galton's method in Hereditary Genius was to count and assess the eminent relatives of eminent men. He found that the number of eminent relatives was greater with closer degree of kinship. This work is considered the first example of historiometry, an analytical study of historical human progress. The work is controversial and has been criticised for several reasons. Galton then departed from Gauss in a way that became crucial to the history of the 20th century AD. The bell-shaped curve was not random, he concluded. The differences between the average and the upper end were due to a non-random factor, "natural ability," which he defined as "those qualities of intellect and disposition, which urge and qualify men to perform acts that lead to reputation ... a nature which, when left to itself, will, urged by an inherent stimulus, climb the path that leads to eminence." The apparent randomness of the scores was due to the randomness of this natural ability in the population as a whole, in theory.

Criticisms include that Galton's study fails to account for the impact of social status and the associated availability of resources in the form of economic inheritance, meaning that inherited "eminence" or "genius" can be gained through the enriched environment provided by wealthy families. Galton went on to develop the field of eugenics.

Psychology
Genius is expressed in a variety of forms (e.g., mathematical, literary, musical performance). Persons with genius tend to have strong intuitions about their domains, and they build on these insights with tremendous energy. Carl Rogers, a founder of the Humanistic Approach to Psychology, expands on the idea of a genius trusting his or her intuition in a given field, writing: "El Greco, for example, must have realized as he looked at some of his early work, that 'good artists do not paint like that.' But somehow he trusted his own experiencing of life, the process of himself, sufficiently that he could go on expressing his own unique perceptions. It was as though he could say, 'Good artists don't paint like this, but I paint like this.' Or to move to another field, Ernest Hemingway was surely aware that "good writers do not write like this." But fortunately he moved toward being Hemingway, being himself, rather than toward someone else's conception of a good writer."

A number of people commonly regarded as geniuses have been diagnosed with mental disorders, for example Vincent van Gogh, Jonathan Swift, John Forbes Nash, Jr, and Ernest Hemingway.

IQ and genius
Galton was a pioneer in investigating both eminent human achievement and mental testing. In his book Hereditary Genius, written before the development of IQ testing, he proposed that hereditary influences on eminent achievement are strong, and that eminence is rare in the general population. Lewis Terman chose "'near' genius or genius" as the classification label for the highest classification on his 1916 version of the Stanford-Binet test. By 1926, Terman began publishing about a longitudinal study of California schoolchildren who were referred for IQ testing by their schoolteachers, called Genetic Studies of Genius, which he conducted for the rest of his life. Catherine M. Cox, a colleague of Terman's, wrote a whole book, The Early Mental Traits of 300 Geniuses, published as volume 2 of The Genetic Studies of Genius book series, in which she analyzed biographical data about historic geniuses. Although her estimates of childhood IQ scores of historical figures who never took IQ tests have been criticized on methodological grounds, Cox's study was thorough in finding out what else matters besides IQ in becoming a genius. By the 1937 second revision of the Stanford-Binet test, Terman no longer used the term "genius" as an IQ classification, nor has any subsequent IQ test. In 1939, David Wechsler specifically commented that "we are rather hesitant about calling a person a genius on the basis of a single intelligence test score."

The Terman longitudinal study in California eventually provided historical evidence regarding how genius is related to IQ scores. Many California pupils were recommended for the study by schoolteachers. Two pupils who were tested but rejected for inclusion in the study (because their IQ scores were too low) grew up to be Nobel Prize winners in physics, William Shockley, and Luis Walter Alvarez. Based on the historical findings of the Terman study and on biographical examples such as Richard Feynman, who had an IQ of 125 and went on to win the Nobel Prize in physics and become widely known as a genius, the current view of psychologists and other scholars of genius is that a minimum level of IQ (approximately IQ 125) is strictly necessary for genius, but this level of IQ is also sufficient for development of genius only when combined with the other influences on individual development of genius identified by Cox's biographical study, namely opportunity for talent development and personality characteristics of drive and persistence.

Philosophy
Various philosophers have proposed definitions of what genius is and what that implies in the context of their philosophical theories.

In the philosophy of David Hume, the way society perceives genius is similar to the way society perceives the ignorant. Hume states that a person with the characteristics of a genius is looked at as a person disconnected from society, as well as a person who works remotely, at a distance, away from the rest of the world. "On the other hand, the mere ignorant is still more despised; nor is any thing deemed a surer sign of an illiberal genius in an age and nation where the sciences flourish, than to be entirely destitute of all relish for those noble entertainments. The most perfect character is supposed to lie between those extremes; retaining an equal ability and taste for books, company, and business; preserving in conversation that discernment and delicacy which arise from polite letters; and in business, that probity and accuracy which are the natural result of a just philosophy."

In the philosophy of Immanuel Kant, genius is the ability to independently arrive at and understand concepts that would normally have to be taught by another person. For Kant, originality was the essential character of genius. This genius is a talent for producing ideas which can be described as non-imitative. Kant's discussion of the characteristics of genius is largely contained within the Critique of Judgement and was well received by the Romantics of the early 19th century. In addition, much of Schopenhauer's theory of genius, particularly regarding talent and freedom from constraint, is directly derived from paragraphs of Part I of Kant's Critique of Judgment.

"Genius is a talent for producing something for which no determinate rule can be given, not a predisposition consisting of a skill for something that can be learned by following some rule or other."

- Immanuel Kant

In the philosophy of Arthur Schopenhauer, a genius is someone in whom intellect predominates over "will" much more than within the average person. In Schopenhauer's aesthetics, this predominance of the intellect over the will allows the genius to create artistic or academic works that are objects of pure, disinterested contemplation, the chief criterion of the aesthetic experience for Schopenhauer. Their remoteness from mundane concerns means that Schopenhauer's geniuses often display maladaptive traits in more mundane concerns; in Schopenhauer's words, they fall into the mire while gazing at the stars, an allusion to Plato's dialogue Theætetus, in which Socrates tells of Thales (the first philosopher) being ridiculed for falling in such circumstances. As he says in Volume 2 of The World as Will and Representation:

"Talent hits a target no one else can hit; Genius hits a target no one else can see."

- Arthur Schopenhauer

In the philosophy of Søren Kierkegaard, genius is contrasted with an apostle; although both types of men are similar, the apostle speaks with authority, whereas the genius does not. In his work, The Difference Between a Genius and an Apostle, published in 1849 as one part of the Two Minor Ethical-Religious Essays, Kierkegaard writes: "A genius and an apostle are qualitatively different. All thought breathes in immanence, whereas faith and the paradox are a qualitative sphere unto themselves. Genius is immediateness. Genius is born. An apostle is not born: an apostle is a man called and appointed by God, receiving a mission from him. Authority is the decisive quality."

In the philosophy of Friedrich Nietzsche, genius is merely the context which leads us to consider someone a genius. In Twilight of the Idols, Nietzsche writes, "Great men, like great epochs, are explosive material in whom tremendous energy has been accumulated; their prerequisite has always been, historically and physiologically, that a protracted assembling, accumulating, economizing and preserving has preceded them – that there has been no explosion for a long time." In this way, Nietzsche follows in the line of German Idealism.

In the philosophy of Bertrand Russell, genius entails that an individual possesses unique qualities and talents that make the genius especially valuable to the society in which he or she operates. However, Russell's philosophy further maintains that it's possible for such a genius to be crushed by an unsympathetic environment during his or her youth. Russell rejected the notion he believed was popular during his lifetime that, "genius will out."