Intelligence: The ability to learn, understand, explain, imitate and solve problems.
This ability, or these abilities, that are much involved in language and mathematics, are the reason the human animal is more powerful than other animals.
There is good reason to believe that there is such a thing as general intelligence, in as much as truly intelligent men and women tend to be similar in being good in both languages and mathematics, good speakers, good and clear writers, with good memories, and are generally fast in learning many different sorts of things, and there also is good reason to assume that high intelligence is positively correlated with a high IQ, which is a good predictor for scholarly success.
But very probably the basis of intelligence is not one singular faculty nor one that can be well summarized by a single number, like an IQ. Much rather, intelligence is like a mountain range: Quite a few abilities, that may all be cooperatively involved in tasks demanding great intellectual effort, but are distinct or at most overlapping, and are like tops in a mountain range, together with necessary valleys coming with these tops.
Also, it is an interesting fact that a good general intelligence seems to be required to be an extreme talent, but that extreme talents in humans tend to be specific, apart from their being usually combined with general intelligence: One is outstandingly good in mathematics, or in foreign languages, or in music, or in sculpturing, or in engineering, or in chess, or in painting, but rarely or never very good in all or many of the things men may excel in.
Indeed, while there have been a considerable number of evidently extremely intelligent men in human history, who are collectively mostly responsible for the great ideas and works of art in it, their relative number in the human population has been small, in the order of 1 or less in a million, and hardly any, except a rare few like Leonardo, has been truly outstanding in several fields, even though most truly intelligent men tend to do quite well in distinct fields, if they try.
Finally, it should be mentioned that extra-ordinary ability is no guarantee for genius, for that also requires originality and individuality and, it would seem, a capacity for hard work driven by interest added to these.