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The Gifted and the Profoundly Gifted
We consider here students who are in grade 8 and below - say 14 years of age and less - and define the terms "gifted" and "profoundly gifted" in the context of mathematics.

By "gifted", we mean a person who is creative in terms of a gift. In mathematics, that would also mean high intelligence. Such individuals in mathematics are precocious or advanced beyond what is expected of their age.

Intelligence quotient, or IQ score, is the popular measurement for comparing an individual's "mental age" to the "chronological age". It is thus clear that IQ is a useful measurement of giftedness in mathematics.

We shall classify a student as mathematically gifted if the student's IQ is more than one standard deviation above the mean IQ for students at the same chronologial age of the student. We shall classify a student as "profoundly gifted" if the student's IQ is four or more standard deviations above the mean IQ for students at the same chronologial age of the student; this corresponds to an IQ of about 160 or above.

The Stanford-Binet Intelligence Scale, while it has limitations, is a widely used IQ measuring tool for identifying extremes above and below the norm.