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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 lower - and define the terms "gifted" and "profoundly gifted" in the context of mathematics.

By "gifted", we mean a person who has a gift in a specific area - say drawing - whether or not the person has a high IQ. Some gifts are strongly correlated with high IQ. Mathematics and music are examples.

Intelligence quotient, or IQ score, is the popular measurement for comparing an individual's "mental age" to the "chronological age". We shall define a student as mathematically gifted if the student's IQ is at least three standard deviations above the mean IQ for students of the same chronological age of the student and the student shows a gift in math. This is why the subtitles of these web pages say "student showing high promise in math."

Some students attending MathPath are "Profoundly gifted." This denotes the convention that the student's IQ is at least 5 standard deviations above the mean. This does not imply that their gift in math is in lockstep with their IQ; but the gift has the potential to be. What we know about the PG at MathPath is that they also love math. This makes sense. For example, a PG at a music camp is likely to love music.

The Stanford-Binet Intelligence Scale is a widely used IQ measuring tool for identifying extremes above and below the norm. The standard deviation values referred to in the preceding paragraph are relative to the Stanford-Binet IQ Test (Version 5).