<p>There are different kinds of intelligence. </p>
<p>Being able to hear in your head what a complex orchestral composition will sound like, and imagining variations that would enhance it, from reading the sheet music, is certainly an indication of extreme intelligence… in music. Being able to memorize 50,000 digits of pi is an indication of a different extreme intelligence. Being able to write and delivery a speech that brings people to tears is an indication of a different extreme intelligence. Being able to solve complex partial differential equations quickly is an indication of a different extreme intelligence. &c.</p>
<p>IQ tests measure a certain kind of “general” intelligence, which mostly deals with things like common knowledge, applying basic logic to word problems, vocabulary, some math and puzzles, reading comprehension and retention. You might describe it as the tests simply measuring your ability to take that kind of test.</p>
<p>In any case, any particular kind of intelligence will still need to be developed by exposure, use, and practice to reach its potential. Think of your physical brain as being like the raw material for a sculpture. Maybe the area that corresponds to math is like mud in one person and like fine marble in another. Then think of learning to use that area of your brain like the sculpture itself. To make a statue of an angel, just chip away anything that doesn’t look like an angel. With enough effort, the mud could look reasonably good, but the marble statue can be incredible, IF you spend the time and effort to carve it right. If you don’t work on it, the hunk of raw marble is just… possibility, not ability.</p>
<p>If you think someone is “gifted” in some subject, understand that they have found and worked on “fine marble” areas in their brains.</p>