For all we know, Clara Schumann may have been a genius, but, oddly enough, having a extremely high IQ is not a prerequisite for being a prodigy. A study of eight prominent child prodigies this year found that they scored between 108 and 147 on a Stanford-Binet IQ test.
Lewis Terman, who invented the test in 1916, defined 'genius' as one who scored above 140, meaning that these prodigies were certainly intelligent, but not extraordinarily so. What the researchers did find extraordinary, however, was that all of the prodigies tested in the 99th percentile in a test of working memory, with six out of eight scoring in the 99.9th percentile.
As the pioneering cognitive scientist George Miller suggested in 1956, most of us are able to hold only seven things in our heads, plus or minus two, at any given moment. Prodigies apparently can handle quite a bit more than that, at least when it comes to their area of expertise.
Research suggests that they can do so by keeping their long-term memory extremely well organized and accessible to their working memory with shorthand retrieval cues. It's a little bit like repurposing your hard disk space to boost the RAM on your computer, creating a 'virtual memory.'
We can all do this to some extent. While you may have trouble holding in your head a list of, say, ten unrelated words, you'll have no difficulty remembering them if they are arranged into a meaningful sentence.
Clara Schumann, for her part, was among the first concert pianists to perform entirely from memory, having been trained to do so by her father. Nancy Reich, author of "Clara Schumann, The Artist and The Woman," notes that at least one audience member regarded her lack of notes as pretentious, yet discussions of her work always praised her faithfulness to the original score.