One of the benefits of training in philosophy is an ability to demystify human ideas, and human language.  A good example is given by Tony Grayling’s article in The Guardian today, which makes the case that human intelligence is more than whatever is measured by IQ tests.  Although Grayling is sometimes prone to unbehooving belligerence (especially when he argues against religious belief), his argument here is clear and calm.  It is not, however, original.  My first investigations into the literature on IQ tests were conducted almost 30 years ago, and even then empirical evidence existed that the test scores of US children were significantly impacted by the race of the persons handing out the test papers; black children do significantly better if the test invigilators are black rather than white.  In the light of such evidence it requires a special kind of either stupidity or malfeasance to believe that only something innate is being tested in an IQ test.  IQ tests test one’s ability to do IQ tests, under the circumstances in which the test is conducted, and nothing more.
However, despite his admirable efforts in demystifying IQ testing, Grayling continues to leave mystified part of the story.  He says:

Some mental aptitudes are hard-wired: gifts for maths and music (which often go together) require no knowledge, and manifest themselves early in life. So does artistic ability. “

Professor Grayling appears to know nothing about mathematics, music or art.   While certainly benefiting from natural abilities (and perhaps lucky wirings of the brain or other physical quirks), no one gets very far without acquiring a great deal of knowledge, and undertaking many hours of training, in each of these fields.  Even Srinivasa Ramanujan, every non-mathematician’s favourite example of a “natural-born genius mathematician” was taught, first by himself (from text-books he found), and then by G. H. Hardy.  Ramanujan was famous for his ability to intuit mathematical relationships between numbers which were completely non-obvious, even to other mathematicians working in the same field.  Some of these intuitions were sublime and very profound.  But even at the height of his powers as a mathematician, these intuitions were just as likely to be wrong as correct.  As John Forbes Nash once remarked of his own madness, there was no difference inside his head between his great mathematical ideas and his paranoid lunacies; only the outside world treated these ideas differently.
The situation in music is the same as in mathematics,   Perhaps the greatest musical prodigy of all time in western culture was Felix Mendelssohn-Bartholdy, more advanced even than the young Mozart.   And some of Mendelssohn’s greatest music, and some of the greatest in the western canon, was composed in his teens — for example, the string Octet, written when he was 16. But listen to his 12 string symphonies, composed between the ages of 12 and 14.    There is a discernible increase in sophistication and musicality across the 12, with the last 3 being considerably more sophisticated musically than the preceding 9, and the 3 before that likewise clearly more sophisticated than the first 6.   These are not the works of someone relying on hard-wired gifts or natural ability, with the music arriving fully formed from some untrained, black-box genius-brain, as Grayling would have us believe.  Rather they are the contingent and constructed works of someone struggling with the material – learning, improving, experimenting and visibly maturing as he practiced and trained himself to be a composer.  One can’t compose music without having lots of very specific knowledge — knowledge of the capabilities and constraints of different instruments; knowledge of the rules (as were then believed) of melody and harmony; knowledge of the patterns and styles used for organizing musical materials across long time durations (eg, Sonata form; key relationships across movements).  None of this knowledge (which is both know-what and know-how) is hard-wired in anyone, and all of it has to be learnt, no matter how good one’s musical ear is.   Most of it is socially constructed (ie, it differs from one society to another, and from one time to another), and thus cannot possibly be innate.
No doubt Mendelssohn had some natural abilities, perhaps congenital (since both his father’s and his mother’s families had musicians across several previous generations), but he also had some very strong sociological advantages:  a nurturing and loving home life, the best teachers in the Prussian empire, the best instruments, original manuscript copies of the works of the great composers, and weekly musical salons organized by his mother in the family living room, where Berlin’s best musicians would play the western canon (as it then was) and also play his new compositions.   Who could but prosper in such an environment. If I had to bet on the ratio of nurture (including training and hard-work) to nature in the case of Mendelssohn, I would put it at 95% to 5%.
Coincidentally or otherwise, the demystified view of genius was presented (with references to the literature) by David Brooks in the NY Times yesterday.