A powerful idea sits at the epicentre of our educational world view. It is the idea that the potential of young people - whether in mathematics, PE, music, languages, whatever - is determined, to a large degree, by genetic inheritance.
Talent is the word we use to rationalise this idea, the notion that brilliant mathematicians, scientists or linguists are born with excellence encoded in their DNA. Teachers and parents connive with this concept persistently with phrases like "Danny has a gift for art" or "Jane is a born mathematician". Many schools have Gifted and Talented programmes.
But what if this seductive idea is all wrong? What if our deepest assumptions about success in education, indeed in life itself, are misconceived? What if giftedness is not just a meaningless concept, but a corrosive one, robbing ourselves and our pupils of the incentive to work hard and excel?
After all, what is giftedness? We all think we know it when we see it. As one maths teacher told me: "Mathematical aptitude is something that a good teacher can just see. It is about the way a young mind copes with numbers that tells you whether they have it in them to excel."
But how does the teacher know that this student, who looks so gifted, has not had many hours of parental training behind the scenes? How does he know that the initial differences in mathematical ability between this youngster and the rest will persist over many years of study? In fact, he doesn't.
One study, for example, found that top performers had learnt no faster than those who reached lower levels of attainment: hour after hour, the various groups had improved at almost identical rates. The difference was simply that top performers had practised for more hours. Further research has shown that when outstanding students seem to possess an early gift, it is often because they have been given extra tuition at home by their parents.
Precisely the same is revealed with child prodigies. At first sight, they seem to have been blessed with amazing skills; skills that have enabled them to take a shortcut to eminence. But a closer inspection reveals a very different story.
Rudiger Gamm, a mathematical prodigy able to find the quotient of two primes to 60 decimal places, was described as "a human miracle" by one magazine. But Gamm devoted his life to maths from an early age, he practises for many hours a day, and he relentlessly learns number facts and procedures. Far from being a mathematician zapped with powers that enabled him to circumvent practice, Gamm embodies the rigours of practice.
So, could "ordinary" pupils who practised hard perform maths feats? In 1896, Alfred Binet - a French psychologist - performed an experiment to find out. He compared two calculating prodigies with two cashiers from a store in Paris. The cashiers had an average of 14 years' experience in the store but had showed no early gift for mathematics. Binet gave the prodigies and the cashiers identical three-digit and four-digit multiplication problems and compared the time taken to solve them.
What happened? You guessed it: the best cashier was faster than either prodigy for both problems. In other words, practice, on its own, was sufficient to bring "perfectly normal" people up to and beyond the remarkable speed of prodigies. The conclusion is inescapable. As Professor Brian Butterworth of University College London, the world's foremost expert on mathematical expertise, has put it: "There is no evidence for differences in innate specific capacities for mathematics."
Of course, none of this is to deny that some kids start out better at maths (or English, or whatever) than others; it is merely to suggest that the starting point we all have in life is not particularly relevant. Why? Because over time, with the right kind of practice, we change so dramatically.
It is not just the body that changes, but the anatomy of the brain. A study of London taxi drivers, for example, discovered that the area of the brain governing spatial navigation is substantially larger than for non-taxi drivers - but it did not start out like this; it developed with time on the job. Similarly, in a study of maths prodigies it was found that they not only use conventional neural networks when making calculations, they also use a system of the brain implicated in episodic memory (this is the immensely powerful memory used to store autobiographical experiences).
Needless to say, your skull contains this system and you, too, can corral it into action when performing multi-digit calculations. But there is a catch: you can only purchase access to this prime neural real estate by building up a bank deposit of lots of practice.
The issue of talent would not matter terribly much if the question was merely academic. Unfortunately, it is not. The talent myth is not just widespread but powerfully destructive, robbing individuals and institutions of the motivation for change.
Consider a young person (or, indeed, anyone else) who buys into the talent myth. They are likely to regard any failure as evidence that they lack the requisite talent and are therefore likely to give up. But someone who believes that excellence hinges on hard work will not regard failure as an indictment, but an opportunity to adapt and grow. They will therefore persevere and eventually excel.
It is hardly surprising, then, that patterns of success and failure in the real world have very little to do with genes and very much to do with our core beliefs about talent. As Edison said: "If I find 10,000 ways something won't work, I haven't failed. I am not discouraged, because every wrong attempt discarded is another step forward."
It is a message that should be stapled to the wall of every school in the country. Matthew Syed is the author of 'Bounce: the myth of talent and the power of practice'