"Just how rare is mathematical talent? Many observers believe that such talent is indeed rare and that we now come close to discovering all of it. According to them we cannot markedly increase the number of Ph.D.'s in mathematics if we wish to maintain traditional standards — the native ability just isn't there. Others (and might be in this group) believe that many more people could create mathematics if they had the proper instruction. It would be pretty hard to devise a controlled experiment to answer this question."