The Development Into the Mathematically Talented

From some schools come many students very talented in certain areas, while from others come none. These results, far beyond what any statistical variability would explain, suggest that talent is developed to a greater extent than is popularly believed. Here we identify seven distinct levels of talent in mathematics and describe the enormous effort needed to move from any level to the next higher. The magnitude of effort and guidance required helps explain why most people view their own ability to reach higher levels of mathematical talent as unrealistic. We also point out that Srinivasa Ramanujan, the extraordinarily intuitive Indian mathematician who is sometimes thought to be the prime example of a self-taught mathematician, did not learn in isolation, but had good schooling and had carefully studied a comprehensive advanced mathematical text. Consequently, we suggest that teachers interested in the gifted view themselves as developing students into being talented at least as much as developing students who are already talented.