From what I've seen, genius for me can be reduced to "what one is able to achieve in some dimension with a limited amount of instruction". I subscribe to the i

From what I've seen, genius for me can be reduced to "what one is able to achieve in some dimension with a limited amount of instruction". I subscribe to the idea that someone can be taught to do anything, given enough time and the right guidance. However we are all limited by our available time and our access to instructors. At the top, this becomes even more pressing - who can teach you when you're at the forefront of whatever you have chosen to specialize in? This is where genius comes in, to quote Schopenhauer, genius hits a target no one else can see... - there will come a point where you will have to be your own teacher and whether you plateau or continue to rise will depend on your being a genius. This manifests in a whole variety of ways - for some, it may be mastering calculus as a pre-teen and while Erdos, still had good and dedicated teachers, there will many who would fail to grok the subject given the same upbringing. For others, it is mastering the art of writing symphonies at the young age of 8 like Mozart. My personal favourite to observe is in sports such as tennis or football where the spectator has the chance to witness moments of true technical brilliance and improvisation under very quick and stressful situations.