Don't confuse "formal training" with working in a vacuum (re: Ramanujan, Heaviside, etc.), all others are basically world-famous academics that went through typ

Don't confuse "formal training" with working in a vacuum (re: Ramanujan, Heaviside, etc.), all others are basically world-famous academics that went through typical doctoral programs and were in constant communication with their fellow academics; I mean, Godel's correspondence with von Neumann is extremely famous, and the same goes for Ramanujan's correspondence with Hardy. The age of the hermit polymath has been over for half a millennium.