Other examples like Grothendieck: Wiles (Fermat), Perelman (Poincare), Newton (calculus), Ramanujan. > Spend too little time and you toil away in a cave, at be

Other examples like Grothendieck: Wiles (Fermat), Perelman (Poincare), Newton (calculus), Ramanujan. > Spend too little time and you toil away in a cave, at best reinventing things that were invented already without your knowledge. Grothendieck disputes this point. He reinvented the wheel many times when he was 17-20 years old, but believes it was training for accessing the required cognitive spaces. He says: A few years after I finally established contact with the world of mathematics at Paris, I learned, among other things, that the work I’d done in my little niche [. . . had] been long known to the whole world [. . .]. In the eyes of my mentors, to whom I’d described this work, and even showed them the manuscript, I’d simply “wasted my time”, merely doing over again something that was “already known”. But I don't recall feeling any sense of disappointment. [. . .] Without recognizing it, I’d thereby familiarized myself with the conditions of solitude that are essential for the profession of mathematician, something that no-one can teach you. [. . .]