I have very little knowledge about Ricci flow and Riemannian Geometry. I can't understand the evolution from the traditional Riemannian geometry to Ricci flow (or geometrical analysis ). Obviously, they look quite different.
In the 1970s and before, seemly, most paper of Riemannian geometry are delicate and short. And the method has not universality in my view.
But now, the paper become complex and long. But they have similar frame, tool and way of thinking . For example, in mean curvature flow and Ricci flow, many same question is studied.
Seemly, the era has changed from division to unity (I'm not sure if I was imagining it). Who can tell me the history of Riemannian geometry in recent decades? One hand, I want to know the story. On the other hand, I want to find a research direction which suitable for me. In fact, now, give me a paper, I cannot discern the magnitude of its significance. Therefore, I don't know which direction is potentially significant.