I'm not an expert in maths' history, but my opinion is:
1) I am fascinated by how some people have developed an absurd amount of things even in very short lives (I'm thinking of Galois, Riemann, Cauchy, Ramanjuan...)
2) I think that the development of maths is chaotic, due to the fact that often to further research on topics in a field you need results of some other field, but very often researcher in the first field know "little" of the second. Also you have things that are conjectured and then solved only centuries later (e.g.: Fermat's last theorem).
3) I think maths is advancing faster, primarily because there are many more researchers now than in the past. At the same time, it's becoming more and more difficult for a single person to give large contributions and the amount of study to get to the edge of the known maths is becoming little by little almost impossible to achieve.
"Ich bin ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft."