/sci/ - Science & Math

I wanted to explore the nature of mathematics and numbers through geometry, however when I see the wiki I come across pic related.

Most of these subjects require me to be very prepared on a myriad of different topics (like topology).

I mean I don't really know what a smooth manifold is (doesn't make much sense to me) or what Riemman geometry is. Algebraic geometry sounds like a nice topic, but I am unsure of what it is really.

So I said I am interested in Geometry, but when I see at these subjects they don't really seem like the things I would like to learn? What should I self study to learn what I described at the beginning?