It is me again to bother you. Since my last post I started to look at some seemingly "serious" mathematics for background study. Accidentally I went into a university bookshop and came across some "differential geometry", "algebraic geometry", "geometric analysis", etc. I am a writer, and my math skill remains at pre-calculus level, but I am (doubly) confident that the subject I learned long ago called "analytic geometry" contains quite a handful of geometric figures and coordinate systems. I was genuinely surprised that those "advanced geometry" textbooks I randomly picked-up contain very few figures, and radically different from what I expected if they have any. Although I work with literature and languages, the descriptions in math textbooks sound to me just like Alienese. I was hoping that the geometric figures might be enlightening somehow, and I was so so wrong.
Well, this is my question: where are the geometric figures in those "advanced geometry" textbooks?
PS The same applies to what I heard about topology. I learned it from wikipedia that mathematicians are like changing coffee cups to donuts in topology, so I guess I might see loads of "cups and donuts", or similar stuff, in topology textbook. I was rather disappointed when I open a book called "Introduction to General Topology", all that I read is about some set things.
PS2 When I was roaming around the web, I learned that a prestigious mathematician called Shinichi Mochizuki proves "abc conjecture". The abc conjecture I read from wikipedia sounds quite "algebra" to me, but on Shinichi Mochizuki's homepage he called himself "inter-universal geometer". I take that "inter-universal" is like something very powerful. But how come a geometer solves an algebra problem?