I'm aware that many maths problems can be expressed and understood in geometry, for example, complex numbers can be expressed in 2 dimensions, that can be useful for some problems. Maths started in geometry.
My question is, can you map all of mathematics to geometry and solve all problems using geometry and geometric reasoning? Secondly, is that worthwhile? Thirdly, why not?
I'm aware that people don't do that, they use sets, or they use other mathematical systems defined by the rules of the system.
I only have basic 1st year university math understanding. My question comes from a few problems I've had over the time I have been a programmer and I found many solutions using geometry, for example for representation of dates and times, if they are represented with dates in the x axis and times in the y, its easier to find contained items using geometry. Many other problems seemed to map to geometry well.
One reason why I ask this question is that I had a creative though that it would be nice is there was a kind of web browser which could browse geometric structures and do reasoning in geometry and if all data was represented in this browser as geometry, graphs, charts, lines, circles, etc. As a "human" I find it easy to think about spacial relations, for example when I was programming 200,000 lines of code in a team, it was easier to imagine it spatially than in any other way. I would image the shape of the text and the logical connections.
Also there is the science fiction book Neuromancer which visualized the web as a network which integrated with the though processes of the person, it wasn't "web pages" but the idea fits well with a geometry based web.
As I said that's a creative idea, not a maths idea, but one motivate is that if I wanted to make such a "browser" I wonder if maths could fit inside it in some way.