[inimino]

First-order logic is much more abstract. I think a major benefit of geometry is that it introduces visual thinking and is very grounded and real because you can see and draw the proofs. This foundation of visual/spatial intuition seems to be very useful in higher math, as a counterpart to the exclusively symbolic manipulation of algebra or first-order logic.

[ghaff]

As an anecdote, I actually had a fair bit of trouble with geometry in high school even though I did very well throughout high school in math/science generally and went on to major in engineering in college.

I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.

[inimino]

By the way, what I mean by "geometry" is basically reading Euclid and working out the proofs with a straightedge and compass. What I see in the high school geometry homework I've come across is something else altogether.