Good question, perhaps its best to start with what I mean by algabreic intelligence, then the contrast will be more clear. Algabreic intelligence uses the simple idea of equality to produce numerical unknowns from the known via standard mechanistic operations. So algabreic intelligence is mechanistic, operational, deductive, and quntitative. In contrast, geometric intelligence is concerned with the higher level abstract concepts of congruity, scale.

To return to my previous analogy, algabreic intelligence is wing flapping while geometric intelligence is the shape of the wing. The former is arduous time consuming and energy inefficient while the latter is effortless, and unreasonably effective.

I agree with where you're going. I've struggled to find the words to describe this correctly - especially that the current brute force approach of bazillion matmul operations being a mock up of intelligence but not intelligence itself perhaps. At least not a good form of intelligence.

I haven't found any thing in the web about the term geometric intelligence. I recommend you write about this