To give an example: A simple multiplication of two numbers is better seen as rotating one of the numbers to be perpendicular to the other and then quantifying the area/volume spanned by them. This gives vector dot product.
While geometry might better address "why", algebra gets into the work of "how to do it". Mathematics in old times, like other branches of science, did not encourage "why". Instead, most stuff would say "This is how to do it, Now just do it". Algebra probably evolved to answer "how to do it" - the need to equip the field workers with techniques of calculating numbers, instead of answering their "why" questions. In this sense, Geometry is more fundamental providing the roots of concepts and connecting all equations to the real world of spatial dimensions. Physics adds time to this, addressing the change, involving human memory of the past, perceiving the change.