30 Sept 30: Babylonian ‘algebra’ from Crest of the Peacock

How could one state a general mathematical principle in a time before the development of algebra and algebraic notation?

I think it's very possible to do this. As we've seen in the reading, the Babylonian explanation simply entails more wording. All the symbols and algebraic notation that we use today can be translated into English. Therefore, we could state a general mathematical principle by simply writing out the words. Mathematical symbolism, at least in my opinion, is just compact wording, so we don't have to write essays every time we do math. Kind of like how we make up a word for an animal instead of describing every time what we're talking about.

Is mathematics all about generalization and abstraction?

Modern mathematics, definitely is. All of the branches of mathematics have taken the Hilbert school of thought in terms of reaching new levels of generalization and abstraction. Before, mathematics was closely linked to physics, and we would make up math for the physics we didn't know. Then, using this reasoning, the math would be developed further, using generalizations. I think there's a quote by Vladimir Arnold, who was opposed to the idea of axioms in mathematics, that says that mathematics today is "too much Hilbert and not enough Poincaré".

how could you imagine stating general or abstract relationships without algebra?  

Lots and lots of essay-like pages, as explained in the first paragraph :).