Babylonian ‘algebra’ from Crest of the Peacock

 I can see that a lot of the Babylonian word problems have to do with agriculture and farming (at least from the examples we have seen so far), that the "variables" they used were quantities they use in farming. I think it has to do with the kind of social background at the time. The Babylonians were using something they see a lot in their daily lives. So to state a general mathematical principle, they had to resort to using terms like "ush", "sag" and "lagab". These were the "variables" resorted to using when there was no proper algebraic notations.

I do not think that mathematics are all generalization and abstraction. The Babylonians probably developed these problem solving skills (including algebra) when they faced real problems in life ( like food distribution, area of farms etc...). They had to come up with systems and ways that allowed them to solve these problems. So the origins of all these algebraic expressions and equation solving systems might well be some really specific life problems they encountered. And from these very specific problems, they developed systems to solve them and later on generalized them.

If I were to work on different areas of mathematics without proper algebra it would be very tough. I was taught algebra when I was really young and a lot of the mathematical concepts I learnt later on are heavily dependent on algebra. Without algebra, we may have to resort to words and phrases of the English language. An example of this is Calculus: Instead of using y'', we may have to say "the rate of change of the rate of change of the displacement of the car". As you can see for something tangible like length, we can just use a word for it, but when it comes to abstract concepts like the second derivative, there is no easy one-word description to represent the quantity. That's why I am really impressed that the Babylonians did play a part in the development of Calculus.