Babylonian 'Algebra'

Reading this piece it was interesting to see how math was done in a time before the development of algebra and algebraic notation. It is amazing how they solved similar problems to us without using algebra, something I cannot even imagine doing. However, I would imagine that is because I do not know any different and learned how to solve mathematical questions using algebra and algebraic expressions. In a time before the development of algebra and algebraic notation, the general mathematical principles could be stated using operations that could then be carried out using the different types of tables the Babylonian’s had developed. Although Babylonian’s may not have had algebraic expressions, I believe they could have likely generalized mathematical principles using the different types of tables they had created. 

This is a tricky question! I do not think mathematics is all about generalization and abstraction. There are very concrete aspects of mathematics, however those concrete concepts and facts can then be generalized and applied abstractly to different contexts. Babylonian’s seemed to be solving problems for a specific purpose, therefore I do not think generalizations and abstractions were a particularly prevalent part of the mathematics they carried out. However, I would imagine that while Babylonian’s were using their more concrete ideas and concepts to solve problems, generalizations and abstractions to the problems and concepts being analyzed were occurring, as a way to to adapt their previously used methods to new problems that presented themselves. 

Although it is hard to imagine stating mathematical relationships without algebra, I think areas such as geometry and graph theory would be reasonable areas to consider without the use of algebra. This is because these areas require more drawing and visualizing, making it less dependent on algebra should it not be available.