Babylonian Algebra

 Babylonian Algebra.

The reason that Babylonians could formulate mathematical principles without the development of algebra or algebraic notation is because of the practical uses of math allowed them to create hypothetical situations, problems and solutions based on their reality.

Babylonians and other ancient civilizations developed mathematical concepts in response to the need to measure land, register wealth, and track transactions. This practical understanding is derived from the ability to envision scenarios where math can be applied. But this practical usage limited their imagination. The fact that almost all the calculations were made based on real quantities prevents them from thinking about concepts like zero or negative numbers.

When the Babylonians were solving problems, the method didn’t use a second-order polynomial but several versions of simplified quadratic equations, replacing higher orders with combinations of powers of two.

Answering the question of whether mathematics is all about generalization and abstraction, I think mathematics started as a tool for solving problems, and once the problems are solved, the look back of the method inspired the generalization and led to the invitation to play with abstraction