Babylonian Style Algebra

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

Mathematics principles were often described verbally or through pictures and diagrams. 


Is mathematics all about generalization and abstraction?

Generalisation and abstract are very important areas of mathematics as it helps people come up consistent with ways to solve recurring problems. However, it isn’t all about generalisation and abstraction. Generalisation and abstraction are just tools used to create a general case for everyday problems. However, there are many problems, especially those in fields like economics, engineering, and physics, that may not be so easy to generalise. Mathematics is more about problem solving and critical thinking, as generalisation does not apply to all problems.

Thinking about various areas of mathematical knowledge -- number theory, geometries, calculus, graph theory, etc. etc. -- how could you imagine stating general or abstract relationships without algebra?

Again, most mathematical principles  were stated verbally or pictorially. For example, the oythofrean theorem might be stated as “in a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.” Stating mathematical concepts back then obviously was more work/writing, but there were no global and abstract symbols used back then.