When I think of one of the underlying themes in math, I think of patterns. Even in the earliest forms of math when people unknowingly used it to decide how much food to prepare, they were forming a ratio of a certain amount of food per person and multiplying that amount by how many people there were. This is a pattern that begins with one unit and continues to the next. This is just one of the types of patterns in mathematics.
I used to love math because it meant purely experiencing the joy of problem solving. This is probably why I like algebra. I enjoy taking a lot of information that sometimes seems unrelated to each, breaking it down into small pieces, and building it back up into one clean answer. It doesn’t matter how I got the the clean answer, but just that I got there. Math is problem solving. There are always multiple ways to find the solution, but a solution always exists even if it is the empty solution.
Another reason I enjoy math is because I think it suits my learning style. With any new information I take in or learn, it is really important for me to first look at the big picture. From there I dive deeper into the topic looking at what things are related and connected. Math is like this in a sense that it takes big ideas and problems and breaks them down. It seeks to solve these problems by finding a pattern starting with the smallest details, and growing from there.
These small details often form a pattern because of the logic or building blocks they are built on. Math is empirical; it is not founded on opinion or values. We can ask “what if?” and “what if not?” and are able to make solid consistent conclusions every time. The nature of the rules of logic is what allow us to find patterns in mathematics.