Arthur, Interdependent Complexity

My name is Arthur and my favorite aspect of mathematics is not a particular field of theory, but rather how the fundamentals are used to describe systematically more complex applications of those core concepts. Two of the founding principles in mathematics come in the form of operations, one being the Symmetric Operation, and the other being the Inverse Operation. These two principles follow us as chief definitions of all forms of mathematics we learn during all stages of life. Starting with basic operations such as addition and multiplication. We see this practice in action, where we must add some number that we are given to another number, thus changing the answer by an equal amount. Where multiplication is just fancy addition. Moving on to algebraic substitution where a letter represents and is equal to a number, then geometric substitution where a shape also represents a number, in area, volume, or mass.

The representation of the core concepts continue to get more complex moving into trigonometry, and calculus where entire functions are represented by a single letter through algebraic substitution. Functions that are designed to perform a simple idea with complex application such as Integration is simply (quickly) adding a whole bunch of areas. The more systemic complexity in the expressions in these simple concepts the more difficult they are to express to others, though the principles of the ideas remain simple.

As an illustration to this point:
The center of mass, for the x axis, in a moment is:
\[ \frac{ \int_a^b xρ(f_1(x)-f_2(x))\,dx.}{\int_a^b ρ(f_1(x)-f_2(x))\,dx.}\]
It may appear to someone not trained in these substitutions that I’ve just spoken in High Arcana, magically conjuring some truth into existence, even though they may understand that the center of mass is a single point where the object balances. Because they understand the basic concept, there no reason that the complexity can’t be explained to this person, regardless of how math literate they consider themselves.

That is what interests me in mathematics.