Home

Essence of Math

Toolness Of Math

The Number Line

Fractions

Negative Numbers

Irrational Numbers

Variables

Equations

Functions

Modulus

Binary Numbers

Complex Plane

Mind-Warm-Ups Real Numbers

Mind-Warm-Ups Vector Spaces

Mind-Warm-Ups-ODEs

PDE

Essence of Math

Toolness Of Math

The Number Line

Fractions

Negative Numbers

Irrational Numbers

Variables

Equations

Functions

Modulus

Binary Numbers

Complex Plane

Mind-Warm-Ups Real Numbers

Mind-Warm-Ups Vector Spaces

Mind-Warm-Ups-ODEs

PDE

The word *mathematics* is a human invention and like many other words of human languages it is intended to represent aspects of existence. For example, when the human body craves food, the human is said to be *hungry*. The representation of the intake of oxygen and the output of carbon dioxide by the lungs as *breathing* is another example. The association of an invented word with an aspect of existence is the essence of human languages. *The identities of words are the aspects of existence they represent. However, the identities of aspects of existence are not the words that represent them*. In other words, *words* are not the *essences* of the aspects of existence they represent. The unawareness of the difference between these two identities is a major educational problem. This problem is prevalent in mathematics. The first inclination of the average individual or even above average individuals (including distinguished mathematicians) is to equate the *essence* of mathematics with its symbolism. The symbolism of mathematics is not its *essence*, rather, it is the language used to realize the *essence* of mathematics. In other to understand the *essence* of mathematics we must go back to the beginning of *Time* for it is *there* that the existential role of mathematics was initialized.

The schools of thought on how the Universe began can be broadly assigned to two groups of thoughts: *faith-based* and *non-faith-based*. The *faith-based* school of thought believes that a Creator created the Universe. The *non-faith-based* school of thought believes that the Universe came into *being* from some *random nothingness* and not from any initial Creator. Both schools of thought agree that the Universe was created when *matter* was initialized *in* Space. Therefore, in essence, both *matter* and the *containership property* of Space made the Universe possible. As was previously stated, the words *containership*, *space*, *matter* are human inventions but the aspects of existence which they describe predate humans. The aspect of existence which *containership* represents is the *capacity to hold things*. *Containership* is primarily a mathematical word because it is derived from the word *container* which represents a space characterized by its dimensions. Consequently, in order to understand the existential role of mathematics we must understand the role of the aspect of existence to which mathematics was first associated. This aspect of existence is the *containership property* of Space and its existential role is to solve the problem of *matter's residency* in space. This was its role in the beginning, it is its role now and forever.

The *containership property* of space is mathematics by association so their existential roles are the same. Over time, many more aspects of existence have been packaged as *patterned thoughts* and have been associated with mathematics. Nonetheless, its *essence* as a *problem-solving tool* remains an existential constant. It is this *problem-solving essence* that constitute the existential identity of mathematics. It is also this *problem-solving essence* that established *mathematics* as the *first* and *oldest* subject. In other words, before there was *matter* there was the *containership property* of *Space*.

Peter Oye Sagay