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