First fix the formatting. The middle part of your text looks like copied from another WYSIWYG editor (different font, indentation of first words in paragraphs, no spaces between paragraphs). It doesn't look good.

Subjective reality is defined as “relating to or of the nature of an object as it is known in the mind as distinct from a thing in itself.”

This definition is incomprehensible to me. Do you think it will be comprehensible to your audience? Besides, "is defined" creates impression of its being a single universally agreed definition, which is not true.

Objective reality usually implies that everything can be proven using rationality, science, and mathematics.

Dubious. First, existence of objective reality doesn't totally banish subjectivity, a believer in objective reality can still hold subjective beliefs. Your "everything" is certainly superfluous.

Second, although it may be sensible for practical purposes to define "objective truths" as propositions which different subjects would agree upon when using certain approved methods of reasoning (i.e. "proving by rationality ..."), many people would argue that "objective reality" has nothing to do with proving and exists independently of mathematics or science. If there were no intelligent agents, there would be no science, but there would still be reality.

Note also another reason why "everything can be proven" is weird when speaking about objective reality: propositions are proven, but the world is made of atoms, not of propositions.

“Reality is that which, when you stop believing in it, doesn’t go away” (Dick).

Who is Dick?

Simply thinking something to be true does not make it so, because “the map is not the territory” (Korzybski, par.1).

Korzybski I know (do all the readers?), but what par.1 refers to remains mystery.

It is mainly the difference between the map and the territory, that marks the difference between objective and subjective reality.

This seems to imply that in your parlance "subjective reality" is the map and "objective reality" is the territory. But you frame the whole essay as a question "is reality objective or subjective", which is not compatible with the map-territory interpretation.

Anyway, if you want to write a four-paragraph essay, you should probably not choose a topic worth several hundred pages thick book.