Timaeus is one of Plato's Socratic dialogues and is often the subject of philosophy research papers. It is believed to have been written around 360 BC, making it one of the later dialogues to have been written by the philosopher. The work itself is largely an exploration of the nature of the physical world and human existence.
The Characters of Timaeus
There are four individuals appearing in the dialogue:
Plato sets the dialogue the following day after an important scene from the Republic, and opens with Socrates dissatisfied with the description of the ideal state. From there, Hermocrates and Critias related the story of Solon's journey to Egypt, where the legend of Atlantis is discovered. Critias then allows Timaeus to digress to the main subject of the dialogue, beginning with the origin of the universe.
According to Plato, we do not know that the lion will come to devour us, but we can have strong opinions about that and these opinions may be correct. Therefore, Plato would encourage Aristotle to move along before the lion approaches.
However, before they leave, Plato must get in that his answer to the Eleatics allows for both change and stability. The Ideas are pure and unchanging. But in the shadowy realm of the senses, midway between Being and non-Being, change does take place. Aristotle and Plato are both correct in denying the Eleatic notion that change and motion are logically impossible. The arguments of Zeno and Parmenides are, however, of interest because they are one of the first attempts we know of to argue about the nature of the universe on purely analytical (as opposed to synthetic) terms.
Your research paper should argue that Plato's idea that we cannot have real knowledge about the physical world and therefore no true science may be right in some ultimate sense, but that it is irrelevant. We cannot know, for example, about certain things that happen to specific particles on the level of quantum physics, but the word "science", as currently used, does not require that knowledge of everything in some ultimate sense, be obtainable. And the achievements of science are undeniable.
Arguments within Timaeus
Plato argues that there is a continuum that runs from absolute Being, that type of Being enjoyed by the Ideas that exist in the mind of God, the Ideas of things of which all earthly creations are but imperfect copies, to absolute non-Being. Between Being and non-Being there is a class of lesser existents and it is in this class that change, growth and decay, occur. Unfortunately, the physical science you would like to see emerge is the study of the realm where growth and decay occur. As such, it is in the domain of the senses not of mind. About the realm of the senses we may form opinions (and these, perhaps, may be correct), but we can have no true knowledge (Timaeus, 51d sqq). All that we call knowledge of the physical world is condemned to be mere guess work.
Timaeus makes the distinction between the physical world, which is changing and corruptible, and the unchanging eternal world. Since nothing in the physical world comes into being without cause, Timaeus makes the argument for a divine creator. Eventually, this discussion gives rise to the idea of the soul and the composition of the universe through the four elements (earth, water, fire and air). Timaeus argues that each element has its own special geometric shape. Earth's element is shaped like a cube; water's is an icosahedron (20 sided); fire's is a tetrahedron; and air's is an octahedron.