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Philosophy of nature
Thales, Anaximander, and Anaximenes are the three greek philosophers from Miletus that form the Milesian School. These philosophers defined all things by their quintessential substance of which the world was formed and which was the source of everything. Aristotle, perhaps being anachronistic, called this fundamental substance the ἀρχή / arche).

Thales

Thales, known as the Father of all Science, was the first of the philosophers to look at the nature of the earth. Thales defined this arche to be the element of water. Thales formed the Thaletian hypothesis of water in which he saw water as the primordial substance that was responsible for the formation of everything on Earth. Thales taught that water was indeed the arche but he struggled to explain some parts of the world and how water made them up, such as fire. Anaximander

Anaximander chose an unobserved, undefined element, which he called apeiron (ἄπειρον "having no limit") as the fundamental substance. Anaximander was the first Greek thinker to break nature down and suggest a balance of forces between the elements that make up nature. He reasoned that if each of the four classical Empedoclean elements (water, air, fire, and earth) are opposed to the other three, and if they cancel each other out on contact, none of them could constitute a stable, truly elementary form of matter. Consequently, there must be another entity from which the others originate, and which must truly be the most basic element of all. The notion of temporal infinity was familiar to the Greek mind in the religious conception of immortality and Anaximander's description was in terms appropriate to this conception. His arche is called "eternal and ageless" (Hippolitus I,6,I;DK B2).

Anaximander was one of the first scientists/philosophers to present a differing viewpoint on how human life was brought about. He was one of the first to present an idea of evolution and stray away from the common thought that humans were formed by the Gods, but his concept differed from the evolution that is known in modern times. Anaximander created the idea that man evolved from fish and that all life was from the water originally.

Anaximenes

Critics disliked the unspecified nature of the apeiron, which caused Anaximenes to define it as being air, a more concrete, yet still subtle, element. He defined the fundamental substance as air, and taught that the world is formed from air, mist and vapor. Although his work and writings have been lost over time,later authors record that Anaximenes suggested that nature was formed from air that condenses from a mist to water and then to a physical matter. Anaximenes held that by its evaporation and condensation, air can change into other elements or substances such as fire, wind, clouds, water, and earth. He showed how fire causes less water which causes more air while condensation causes more water which leads to more physical matter. Anaximenes' ideas about air started to have a divine appearance due to air having the ability to bring about all matter and change physical state.

The three philosophers that formed the Milesian School taught differing ideas and concepts about the philosophy of nature and cosmology. Thales was the first of these philosophers and he taught more concrete ideas. Anaximander created more abstract ideas that were not liked by the people as much as Thales teachings. His ideas were less believable because they discussed the idea of an undefined substance that created everything and that brought balance in natural forces. Anaximenes strayed away from Anaximander's thoughts and teachings due to how abstract his thoughts were and formed his own on the basis that air was the element that formed all matter. Anaximenes teachings were looked on as making air a divine element. These philosophers had differing theories, but their teachings on the philosophy of nature and cosmology drew attention to similar fundamental questions.

Cosmology
The differences between the three philosophers was not limited to the nature of matter. Each of them conceived of the universe differently.

Thales

Thales was the first philosopher to look at the arche of the world as well as he was the first philosopher to look at the shape of the earth and everything surrounding it. Due to his belief that water was the primordial substance, Thales taught that the earth was a floating disk that was floating on water. Along with looking at how the shape and makeup of the Earth, Thales studied what was surrounding the Earth was the first to predict an eclipse. He predicted that there would be a total lunar eclipse in the 6th Century on May 28, 585 B.C. Anaximander

Anaximander placed the world at the center of a universe composed of hollow, concentric wheels filled with fire, and pierced by holes at various intervals, which appeared as the sun, the moon, and the other stars. Anaximander thought that the earth was a suspended cylinder where the height of the cylinder was one third the diameter of the flat end. The earth was suspended in his teachings due to his belief that it was the same distance from the planets, stars and everything that was surrounding it. He taught that the top flat side of the cylinder was the inhabited part of the earth. Along with forming a concept of the universe and the earth, Anaximander was the first scientist/philosopher to form a map of the inhabited part of the earth.

Anaximenes

For Anaximenes, the sun and the moon were flat disks traveling around a heavenly canopy, on which the stars were fixed.