senses and experiences (memory) can be in error thus, the nature of the Universe must be logical and mathematical in nature math concepts and relationships are idealizations of physical world = Platonic world

The fact that the Universe is rational also implies that since our senses can deceived then they are unreliable and possible sources of error in our understanding of the workings of Nature. Thus, came the belief that underlying order of the Universe can be understood by pure thought and can be expressed in mathematical form. Thus, mathematics lies at the heart of science and is rarely questioned. But is mathematics a human invention or does it have an independent existence? .. There exists two schools of thought. One that mathematical concepts are mere idealizations of our physical world. The world of absolutes, what is called the Platonic world, has existence only through the physical world. In this case, the mathematical world would be though of as emerging from the world of physical objects.

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Pythagoras, contorniate medallion engraved between AD 395 and 410

Pythagoras, and his school, laid down the foundation of mathematical science it differed from modern science in the sense that math concepts were given physical reality

Much of the philosophical foundation to our mathematical sciences is due to the Pythagorean school. Pythagoras lived in the 6th century B.C., most of the work we attribute to the individual is more than likely a composite of work done over many centuries by his school. .. The Pythagorean school presented us with our first physical models, but the role of mathematics was much more dominate than it is today. For example, the Pythagoreans believe that matter was make of numbers. Not idealized numerous fragments, but actual numbers themselves. In some sense, this is an atomic theory, but with pure mathematics replacing matter objects. .. The world being composed of numbers was reached by the Pythagoreans due to their interest in gnomones. This naturally led to the development of the Pythagorean Theorem.

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.. the Pythagorean Theorem, a key concept for physics, was ultimately destructive to the Pythagorean view that the universal was constructed of simple math

.. The discovery of the Pythagorean Theorem led to a crushing blow to the Pythagorean school since it uses the idea of irrational numbers, which was repugnant to the philosophers of the time.

Empedocles developed the first theory of matter proposed that the Universe is composed of some combination of Earth, Air, Fire or Water

Both Plato and Pythagoras influenced the first logically consistent macroscopic worldview, developed by the Greeks in the 4th century B.C. This early worldview was an extrapolation of the Greek theory of matter proposed by Empedocles. This theory states that all matter in the Universe is composed of some combination of four elements: Earth, Water, Fire, Air. These four elements arise from the working of the two properties of hotness (and its contrary coldness) and dryness (and its contrary wetness) upon an original unqualified or primitive matter. The possible combinations of these two properties of primitive matter give rise to the four elements or elemental forms. .. Perhaps only a culture whose leaders were involved with logic and geometry would put the concepts of chemistry in such a logical and geometric form. Fire and Water are obvious opposites, and so are Earth and Air. These opposites share no common properties. There are four properties, each shared by two non-opposite elements: fire and air share the property of hotness, water and air the property of wetness, and so on. Since the four elements are two pairs of opposite elements, so also are the four properties - hotness being the opposite of coldness and wetness the opposite of dryness. Each of the four elements was held to exist in an ideal pure form, which could not actually be found on earth. The real things around us were considered impure, or mixed, forms of these four ideal elements. Thus the different airs, or gases, were the form of air mixed with different proportions of the forms of fire or water; smoke was a mixture of the forms of air and earth with some of the form of fire added. But there was an ideal or pure form of earth, air, fire, and water, and the real ones which we see and use were not ideal but of lesser purity. In other words, the real or observed different kinds of the same element are due to different degrees of the same properties. The elements could be changed into one another by removal of one property and addition of another.

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