Plato was a philosopher who wrote dedicated those words of wisdom to his master Socrates. As a mathematician, he was fond of geometry. He warned his disciples, not to enter his academia without having any knowledge of geometry. Pythagoras was his inspiration for curiosity in mathematics as a language and arche-type of nature. Later, Galileo affirmed this affection to mathematics through his Magnum opus. Plato was fascinated by mathematical reality upto an extent that he believed that the physical reality is merely an illusion, which is in nature of change. His "allegory of cave" in Republic reflects upon this dilemma, in which the prisoners of the cave is in already. Only a prisoner who frees himself from the cave, and goes outside it. He was bewitched by the beauty of Sun. The dazzling beauty of Sun makes him realize that the Cave is a false reality, and prisoners are devoid of the experience of Sun. He decides to enter into the cave to make them aware that the reality is awaiting you outside cave. His arguments make him unpopular, and the fate was his persecuted prosecution. The theory of two worlds were canonized through writings of Bishop Augustine. And Plato was symbolized as the master thinker of Christianity. The transcendental approach to reality was conceptualized by Plato while keeping in mind the natural philosiohers, like Anaximander, Democritus, Anaxemnes, Heraclitus, Permenides, etc. Particularly, Heraclitus proclaimed that "everything is in flux". On the other hand, Permenides thought about a fixed Universe without any material change. Einstein's four dimensional Universe, known as the Block Universe, is a fitting illustration of this hypothesis. Plato developed his theory of two worlds; one is visible and constantly changing; physical realities, as per Hindu mythology, this phenomenon is known as Maya. And the second world is a fixed form of the world, the world of forms, the mathematical reality. His skills of geometry helped him in theorizing the concept of mathematical reality. His disciple Uclid is famous for the development of the Uclid theorem in geometry.
In the era of quantum world, or it may be called as "quantum cave" the physical reality has obscured from the human perception. What is truth if not hypothetical, conjectural, and probable? The only certainty is mathematical reality. But the final truth as a material and physical reality is uncertain. The theory of form has made the Earth a mathematical reality. But more you quantify it less you are certain on quantum level that what is really truth behind the creation and growth of cosmos. The perception of truth has changed over the years. The rules and theorem of mathematics have come to the advanced stage, but the cosmos and its mysterious horizon is obscured and withering away from human's sensorial perception. It remains in/through intuition and dreams. The real is non-natural. It is projection of human's intelligence. Our world could be named as a formal and mathematical reality. Which is precisely so certain that it doesn't fit in a world of Quantum mechanics. "There is something in everything and everything in something". As someone rightly said. But what is the reality in cosmic sense? All phenomenons seem to be a projection of human's intelligence. Quantum Cave needs a Socrates to find a Sun who represents the beauty of truth. For mathematics can play a role of companion. The true guide is intuition.
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