This idea of being skeptical so that a truer understanding of nature can be found is still very much a part of modern science. Mathematics gives us the power of perception. Though the physical applications of mathematics may change, the thoughts themselves are eternal and are in another realm of existence. Mathematics is thought and, therefore, it is eternal and can be known by anyone. They are the tools we use to map the world.
Experience is the key.
Out of Plato's teachings grew the belief that when one studies mathematics, one studies the mind of God. Mathematical symmetries are the language of universal design and harmony. Their faith in an ordered universe compelled them to make precise observations and they were sustained by their belief in the power of reason. In one form or another modern scientists have this faith in an ordered universe and the power of human reason. A paradigm is a general consensus of belief of how the world works.