In ancient times, people believed that the sun and moon revolved around the earth. The prevailing concept of the heavens was that the sun and moon and the stars moved in fixed, perfect circles across the sky each day and night above a firm and fixed earth, the immobile home of all life in the universe.
As technology advanced and the science of astronomy developed, and more specifically the closeness and care of observation of the heavens grew more rigorous, certain inconsistencies in this model of the universe became apparent. For example, certain "stars" appeared to wander across the sky rather than moving in a fixed path. These "stars" came to be known by the term planetae, the Greek word for "wanderers," and they are today what we call planets.
Around the time of Ptolemy--although certainly before him--the state of science was such that the motion of the planets could be described through a somewhat complicated but reasonably consistent system of "deferents" and "epicycles." To understand what is meant by the term "epicycle," consider a small circle or wheel rolling along the surface of a larger wheel (the deferent). A given point on that circle will vary from the path of the edge of the larger wheel by a small amount (from zero to the diameter of the small circle) and thus "wobble" as the smaller wheel rolls along.
As it turns out, that description--dubbed the "Ptolemaic System"--is reasonably accurate to describe the motion of the planets through the night sky from a vantage point on Earth. It is wholly inadequate to explain why the planets appear to move through the night sky, but that's all right. The Ptolemaic System persisted as the prevailing theory of planetary motion for more than 1,000 years.
Over that time, however, more and more detailed observations--culminating in the discovery by Galileo Galilei that Jupiter has moons that orbit it rather than the earth--it became clear that the Ptolemaic model wasn't adequately describing the universe as we all knew it to be, with Earth at the center. After all, to hear some people tell it, the Bible makes it clear that Creation centers on a fixed Earth. And yet Ptolemy's system wasn't accurately predicting the position of Mars, for example.
At that point, the people who spent time thinking about these things--astronomers, physicists, philosophers, and other scholars--had a decision to make. The Ptolemaic System could be revised to add finer detail--epicycles on epicycles, in an increasingly complex Rube Goldberg creation--or, maybe, the central thesis of geocentrism was to blame.
Some decades before Galileo, Nicolas Copernicus, a Polish philosopher (and many other things; he was, like Leonardo, a polymath, proficient in a wide array of disciplines), had posited a theory of planetary motion what was heliocentric--sun-centered. Galileo, a gregarious personage of the 16th century who moved in impressive circles (he was a personal friend of Pope Urban VIII, the most powerful person in the world at that time) and perhaps the most famous scientist of his day, became a champion of heliocentrism.
At that time, the Catholic Church was not wholly opposed to heliocentric theory, but Urban, aware of Galileo's work in the area, asked that the book Galileo would write on the subject treat other theories with equality on an even-handed basis. Galileo's work, now treated as foundational to physics, was presented as a dialogue between advocates of geocentrism and heliocentrism. Despite Galileo's efforts to be even-handed, the character who advocated geocentrism came off as a fool. Even worse, Galileo put some of Urban's words in the mouth of this character. This bit of suspected heresy earned Galileo a trial before a formal inquisition and ultimately cost him his freedom; he spent the rest of his life under house arrest.
Galileo would be vindicated by the work of Isaac Newton and Johannes Kepler, who between them developed and derived the laws of motion and the mathematics necessary to conclude that the sun is at the center of our solar system. That did not stop some lesser lights, who persisted in the drawing of ever-more-complex systems of epicycles well into the 19th century before dying out.
The lesson of epicycles and the demise of the Ptolemaic System is an important one for scientists and philosophers, and for people generally. When the observed facts do not match up with our understanding, it is our understanding that has to give way in favor of something new, not the facts. Holding on to first principles where they are contradicted is lazy. We have to be willing to question our prior conclusions, no matter how dearly they are held.
We don't know everything about the universe--far from it. In fact, the more we know, it seems the more we realize that we don't know. Some people use this as an excuse to believe in the supernatural, leading to a peculiar sort of "proof" of things. My 9th-grade geometry teacher referred to this as the "miracle theorem," a special rule that would solve all problems whenever it was invoked. It most often shows up in a particularly difficult proof, as something like this:
1. Given A, B, and C.
2. Given that A = B, and given that C=60.
3. A miracle occurs.
4. Therefore, B > C. QED.
Of course, that's not proof of anything. After all, if the miracle theorem can be invoked in any proof, it can be invoked in every proof, and there is no point in learning anything or thinking about anything. Which might be what the people who advocate this kind of philosophical structure have in mind, come to think of it.