And how does evolution and the "big bang" fit in here? They are taught as scientific but have never been proven. They are refered to as theories, but taught as factual.
We use the word "theory" in regards to the concepts of how something works. One can take classes in "electrical theory". This means that you learn about how electrons flow when induced by cations and anions in a battery, or when induced by an electro-magnetic flux field created by a generator. One can take such a class without ever touching a wire or magnet. Electrical engineering students take such classes, but also do work in lab, doing practical application. In Ben Franklin's time, electricity was indeed nothing but "theory". Nevertheless, we accept it as fact today, even though we still teach classes in electrical "theory".
When Darwin observed the flora and fauna in the Galapaos, he proposed the theory that they had evolved. When Gregor Mendel bred his garden peas, he proposed a theory that traits were inherited. At those points in time, neither man knew how. Today, we do know how. Virtually all biologists accept evolution as factual due to the following. We observe DNA evolving all the time. We know that base pairs mutate. We know the mechanisms of how and why it happens. We see the genomes of things changing right in front of our eyes-in everything from the rhino virus cold germ, H1N1 influenza virus-which never existed until last year, to new dog breeds created through manipulating genes through cross breeding and new varieties of moths that show up on their own. We understand how genes are swapped and new ones come into existence through recombination of DNA in sexual reproduction. The fossil record continues to produce more and more of the connections through the flow of time. Geologic forces have buried ancient remains and many have completely decayed, so we will never recover every single organism that ever existed. Some want to say that because we don't have every single piece, that evolution cannot be. An analogy would be that a prosecutor shows a jury the record of a security camera which took one pic per second and records a murder. Shown are a man with pointing a gun at another person who is standing. The other person is then shown falling in a couple of shots and there is smoke near the gun in the other man's hand. Ballistics tests confirm the barrel and fatal shot match. The defense attorney points out that there is no frame showing a bullet in flight. Just because there is no frame made at that nanosecond, does not reduce the probability of murder to zero. There is too much to support that, and no scientific evidence to the contrary. As to reproducibility, we reproduce genetic change all the time. It appears that biochemists are on the cusp of creating artificial life from non-living things by taking the amino acids from which DNA is made up and in the laboratory, putting them together into RNA or DNA that will be able to replicate itself. Living things DO evolve; does that disprove the involvement of a higher power in the process? No. Evolution does not disprove such a thing. Could there be a higher intelligence behind the amazing universe? Science measures what is and how. It does not measure why. Richard Dawkins says evolution disproves God. It doesn't. Science sees what is happening and can also show sequence of events. There is overwhelming evidence that the Earth is 4.3 to 4.5 billion years old. That evidence continues to grow and grow. There is no scientific evidence to support the Earth being only 5000 years old.
As to the big bang, this is a far more complex situation. For half a century there raged disagreement among cosmological astronomers regarding a "steady state" universe as opposed to one that is collapsing or expanding, and at what rate. Edwin Hubble shocked the world with his discovery that the Milky Way isn't all there is. More and more evidence accumulates supporting the Big Bang. You can actually hear the big bang. Turn on analog radio or TV to a wavelength no being broadcast nearby. All that "static" is leftover radiation. Analysis of Doppler Shifts of light wavelengths shows that the universe is not only expanding, but expanding at an exponentially accelerating rate. We do not yet understand the nature of what genuinely still is "theoretical" dark matter and dark energy. String Theory is still theory. Whether there are 10 or 11 dimensions to our realm is still unclear. Whether parallel universes exist in a multiverse is still unclear, but the absolutely bizarre effect gravity has on the world of quantum physics opens the door to the possibility. Tests and observations seem to be showing that gravity somehow leaks out of one realm into another. All we can do is come up with speculative hypotheses and then continue testing to see what happens. That is the purpose for the new giant particle accelerator on the French-Swiss border. The model we have in quantum physics and the model we have in Cosmology don't fit with each other. Physicists openly admit that and continue to attempt to figure it out. That's what science and experimentation are all about: testing and observing. The evidence we currently have surely points to a Big Bang, but the details of how all that worked out are things we are just beginning to painstakingly put together. Though the universe is flying apart at an ever accelerating rate, a majority of it seems to also be turning and heading toward one spot 70 to 90 billion light years away, something much too far away for any present instrument to see. We have no idea why or how at this point in time.
Aristotle said that we figure out what's real by looking. Our eyes can be deceiving. Today we use more than eyes and ears. We use radar, sonar, infrared, ultraviolet and all kinds of other detectors to measure for us. It seems now that all matter is actually some form of energy, and that every bit of that was once contained in one infinitely small singularity, from which everything we know about sprang forth between 14 and 15 billion years ago. Could it all be an illusion? Of course. Do I exist? "Cogito, ergo sum." Rene Descarte: "I think, therefore I am." But could I be asleep, simply dreaming that all this around me exists? It is possible. Could I be nothing but a spirit, and all that I take as real simply something that seems real? Well, yea..it could be. If someone punches me, it hurts; nevertheless, physics tell me that my body and his fist are virtually nothing but empty space with atomic nuclei separated by enormously relative distances, and that the atomic particles themselves are mostly empty space. (The punch still hurts though.) So as to absolute, total, incontrovertible truth, well that's a really deep question that philosophers still wrestle with.