The geologic timetable espoused in schools and universities today talk about the incredible amounts of time necessary to create the formations we see today. Those unfathomable lengths of time and slow processes mean that humans will never actually be able to observe and test the hypothesis. So in most senses, historical geology is not science, which adheres to the scientific principle, it's simply speculation. Observed Reality
However, it's not really even speculation as real-world evidence and observations contradict the uniformitarian view. Over and over again humanity has witnessed geologic formations created virtually overnight. From volcanic eruptions like Mount St. Helens to fast growing stalagmites, the "millions and billions of years" narrative ignores actual observations and simply assumes slow, steady processes were involved rather than fast, catastrophic ones. For example, a research team recently made rock out of carbon dioxide in 400 days when scientists believed it would take thousands of years to form. Diamonds and other gemstones were also thought to take millions of years to form and be transported to the earth's surface, but now we make them in a matter of minutes in a lab and sell them commercially. We've also discovered modern man-made objects such as clocks, bells, pots and spark plugs cemented in rock strata which is supposedly millions of years old. This is so common in fact, that there is an entire scientific category for these finds called Ooparts (Out of Place Artifacts). In recent headlines, a giant fissure in the earth opened up in a matter of weeks in Wyoming, proving once again that massive geologic features can be formed very rapidly—millions of years are simply not required.
Radiometric Dating
If you were educated in a public school, you probably were taught that radiometric dating techniques have proved the old age of the earth conclusively. What is not taught is exactly how these dates are arrived at, nor all the assumptions one must begin with before making the first calculation. A few major assumptions are:
(1) The radioactive element decays at a constant rate (2) The rock crystal being analyzed is not contaminated by infusion of excess end product (3) The rock crystal contained no end product when it was formed (4) Leaching of the parent element out of the rock sample did not occur.
All of these assumptions have been proven multiple times to be faulty, so scientists developed the isochron verification technique in an attempt to cross-check the results and offer fool-proof confirmation. Then it was discovered that isochrons were also susceptible to the same underlying assumptions and the independent "fact checker" became just as worthless. The truth is that rock samples have to be carefully selected, the particular radiometric dating method has to be carefully chosen, and the assumptions carefully picked in order to arrive at an acceptable date. This is a classic "garbage in, garbage out" scenario as a different sample from the same rock, or a different dating technique, or a slightly different set of assumptions would produce a radically different date. The fallback argument for this reality is that while all the techniques produce wildly different age estimations, they all range in deep time—millions or billions of years old. So while the accuracy may be in question, the fact that the rock is undeniably old is not. But this argument is like having your wife step on a bathroom scale multiple times and getting a different reading every time with a range from 5,000lbs to 500,000lbs, then arguing there's no possible way she weighs less than a full-size truck. Clearly the scale is broken and is completely useless for either attaining an accurate reading of a single object, or being able to compare the weight difference between two different objects—the range is meaningless when the scale is proven unreliable.
Years ago, a team of scientists took rock samples from all over the world and sent samples to different labs in a blind test to see just how reliable and consistent radiometric dating techniques could be. The resulting R.A.T.E. (Radioisotopes and the Age of the Earth) study was published and the findings were quite embarrassing for the scientific community as they found radiometric dating to be utterly unreliable, self-contradicting, and inconsistent. The non-technical, populist book written as an overview of those findings, "Thousands... Not Billions", can be purchased here. For the original published scientific work, you can read the free pdf file here.
Problematic Solutions
So if we've witnessed geological formations form rapidly and we know radiometric dating techniques are highly speculative, why are we only taught the long-age uniformitarian view of the earth in school? As it turns out, this incredibly long geologic timetable serves a purpose—to give biological evolution a small chance at being viable. Without these billions of years, even the most fervent adherent to macroevolution cannot fathom it being able to take place. But the "slow and steady" traditional Darwinian evolutionary theory has little evidence to support it. In fact, all the evidence that Darwin predicted science would find to validate his hypothesis has turned out to be untrue. He predicted there would be countless transitional species found in the fossil record—but the truth is there aren't any. He predicted the cell would be found to be an incredibly simple structure—but the truth is that cells are incredibly complex, highly organized structures that boggle the scientific mind. The discovery of DNA then further discredited Darwin's hypothesis. Actually, the traditional Darwinian evolutionary theory has so little evidence to support it, several evolutionists have abandoned it altogether in favor of a theory called punctuated equilibrium. This new hypothesis states that evolution happens rapidly—so rapidly in fact that it is impossible to find any transitional species in the fossil record! So now a lack of evidence is used as the evidence that evolution occurred. The irony is that Darwinian evolution has long been defended against the test of observation because it happens so slowly—it happens, we just can't witness it because it takes so long. Now we can't witness it because it happens so quickly. Somehow, the lack of evidence and the inability to test and observe something has become the proof of its existence despite mutually exclusive scientific claims. Catastrophism However, the Bible clearly states that a cataclysmic world-wide flood occurred in history (a fact widely recounted and documented by over 300 flood myths from nearly every single culture around the world). This single event could easily have created the vast majority of the geologic formations we see today and it would have formed them in a very short period of time. In fact in most cases, this rapid mechanism explains the observable data sets much better than the traditional long-age mechanisms do. Vast formations like the Grand Canyon could not have been created by slow water erosion caused by the Colorado River as that river would've had to flow uphill for millions of years to erode a channel through the plateau. A flood makes the data make much more sense as the sediments would have been soft and rapidly deposited in the layer-cake formations we see as the water ran off into rivers and oceans. The fact that the most common rock we see in the world today is limestone—a sedimentary rock that is formed from dried sea beds—proves that the surface of the earth was under water at some point in history. The fact that fossils exist at all is also a strong indication that these rock strata were formed rapidly due to flood waters burying organisms in thick layers of sediment nearly instantaneously—often perfectly preserving them in a moment of time.
So if we were to honestly evaluate the empirical evidence, uniformitarian geology doesn't seem to fit the observable data. But to admit that is to throw a monkey wrench into the evolutionary cogs, so the majority of the scientific community simply ignore the data and continue on with their cherished ideology. The giant chasm that just opened up in Wyoming won't phase them a bit—it can't. There is simply too much invested in the current models and theories. "Too big to fail" is not just an axiom reserved for banks in our modern society.