"The resulting knowledge has led to the current understanding that the earth is 4.55 billion years old."
You can find that statement in this article:
How Science Figured Out the Age of Earth - Scientific American
If I wanted to find something Dr. Jerry Bergman, cited by several young earth creationists as a credible source in this thread, wrote I could find something he wrote in David Duke's (former Grand Wizard of the KKK) magazine.
Never heard of Jerry Bergman until this thread frankly. Though your article says it was written by one hight Paul S. Braterman, not a man named Jerry Bergman. So I'm not quite sure your point on that one.
This article made me laugh. I noted that it does not mention that when old earth mythology first formed, they thought in only millions of years. The reason they have had to continually revise it is because their own theories don't line up with either reality or their own myth. Every new theory they come up with necessitates them to revise the age upwards to gain time for their theory to have plausibility. This is amusing because they have essentially gone so far overboard with adding time that it has essentially become ludicrously impossible and negates almost all their own theories.
To examine their three points which they think support the old earth mythology, but which ironically prove it to be absurd. Sediment layers, radioatomic dating, and earth & cosmos models.
Firstly, the sediment layers. In the old earth mythology even this disproves so much of the myth. For we all ready know you can only have sediment if it is deposited by water. Furthermore the fact fossils are found in many different layers, and that there are even polystrata fossils proves that they were laid down in a cataclysm. Even moreso, the fact there are fossils at all. For if there was a gradual laying down of the layers, no fossil could be made due to decay and scavengers. Even moreso just to have fossilization occur one must have a lot of water and earth cover up the specimen in a very brief timeframe.
So it is clear that the only way you can have the layers or the fossils is via massive worldwide cataclysm involving lots of water. This would be the Flood. This is actually not that controversial outside of hardcore atheist circles. Just about all religions of antiquity and even the more secularist of ancient histories describe this event as happening. In fact the Flood is one of the very few things human civilizations have ever commonly agreed upon. And in theory, you could still have the worldwide Flood, and still have an old earth mythology.
The next point of radiometric dating is the most dominant today. Yet radiometric dating is also the most flawed and depends on the assumption of constant and uniform earth. For the only way to have a reliable radiometric date is if we live in a uniform and constant and relatively peaceful world in which cannot exist outside factors to change the properties of materials. However, we live in a self-evident dynamic world. Radiometric dating cannot be trusted as the properties of any single object are subject to change by various factors (ie: time and decay, the classical elements, spirit, and God.) Furthermore there have been many experiments on radiometric dating which solidly prove it to be extremely inaccurate (ie: tests wherein a freshly killed creature were dated back to hundreds of thousands of years.) Even though radiometric dating is a lie, this does not negate old earth mythology by reason that within the mythology itself are mythological cataclysms which would alter the property of materials anyways.
The last point which the article curiously underwrites is actually the most important, which is the formation and shape of the earth and cosmos. This is important because the old earth mythological model for the earth and cosmos actually undermines almost all of the other old earth theories when they are taken in combination. A good example of this is the relationship of the earth and moon in the old earth mythology. For this are made three assumptions; 1. earth is a tilted, wobbling, spinning sphere 2. gravity exists 3. they have existed for billions of years. These three would mean that the moon would have either escaped orbit or collided with the earth millions to billions of years ago. So one can easily see that either one of these theories, or all three, must be false.