I’ve also wondered about this! It’s a great question worthy of our curious exploration.
I find Carol Hill’s explanation helpful. Unlike many explanations that I’ve looked at, I think she avoids being anachronistic. She helps us to understand the cultural understanding of numbers at the time these documents were written.
At least from the late third millennium BC onward, “sacred numbers” were used in religious affairs for gods, kings, or persons of high standing. Just as a name held a special significance to the ancients (e.g., Noah, Gen. 5:29)—beyond its merely being a name—a number could also have meaning in and of itself. That is, the purpose of numbers in ancient religious texts could be numerological rather than numerical.25 Numerologically, a number’s symbolic value was the basis and purpose for its use, not its secular value in a system of counting. One of the religious considerations of the ancients involved in numbers was to make certain that any numbering scheme worked out numerologically; i.e., that it used, and added up to, the right numbers symbolically. This is distinctively different from a secular use of numbers in which the over- riding concern is that numbers add up to the correct total arithmetically. Another way of looking at it is that the sacred numbers used by the Mesopotamians gave a type of religious dignity or respect to important persons or to a literary text.
I think she also offers a helpful way to approach the difference:
To take a number symbolically or figuratively does not mean that the Bible is not to be taken literally. It just means that the biblical writer was trying to impart a spiritual or historical truth to the text—one that surpassed the meaning of purely rational numbers.
Once we have this understanding in place, we can assess the numbers from another direction. If they are the literal, exact amount of years these people lived, the details are strangely patterned. Carol calculates:
For the entire 60-number list (antediluvial and postdiluvial), none of the ages end in 1 or 6—a chance probability of one in about one-half million. Surely, if the ages of the patriarchs in Genesis are random numbers, as would be expected for real ages, this could not be the case. It is inconceivable that all of this should be accidental!
We know from, say, the design argument, that when we find such mathematical improbabilities it is wiser to look for design and intention in the ordering of this complex situation.
She also points out another problem:
Further evidence that the patriarchal ages in Genesis are not real numbers is the “overlap” of the patriarchs’ life spans. If the genealogies in Genesis 5 and 11 are both literal and complete, then the death of Adam has to be dated to the generation of Noah’s father Lamech.41 Shem, Arphaxad, Shelah, and Eber would have outlived all of the generations following as far and including Terah. Noah would have been the contemporary of Abraham for 58 years and Shem (Noah’s son) would have survived Abraham by 35 years. But where does the Bible indicate that any of these men were coeval?
Her entire article, linked above, carefully examines the question from many different angles.
I would also commend Dr. LeFebvre’s book, The Liturgy of Creation, where he draws out more details for his argument for reading Genesis 1 as a sacred calendar narrative.