Put it another way, here's a breakdown of Base 10:

Base 20 follows the same pattern, instead of powers of 10, each additional field to the left is an increasing power of 20.

Now let's look at the Mayan system. If it were a true vigesimal system, the position called: 'Baktun' would be a position multiplier of 160,000, not 144,000. Similarly the positions 'Katun' and 'Tun' do not reflect true Base 20 mathematics. The discrepancy comes from the 'Uinal' position. Its maximum position is 17, not 19 as to be found in a true vigesimal system.

Breakdown of Mayan Math

Mayan	Pictun	Baktun	Katun	Tun	Uinal	Kin
Icon
Field Range	0-19	0-19	0-19	0-19	0-17	0-19
Position Multiplier	x 2,880,000	x 144,000	x 7,200	x 360	x 20	+ Units
Base 20 Position Multiplier	x 3,200,000 (205)	x 160,000 (204)	x 8,000 (203)	x 400 (202)	x 20 (201)	+ Units (200)

Compared to contemporary civilizations (Sumerians, Babylonians) at the time, the Mayans were a more technologically primitive society. They held an attraction for the number 20, yet veered away from a true base 20 mathematical system in a way that is more suggestive of ritual than practical application. Their mathematics did had two interesting elements: the number 0, and a concept of very large numbers.

The Mayans were not the first to consider nothing as a number. The Sumerians and Babylonians had symbols to represent the absence of a value. By contrast, the Romans had no place for nothing in their numerical representation. 1000 was simply: M, and the number 1001 was the simply MI.

Understanding zero doesn't mean that the technology of the civilization is doomed to remain stagnant. On the contrary, lack of understanding of fractions does. Perhaps one of the most elegant illustrations of the use of the fractions is the understanding of Pi, but not the only one. The Babylonians and the Egyptians may have had vague approximations for Pi, but it was the Greeks who truly discovered the significance between the circumference and its diameter. The Romans understood the lessons from the Greeks and employed this knowledge into the creation of the arch, the barrel vault and the dome. The Greeks may have discovered Pi, but the Romans knew how to use it. But if the Greeks didn't use Pi in their buildings, they had no problem using ratios, for they had very strong stylistic and philosophical attitudes toward proportion.

The Egyptians took their knowledge of fractions and employed it in their creation of their pyramids; each successive layer of the structure becoming more and more challenging and difficult to build, a perfect balance between the weight of the stone and the angle of its placement had to be made otherwise the entire structure could collapse on itself.

The Mayan superstructures did not exhibit the kind of technology that we see by the Egyptians or the Romans, because their mathematics was not advanced enough.

Because the Mayans did not understand fractions, their astronomy was not particularly accurate. It simply is erroneous to think that because they only considered 365 days in a year with no corrections ever, that somehow the Mayans were able to forecast a future date 1,872,000 days away!

Because there is so little that we can definitely say we know about the Mayans, we must resist the temptation to apply sensationalistic and fantastical explanations to their capabilities.