The Mayan civilization is tagged to 'start' at 3114 BC and survived (albeit as a severely declined force) until the Spanish conquest of the Yucatan in 1546 AD. The great classical Mayan cities, such as Palenque had already been abandoned by the time the Spanish had arrived. The true classical period of Mayan civilization is generally taken to be the period 2500 BC - 250 AD.

Technologically speaking, in the period 3000 BC to 500 AD, the civilizations of the Americas saw imperceptibly slow advancement in invention and tool use. The major ages of man comprise the mastery over the materials stone, copper, bronze, iron, with each material requiring more expert knowledge than the last in its creation and use. The Mayans never truly advanced into the bronze or iron age, but remained stuck in the stone and copper ages. They had no sophisticated farm tools.

Other civilizations during this period had already advanced into the Iron age and were distinguished by invention, such as the chariot or the abacus. Let's take a quick tour of the major achievement of a sampling of cultures during their classical period for comparison:

Sumerians (classical period 2900 BC - 1800 BC) saw the following mathematical achievements: Arithmetic, geometry, algebra, multiplication and division tables, factions. In addition, the Sumerians invented the abacus.

The Babylonians (classical period 1800BC - 330 BC) took the knowledge of the Sumerians and expanded upon it. Their astronomical calculations were astonishingly accurate. They invented the astrolabe, had true calculations for day length, had catalogs of stellar constellations, understood fractions, geometry, and quadratic equations.

The Greeks (classical period: 1200 BC - 400 BC) Invented the concept of the infinitely small (infinitesimal) and the infinitely large (infinity). Perhaps more than any other civilization, we are indebt to the Greeks for their advancement of mathematics and mathematical knowledge. It was the Greeks who first advocated the concept of proof - that a thing was not knowable unless it could be proved to be so. For the Greeks, mathematics took on a more esoteric pursuit, with puzzle solving (like calculating the diameter of the earth to amazing accuracy) was simply for the sake of solving the puzzle. They had a thorough understanding of fractions, Pi, and discovered irrational numbers.

The Romans (Classical period: 800 BC - 450 AD) took the Greek theoretical knowledge and gave it a practical bent with mastery of Pi as seen in the arch, barrel vault and dome. They understood fractions, geometry, linear and quadratic equations. The Romans were master engineers and their inventiveness is demonstrated with the water wheel, building cranes, surgical instruments and war machines.

Like the Romans, Egyptian (Classical period: 3000 BC to 300 BC) mathematics took on a very practical bent. Even though the Egyptians did not have the arch, they understood fractions, algebra, geometry, and had enough mathematical sophistication to understand the challenges in building smooth sided pyramid.

Not to leave out the Indian and Chinese civilizations, whose mathematics were extremely advanced as well. Jainian mathematics evolved out of Indian Vedic mathematics and it thrived from about 400 BC to 200 AD. Their discoveries were quite sophisticated, ranging from understanding of negative numbers, fractions, quadratic equations to power number notation. Chinese mathematics had become prominent by 1200 BC. The Chinese had invented their own system, of trigonometry, geometry, algebra. They understood fractions and negative numbers.

Much of the information of Mayan mathematics is found in surviving manuscripts like the Dresden codex, of which many scholars disagree on the glyphs and their meaning. JES Thompson urged caution when others around him wanted to see into the Dresden Codex as a mystical roadmap of astronomical brilliance. To JES Thompson, it simply wasn't there. If the Dresden codex was a series of lunar or Venusian calculations, they simply did not work. To quote JES Thompson: None of the examples noted above indicate an uncorrected lunar pattern based on computation. Either they were the result of poor observation, or, if computed, show either an attempt to adjust the computation to observations by the addition or subtraction of two, three, or four days or the substitution of one type of computation for another which had proved defective. In reference to theories about Venus, JES Thompson asserts: The total of 9100 days in the first column, as it stands, has no apparent connection with the Venus year, and appears to be wrongly written.

Outside the true classical period of our Mayan culture is the year 900 AD. This year, although outside the classical center of the Mayan civilization, it still falls within the period dominated by the Maya, before the arrival of the Conquistadors in the sixteenth century. By the year 900, we see no advancements in mathematical knowledge at all. Yet, look what is happening, by contrast half a world away. It was the first planned gathering based on a astronomical event that continues to this day.

Even a society considered primitive by many, the Vikings, had a very strong understanding of astronomy and the movement of the stars from which to navigate and plan their calendar.

930 AD was the year of the first assembled parliament - the Althing. The importance of the Althing cannot be overstated, as this one annual event demonstrates so many sophisticated aspects of a civilization. The Althing met for two weeks at the summer solstice. Icelanders from all over the island not only knew when the summer solstice was, they had a calendar system that allowed them to plan and prepare for the event far in advance of the meeting date. Knowing when the Althing was to start in advance allowed ancient Icelanders travel time over the rugged terrain.

This one annual event of the ancients Icelanders demonstrates a capability well beyond language and communication; it demonstrates centralized leadership, consensus of calendar, and understanding of basic astronomy.

Mayan Society never demonstrated any of these fundamental elements. Mayan technology was still in the Stone/Copper Age. Mayan mathematics had not evolved to the point where it could rival the Sumerians or Babylonians. Lacking the concept of fractions severely limits the ability to predict a future astronomical event with any long term accuracy.

Although writing about the suspect Venus calculations, JES Thompson makes an observation that is fitting regarding the Maya mysticism and alien theories:

the Venus glyphs appear to be so self-contradictory, that, by taking certain examples and ignoring others, one can produce the results one wants.

There is no solid proof that the Mayan civilization had the mathematical, astronomical, social brilliance ascribed to it by some.