XULTUN — Guatemala's Ministry of Culture announced on Monday the discovery of a 1,200-year-old complete mathematical and astronomical formula attributed to a named Maya astronomer-mathematician. The formula, unearthed at the Xultun archaeological site, represents the first time scientists have identified a Mesoamerican mathematician by personal name, marking a breakthrough in understanding the intellectual traditions of the ancient Maya civilization.

Culture minister Luis Mendez told reporters researchers at Xultun unearthed a "complete mathematical and astronomical formula" authored by Sak Tahn Waax, which translates to White-chested Fox. Mendez said it is the only work of its kind attributed to a mathematician from the Maya Classic period. "The glyphs appeared in 'a context where art was intertwined with science, mathematics, astronomy and everyday life,'" Mendez said.

Archaeologists identified the name of a Maya astronomer and mathematician for the first time, confirming the individual as Sak Tahn Waax. Sak Tahn Waax is believed to be the author of the formula and is the first Mesoamerican mathematician whom scientists have identified by name. It is the oldest recorded name of an astronomer-mathematician ever known from anywhere in the Americas.

The discovery was made possible by the epigraphic analysis of more than 50 mathematical and astronomical microtexts written on the wall of a small masonry building at the San Bartolo-Xultun archaeological site on the Mexican border. Researchers used drawings, photographs and scans of the inscriptions, which were later digitally enhanced. The analysis revealed 11 hieroglyphs that could finally be deciphered. Text 19, one of these murals, consists of those 11 hieroglyphs and was deciphered by Franco Rossi and his colleagues at the Massachusetts Institute of Technology.

"This is the first direct mention of an ancestral Maya astronomer-mathematician by personal name," says Franco Rossi at the Massachusetts Institute of Technology. Rossi added that the hieroglyphs had to be scanned, photographed and magnified under different illumination angles, and compared to other, later, astronomical-mathematical writings before their meaning could be deduced. "Whether this is an instance of the scribe himself signing his own calculation or attributing the intellectual work to another, we have a formula and the name of its creator, which serves to demonstrate the importance of this kind of intellectual contribution for Classic Maya people," Rossi said.

The mathematical formula was made around 1,200 years ago and predicts the orbital cycles of Mars and Venus. The calendar system uses maths in relation to time periods drawn from a 260-day calendar, a 365-day solar calendar, a 584-day approximation of Venus’s synodic cycle and a 780-day approximation of Mars’s synodic cycle. The total length of the formula is five Venus synodic cycles or 2,920 days. The date that Text 19 most likely refers to is 7 November of AD 781 in the Julian calendar.

Researchers identified calculations and tables that employ astronomical and calendrical units of time. The team reconstructed how the scraps’ symbols tabulated the time it took for planets such as Mars and Venus to come back to the same position, relative to the sun. The etchings numerically related all these cycles to one another in a single mathematical formula next to the author’s signature. Exactly how this formula would have been applied is unknown.

"We think it is meant to concisely and meaningfully show the relationship between these two planets and human counts of time in ways that could then be applied to political ceremony, predictive astronomy and understandings of seasonality," says Rossi. Heather Hurst, an archaeologist at Skidmore College and senior author of the study, described the moment of discovery with vivid language. "I think it was his mic-drop moment," Hurst said. She added, "He was like, 'Here's my crazy math—boom!'"

Hurst noted that Sak Tahn Waax was probably male and suggested the formula reflects a sophisticated intellectual exercise. "He’s playing with neat coincidences like least common multiples and then mixing that into their existing 260-day ritual calendar," Hurst says. The signature of Sak Tahn Waax was found inscribed in a 1,000-year-old chamber beneath present-day Guatemala.

The mural-lined chamber at the Xultun site is thought to have been part of a residence belonging to an artisan family or guild of paper makers and scribes. It is not clear if Sak Tahn Waax himself lived there or if someone else was simply quoting his famous formula. The name was found in drawings and inscriptions dating from 400 BC to 900 AD.

The research was published in the journal Antiquity. Since 2010, excavations at the site of Xultun, Guatemala, have revealed astronomical and mathematical inscriptions inside a small masonry building. On the east and north-east wall of the building are around 50 texts that scientists believe are "rough drafts" made by Maya mathematicians. The discovery dates back to 2010, when a team was excavating the site. One of Hurst’s colleagues happened upon a hole dug by looters which exposed part of a painted mural. The research team finished the work, unearthing a large chamber with mural-covered walls encircling the center. On one wall, the researchers spied what first appeared to be patches of dirt or debris on a mural; further scrutiny showed these were actually thin scraps of plaster that were inscribed with strange markings.

Why It Matters

The discovery provides rare personal attribution in a historical record where individual creators were seldom named, especially in scientific contexts. Much of the Maya's advanced knowledge of mathematics and astronomy was lost after the mass burning of their books by Spanish missionaries, making this direct link to a named intellectual figure exceptionally valuable for reconstructing Maya scientific thought.

The Maya civilization flourished in Central America between roughly 2000 BC and AD 1697, went into decline around 900 AD, and ultimately collapsed with the arrival of Spanish conquistadors at the turn of the 16th century. This formula may represent a precursor to knowledge later preserved in surviving texts like the Dresden Codex, offering a glimpse into the origins of Maya astronomical traditions.