Mathematics formula found on Maya wall rivals insights of ancient masters

www.nature.com · 2026-07-14 · by Long Nguyen ·generic
Mathematical texts from a Maya site in Guatemala identify an astronomer called Sak Tahn Waax.

Mathematics formula found on Maya wall rivals insights of ancient masters

The well preserved Temple of the Great Jaguar in Tikal, Guatemala. The form is a distinctive pyramid shape with stepped design in a forest clearing.

The Maya temple Tikal in Guatemala is about one day's walk from Xultun, where researchers discovered mathematical formula scribbled on the walls.Credit: Kryssia Campos/Getty

A mathematical formula inscribed on a wall at the Maya site of Xultun in Guatemala has revealed the name of an important Maya mathematician-astronomer for the first time. Researchers suggest Sak Tahn Waax, or ‘White-Chested Fox’, was a scholar comparable with mathematical giants of the past.

In a study published 14 July in the journal Antiquity1, Heather Hurst, an archaeologist at Skidmore College in Saratoga Springs, New York, and her colleagues describe their analysis of a mathematical text from a chamber in Xultun that was originally excavated in 20112.

The chamber’s walls are painted with human figures and hieroglyphic texts. These include mathematical calculations based on astronomical calendars, which were used by the Maya people to decide the timing of events such as the inaugurations of kings. Hurst and her colleagues suggest that the chamber was a workspace for scribes making codices in the mid-eighth century ad.

The authors analysed one set of hieroglyphs in particular, referred to as Text 19. Hurst says that this set of mathematical calculations expresses the relationships between several calendar systems in a playful manner that hasn’t been seen before in Mayan texts. “I think it was a mathematical flex. Somebody was saying ‘I’ve got this amazing pattern, and it’s so good it needs to be written down’. It was like, ‘Boom! Mic drop!’,” says Hurst.

“The discovery shows people that the Maya were very clever, creative, intellectually curious people who taught and learnt and sometimes did math for the sake of it,” says Eric Heller, an archaeologist at the University of Southern California Dornsife.

Identity revealed

Text 19 is a small, L-shaped group of eleven hieroglyphs with a combined height of about 10 centimetres. Hurst and her colleagues found that the first nine hieroglyphs of the set encode the Maya calendar and astronomical cycles.

The formula shows how one 2,920-day cycle could be divided up into the calendar units used by the Maya people. This 2,920-day cycle was important because it tied together key astronomical cycles, corresponding to both five Venus cycles (584 days each) and eight solar years (365 days each). However, the Text 19 calculations also relate the 2,920 days to Uinal (months with 20 days), Tzolkin (_the 260-day sacred calendar), _Tun (a year with 360 days) and Mars years of 780 days.

“It’s just super nerdy math,” says Hurst. The hieroglyphs also show only partial dates, which made them hard to decipher. “They’re doing this abbreviated shorthand, so they give you the first half of a notation and the second half is implied.”

An infrared black and white image of the Text 19 from Xultun clearly showing the glyphs.

The mathematical formula on Text 19 appear as glyphs.Credit: Photograph by G. Ware, courtesy of the San Bartolo-Xultun Regional Archaeological Project

Until now, the identities of the mathematician-astronomers behind such calculations had remained mysterious. Hurst and her colleagues found a phrase in the penultimate hieroglyph in Text 19 meaning “so says”. This was followed by the name Sak Tahn Waax, in the final hieroglyph, suggesting that the writer was taking or giving credit for the calculation. “We know it’s a male name because it’s missing a prefix,” she says.

The fact that the writer is named is significant, because it suggests that mathematicians were recognized in Maya society as much as artists were, says Gerardo Aldana, an anthropologist at the University of California, Santa Barbara.

Equalling the greats

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Tenure-Track Faculty Position, Department of Molecular and Systems Biology, Geisel School of Medicine at Dartmouth, Hanover, NH Hanover, New Hampshire Dartmouth Geisel School of Medicine - Department of Molecular and Systems Biology

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