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Mathematics formula found on Maya wall rivals insights of ancient masters Mathematical texts from a Maya site in Guatemala identify an astronomer
called Sak Tahn Waax.
By Chris Simms
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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 rCyWhite-Chested FoxrCO, 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 chamberrCOs 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 hasnrCOt been seen before in Mayan texts. rCLI think it was a mathematical flex. Somebody was saying rCyIrCOve got this amazing pattern, and itrCOs so good it needs to be written downrCO. It was like, rCyBoom! Mic drop!rCO,rCY says Hurst.
rCLThe 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,rCY 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.
rCLItrCOs just super nerdy math,rCY says Hurst. The hieroglyphs also show only partial dates, which made them hard to decipher. rCLTheyrCOre doing this abbreviated shorthand, so they give you the first half of a notation and
the second half is implied.rCY
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 rCLso saysrCY. 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. rCLWe know itrCOs a male name because itrCOs missing a prefix,rCY 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.
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doi:
https://doi.org/10.1038/d41586-026-02170-8
References
Rossi, F. D., Stuart, D. & Hurst, H. Antiquity
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