Imagine an office abandoned for twelve centuries. The walls are covered with numbers, glyphs, and calculations scrawled in black on a yellow background. And right at the end, almost discreetly, a name. This is exactly what a team of archaeologists has just deciphered in the ruins of Xultún, in the northeastern Petén region of Guatemala: the signature of a Maya mathematician of the 8th century, the first ever formally identified in the entire history of classical Maya civilization.
His name: Sak Tahn Waax, which can be translated as "White-chested Fox." His formula, painted around 781 CE on the east wall of a small chamber in structure 10K-2, describes the coordinated motion of Venus and Mars in a way previously unknown. The study published on July 14, 2026 in the journal Antiquity, signed by Franco D. Rossi, David Stuart, and Heather Hurst, states that this text — dubbed "Text 19" — is "the only example known to date of a classical-period Maya mathematician explicitly credited for his work."
A twelve-hundred-year-old whiteboard
The site of Xultún, first reported in 1915 and actively excavated since 2008, keeps surprising us. The chamber in question was discovered in 2010 and excavated in 2011. It is tiny — about six square feet — and its walls bear more than fifty mathematical and astronomical microtexts. David Stuart, an archaeologist and epigrapher at the University of Texas at Austin, described it as "an old whiteboard in someone's abandoned office". The image rings true: this is a workspace, not a monument. A place for calculating, testing, and starting over.
For years, Text 19 remained opaque. Franco D. Rossi took more than a decade to spot the decisive connection, before consulting David Stuart. The reconstruction drew on scale drawings, photographs, digital image processing, and multispectral imaging — all tools for reading what stucco and time had nearly erased. Then, after eleven glyph blocks arranged in an inverted L, two signs turned out to be something else: they were no longer numbers. They formed a name. "Now we have a name", David Stuart simply said.
When the planets fall into place
But what exactly did Sak Tahn Waax calculate? This is where the mathematics comes in — and it deserves a closer look, because this is not geometry in the Greek style. No theorems, no formal proofs. It is an arithmetic of cycles, a hunt for numerical coincidences among independent celestial rhythms.
Here is the concrete problem. Venus takes about 584 days to complete a full synodic cycle — that is, to return to the same position relative to the Sun, as seen from Earth. Mars has its own rhythm. The Maya ritual calendar, the Tzolk'in, runs on a 260-day cycle. The solar year, the Haab', has 365. These cycles do not align naturally: they are like gears with coprime numbers of teeth, which only fall back into sync after a very long time.
Sak Tahn Waax's formula targets precisely this coincidence. It seeks to reach a period of 2,920 days — exactly five Venus synodic cycles (5 × 584 = 2,920). This number is also equal, to a very good approximation, to eight tropical years and to 99 synodic lunar months: this is what Greek astronomers called the octaeteris. As Anthony Aveni, William Saturno, and David Stuart show in the Journal for the History of Astronomy, this number is no coincidence: it is the result of a deliberate search for commensuration, that is, the smallest duration common to several planetary and calendrical cycles.
In other words, Sak Tahn Waax was looking for what we would today call a least common multiple — or rather an intelligent approximation of one, since celestial cycles are not perfect integers. Heather Hurst, a co-author of the study and an archaeologist at Skidmore College, puts it with disarming candor: "He plays with neat coincidences like least common multiples, then mixes them with the 260-day ritual calendar." She adds, about the final signature: "That's his moment of glory."
A signature that changes everything
What sets Text 19 apart from every other known Maya mathematical text is not only the sophistication of the calculation. It is the final formula: "che-he-na," followed by the name SAK-TAHN-wa-xi. This expression can be read as "thus said Sak Tahn Waax" — a claim of authorship, an intellectual signature. Researchers cannot say for certain whether Sak Tahn Waax wrote it himself, whether a disciple attributed the calculation to his master, or whether he was claiming collective work. But the fact that a name appears after a mathematical formula is unprecedented in the entire classical Maya corpus.
Anthropologist Gerardo Aldana, quoted by Nature, sees this as a sign that mathematicians were recognized in Maya society on the same footing as artists. Signatures of Maya sculptors and painters were already known. Now we know that the Taaj — the term for Maya specialists in astronomy and mathematics, according to a statement from the Guatemalan Ministry of Culture and Sports — could also leave their name on their work.
For Oswaldo Chinchilla, an anthropologist at Yale University quoted by Scientific American, the significance is clear: "This is not just a mathematical exercise, it is the exercise of a named individual whose knowledge was worth recording."
Archimedes, Ptolemy — and Sak Tahn Waax
The comparison with the great names of Greco-Roman antiquity is not made lightly. It points to a real historiographical asymmetry: Archimedes, Ptolemy, and Al-Khwarizmi are taught in every history of mathematics textbook. But pre-Columbian civilizations are nearly absent from them, as if their contributions had no face, no author, no individual behind the calculations.
Yet the Maya of the classical period (250–900 CE) had developed a base-20 numeral system — the vigesimal system — including an explicit symbol for zero, long before this concept took hold in Europe. They had built eclipse and Venus cycle prediction tables of remarkable precision, as documented in the reference work Astronomy in the Maya Codices by Harvey and Victoria Bricker, without a telescope, without a computer, without any of the instruments we take for granted. Anthony Aveni, an archaeoastronomer at Colgate University, puts it bluntly: "They did it without the help of telescopes, without computers, without any technology."
The discovery of Sak Tahn Waax does not suddenly reveal that the Maya knew how to calculate — that much was already known. It does something more subtle: it gives that knowledge a name, a date, an individual. It turns a civilization into a gallery of people. And that is another way of counting.
Gabrielle Vail, an archaeologist at the University of North Carolina at Chapel Hill, believes that the Xultún formula may even have inspired ideas preserved in the Dresden Codex, the most complete of the three surviving pre-Columbian Maya manuscripts. If this lead is confirmed, Sak Tahn Waax would not only be the first named Maya mathematician. He might also be one of the earliest links in an intellectual tradition that has crossed the centuries — until a looters' tunnel, a forgotten chamber, and a team of patient archaeologists brought it back to light.
Key takeaways
The mechanics of the cycles behind the formula
For those who want to understand why Sak Tahn Waax's calculation is mathematically elegant, here is the heart of the reasoning — without heavy equations, but with the precision it deserves.
A synodic cycle is the time between two consecutive alignments of a planet with the Sun, as seen from Earth. For Venus, this period is about 583.92 days. For Mars, about 779.94 days. The Maya ritual calendar, the Tzolk'in, lasts exactly 260 days (13 × 20). The approximate solar year, the Haab', lasts 365 days.
The problem Sak Tahn Waax poses is this: find a number of days N such that N is simultaneously an approximate multiple of several of these cycles. This is a commensuration problem — in modern terms, a search for an approximate least common multiple within a set of real numbers not rationally related to one another.
The solution he settles on: N = 2,920 days.
This number, 2,920, is what the Greeks called the octaeteris (from the Greek okta, eight, and etos, year): an eight-year period that reconciles the solar calendar and the Venus cycle. As Aveni, Saturno, and Stuart show in the Journal for the History of Astronomy, the Maya of Xultún also worked with the number 56,940, which corresponds to 97 Venus cycles and turns out to be a common multiple of several planetary cycles — a structure also found in the tables of the Dresden Codex.
What makes Sak Tahn Waax's approach remarkable is not that he found this number — Babylonian and Greek astronomers already knew the octaeteris. It is that he integrated it into a system combining Venus, Mars, and the 260-day ritual calendar all at once, in a single, concise, signed formula. As Floyd G. Lounsbury writes in his reference article on Maya numeration, Maya sky specialists were not mere observers: they were calculators whose social and intellectual role was to find these concordances and turn them into transmissible knowledge. By signing his formula, Sak Tahn Waax simply wanted it known that it was him.
