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The identification and work of an eighth-century Maya mathematician | Antiquity | Cambridge Core
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▻https://www.cambridge.org/core/journals/antiquity/article/identification-and-work-of-an-eighthcentury-maya-mathematician/FDE9610F9D80ADBC245CAC2B8F204070

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Abstract
Maya glyphic texts from the Classic period (250–900 CE) typically chronicle the exploits of historical or divine characters; everyday or functional records are rare. Here, the authors offer a reconstruction and transcription of a ‘microtext’ painted on an interior wall of Structure 10K-2 at the site of Xultun, Guatemala. The text records a unique astronomical formula that concludes with a name, attributing the work to an individual named Sak Tahn Waax (‘White-chested Fox’). To date, this is the only known example of a Classic Maya mathematician directly credited for their work, attesting to the value of its intellectual authorship.

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The Text 19 formula
Text 19 is located at the centre of the east wall and comprises 11 glyph blocks arranged in an inverted ‘L’ (at 180° rotation) in black paint. It is 192mm high and 28mm wide at glyph C4, and approximately 80mm wide at glyphs A1 to C1 (Figure 1). The preservation of this painted inscription is comparatively good, with some areas of loss.

Maya texts are often structured by units of time. The organisation of Text 19 moves through a sequence of five specific date records spaced by precise time intervals regularly used by ancient Maya scribes, followed by a two-glyph attribution to its author, Sak Tahn Waax. The calculations all involve familiar astronomical and/or calendrical units of time, which are reported in a conventional manner with ‘Distance Numbers’ between inscribed dates. However, the selected intervals and relationships drawn by the groupings in Text 19 are unique among Maya texts. This creative thought expression, alongside the personal name that we suggest might be the author’s signature, constitute a formula that represents one person’s own distinctive ‘patterning’ of well-known calendrical and astronomical interval permutations and commensurations.

Text 19 presents a total count of 2920 days composed of smaller counts that encode at least six units of time that were of great interest to Classic Maya timekeepers. The interval of 2920 days (8.3.0 in Maya notation) is significant as it is the lowest common multiple of the Venus synodic period of 584 days (583.92 days) and the Haab or solar year of 365 days. In other words, the position of Venus relative to the sun repeats almost exactly every 2920 days, which is equal to eight solar years or five synodic Venus periods (Förstemann Reference Förstemann1894: 431–43; Teeple Reference Teeple1926: 402–408). This interval is found throughout the corpus of Maya inscriptions, perhaps most famously within the Dresden Codex Venus tables, where these periods are tracked in relation to various embodied manifestations of Venus (Förstemann Reference Förstemann1894; Bricker & Bricker Reference Bricker and Bricker2011: 163–248). At Xultun, the scribe who created Text 19 was interested in how the 2920-day cycle could be parcelled into time intervals other than the five synodic periods of Venus (584 days) that generated it. The text engages six other time cycles embedded within the full count, these being (from smallest to largest): Uinal of 20 days; Tzolkin of 260 days; Tun of 360 days; Haab (solar year) of 365 days; Venus year of 584 days; Mars year of 780 days. Names for these periods and units of the Maya calendar correspond to Yukatek Mayan terminology found in sixteenth-century documents, using colonial-era orthography. This follows long-standing conventions in Maya studies and helps to distinguish common scholarly terminology from the names we see spelled in the ancient texts, which were often different and varied (‘Zac’ was usually Saksihoom in the Classic period, for example).
[…]
In nine hieroglyphs, Text 19 elegantly expresses the varied relationships among six temporal cycles, including those related to Mars, Venus, the Tzolkin and the Haab solar year, all represented within a single count of days that spans an eight-year period (Figure 4 & Table 1). The five dates are spaced within the 2920-day interval to highlight smaller sub-intervals. As a text, the passage sheds light on how observable celestial phenomena and planetary cycles were not only tracked in relation to one another, but how Maya mathematicians parsed and bundled shorter cycles within larger counts of time. Within the full count, the scribe also chose to embed intervals in a gradually increasing sequence: the first interval is one Uinal (20 days), the second is one Tzolkin (260 days), followed by two Mars years (1560 days) and three Haab cycles (1080 days) and the total length of the formula is five Venus synodic cycles (2920 days). These intervals follow what is known as a Fibonacci sequence in western mathematics; however, the degree to which ancient Maya mathematics incorporated and understood this pattern in nature is unknown.

Despite its poor preservation in places, the formula can be reconstructed from the visible details, including the 11 Akbal, the two Haab positions and the three time intervals. Our reconstruction paired with the palaeography of the painted glyphs suggests that the best fit for the initial date is the Long Count 9.17.10.17.3 4 Akbal 6 Muan, corresponding to 7 November 781 CE in the Julian Calendar (11 November 781 CE Gregorian) (see Table S2).

The signature
The most significant part of Text 19 is its two final glyphs, C8 and C9, which are non-calendrical in nature (Figure 5). The first of these reads che-he-na, or cheheen: a quotative particle translatable as “so says…” (Grube Reference Grube and Dedenbach-Salazar Sáenz1998; Kaufman & Norman Reference Kaufman, Norman, Justeson and Campbell1984: 77–167; Hofling, Reference Hofling2011: 239; see also OSM). This phrase is followed by a clear personal name, spelled SAK-TAHN-wa-xi or Sak Tahn Waax, ‘White-chested Fox’. Here, cheheen serves to indicate that a person named Sak Tahn Waax in some way expressed or ‘said’ the mathematical and astronomical notation that precedes it. We interpret the closing statement as an attribution statement that connects the formula to a historic individual: “…so says Sak Tahn Waax”. It is possible that Sak Tahn Waax calculated and painted Text 19 directly, or it might be that the scribe cited the name in reference to another person, perhaps some noted mathematician-astronomer. In either case, it is a direct personal attribution of mathematical and astronomical work, and unique in the corpus of Maya texts.

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Figure 5.
Attribution of mathematician ‘White-chested Fox’, using the phrase che-he-na followed by name spelled SAK-TAHN-wa-xi (multispectral photograph by G. Ware; drawing by D. Stuart).