Zeta ζ

Zeta is the sixth letter of the Greek alphabet but carries the numeral value 7, because the value 6 belonged to the obsolete letter digamma (later written as the stigma). Zeta derives from Phoenician zayin ('weapon'). It has no notable independent mystical tradition beyond its place in isopsephy. The Greek letters doubled as numerals in the Milesian (alphabetic) system, in which each letter carried a fixed value; the practice of summing a word's letters into a number, called isopsephy, is the Greek counterpart of Hebrew gematria and appears in inscriptions, the Greek Magical Papyri and early Christian texts. Zeta's Phoenician ancestry places it in a borrowing whose exact point of contact, somewhere among Al Mina, Cyprus, Crete and Euboea in the Aegean world, is still disputed, though the borrowing itself, conventionally dated to around the 8th century BCE, is agreed to be the ancestor of every European alphabet still in use, including the Latin one covered elsewhere in this atlas.

The Greeks' own contribution was to give vowels dedicated letters of their own, something the consonant-only Phoenician script never did. Its isopsephy value of 7 belongs to the Milesian alphabetic numeral system, which also needed three further, otherwise obsolete letters, digamma (also called stigma), koppa and sampi, to cover every value from 1 up to 900; none of the three survives among the 24 letters in ordinary use today.

Zeta's single most consequential modern use lies in a mathematical object named centuries after the letter itself: the Riemann zeta function, introduced in its modern complex form by Bernhard Riemann in an 1859 paper, extends an infinite sum studied earlier by Leonhard Euler and now sits at the centre of one of mathematics' most famous unsolved problems, the Riemann hypothesis, concerning where the function's value equals zero.

None of this borrows from zeta's ancient Semitic root zayin, meaning sword, or from the letter's classical Greek sound value, covered elsewhere in this atlas; the choice of zeta for the function reflects only established mathematical convention for naming functions with Greek letters, following the earlier example of Euler's own gamma function. Physicists occasionally use zeta for damping ratios and other technical coefficients in engineering equations, again without reference to the letter's older meanings, and astronomers, following the Bayer star-naming system of 1603, conventionally use Zeta to mark a constellation's sixth-brightest star, continuing the same ranked sequence that runs from Alpha through the rest of the Greek alphabet. The mathematical zeta function and the ancient letter share nothing beyond a name chosen by later convention, in the same way the gamma function, discussed elsewhere in this atlas, borrows a Greek letter without borrowing any of its older meaning.