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.