ζ(s) has been in use since 1859, when Riemann introduced it. Riemann's paper isn't as thorough as it could've been, but it seems clear he knew exactly what he w

ζ(s) has been in use since 1859, when Riemann introduced it. Riemann's paper isn't as thorough as it could've been, but it seems clear he knew exactly what he was doing, being one of the founders of Complex Analysis: http://www.claymath.org/sites/default/files/ezeta.pdf http://www.claymath.org/sites/default/files/ezeta.pdf This series is ζ(-1). I don't know about the Youtubers or Scientific American, but mathematicians studying Complex Analysis know exactly what it means.