Math

Author's comments: The following article appeared in November 2007 in the popular scientific review, Pour la Science, but in a version slightly revised by the editors and their consultants for expository purposes and with diagrams added. I am sure the revised form is indeed easier for a layman to understand, but some assessments were added that are not mine. Rather than interfere with the editors' difficult task of turning arcane material into something meaningful to their readers, I let the revised version stand.

Author's comments: The article is an exercise in the reading of mathematics from earlier times.

Author's comments: This note contains a few recollections of a year I spent in Turkey in 1967/68, where my office was adjacent to that of Cahit Arf, known, among other things, for the Hasse-Arf theorem and the Arf invariant. It was he who referred me---as I was first attempting to define local \(\epsilon\)-factors for Artin \(L\)-functions---to the paper of Hasse published in the Acta Salmanticensia. Hasse's paper was my first introduction to the methods that had already been introduced for calculating and comparing the \(\epsilon\)-factors.