Robert P. Langlands
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. The note was published in the winter number of Ali Nesin's Matematik Dünyası for the year 2004.
Author's comments: The article is an exercise in the reading of mathematics from earlier times. An explanation of Descartes's solution of the problem of Pappus as included in the appendix "La géométrie" to "Discours de la méthode" and an explanation of a solution to another form of the same problem by Fermat, described briefly in a letter included in his collected works, are taken as an occasion to compare the mathematical styles of the two men and to observe their mutual debt to Apollonius as well as the differences in their depth of understanding of his work. The purpose is not scientific or historic; it is simply to encourage the private reading of classical mathematics by those who like me have no special knowledge of the history of mathematics.
This article appeared on pages 54-61 of the mathematical magazine Matematik Dünyası, No. 2, 2005. The magazine (as mentioned above, edited by Ali Nesin), is published in Istanbul and has a wide circulation among mathematics students and teachers in Turkey.
Author's comments: This review comes with a supplement (footnote) that contains the comments of several leading specialists and will be much more useful to the potential reader of the book, whether a novice or a specialist, than the review itself.