Robert P. Langlands

Solomon Bochner in his office at Rice University
(Photograph courtesy of William Veech and the Rice University Archives, Woodson Research Center)

Author's comments: These notes are a very first draft of the very first part of a continuing series of lectures that will be held at the Yildiz Teknik Universitesi in Istanbul and may ultimately become an informal essay on various simple aspects of mathematical history and related matters. As they now stand, they are no more than a tentative beginning both linguistically and conceptually. They are posted primarily for use by the audience at the lectures. I apologize in advance for all their failings, grammatical and mathematical.

Footnotes: pdf

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.

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.