Math

Author's comments: The following three documents were composed on the receipt of the Shaw Prize in 2007. They have appeared or will appear in publications of the Shaw Foundation. The first two, a very brief autobiography and a slightly longer memoir, need no explanation. They are informal. So is the third, an attempt to explain clearly the nature of what is often referred to as the Langlands program.

Portrait engraved by van Schooten the younger, editor and translator of the Latin edition of La géometrie.
Descartes said of it, "La barbe & les habits ne ressemblent aucunement."
(From the Rosenwald Collection at the Institute in Princeton)

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 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 following brief discourse was delivered in Erlangen in October 2004, on the occasion of the award of the Karl Georg Christian von Staudt-Preis to Günter Harder. It does not do justice to his many contributions to mathematics, but does attempt to express my great admiration of him and my great respect for the passion and the tenacity with which he continues to reflect on what seem to me some of the central problems of the modern theory of numbers.

Authors's comments: These are my responses to questions of Farzin Barekat, a graduate student at the University of British Columbia, where I was an undergraduate student for four years and a graduate student for one year. The questions and my responses were transmitted electronically. An abbreviated version of my responses will be published in a newsletter of the mathematics department of the university.

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

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