x TRANSLATOR’S PREFACE Does he make the English elegant and accessible? Or does he convey to the reader the flavor of the original? I have resolved this problem on a case-by-case basis, hoping that the result reads smoothly without distorting the spirit of the original. In this work, I have received invaluable help from an initial translation prepared by Hari Bercovici, of Indiana University. While most of his work has been altered and fine-tuned, the core of it remains, and Bercovici made significant contributions to the resolution of a number of difficult problems of translation. In addition, the illustrations—faithful copies of Hadamard’s own—are almost entirely the work of Bercovici. I am grateful for this opportunity to thank him for generously allowing me access to his work. In return, I take on myself the responsibility for any errors that may have crept in, and that the patient reader will doubtless find. Others to whom I am grateful for help in this work include Wing Suet Li, Florence Fasanelli, Al Cuoco, Larry Zimmerman, and Sergei Gelfand. My wife, Carol Saul, a great supporter of everything I do, has been immeasurably tolerant of my preoccupation with this work. This translation was supported by grant number NSF ESI 0242476-03 from the National Science Foundation. Hadamard’s career as a high school teacher does not seem to have ended suc- cessfully. He did not stay long in the profession, and there exist notes by his superiors testifying to his difficulties in getting along with his students.2 However, he seems to have learned from his experiences how to approach them intellectually, thus allowing other teachers, with other skills, the benefit of his own genius. It is in this spirit of combining the skills of the teacher and the mathematician that I offer these materials to the field. Mark Saul May 2008 2 Hadamard’s mentoring of Maurice Fr´ echet, which started in the latter’s high school years, is a notable exception to this circumstance.
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